Enhancing Secondary School Students' Productive Disposition using GeoGebra Software integrated Process Oriented Guided Inquiry Learning in Geometry

Enhancing Secondary School Students' Productive Disposition using GeoGebra Software integrated Process Oriented Guided Inquiry Learning in Geometry | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Enhancing Secondary School Students' Productive Disposition using GeoGebra Software integrated Process Oriented Guided Inquiry Learning in Geometry Gizachew Belay This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8671177/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study investigated the impacts of combining GeoGebra software and Process-Oriented Guided Inquiry Learning (GGS-POGIL) with the productive disposition of second level students towards geometry in Addis Ababa, Ethiopia in terms of enjoyment, confidence and felt value of mathematics. A quasi-experimental design with pre- and post-tests compared a GGS-POGIL group, a POGIL only group and Comparison group using the Productive Disposition Questionnaire. Results were that there was a significant increase in mathematics enjoyment and confidence in GGS-POGIL group compared to others (p < 0.01), showing the combined effects of interactive visualization and inquiry-based learning. However, there was no significant improvement in student perceptions towards the importance of mathematics, which one might assume indicates a need for further strategies to indicate real world relevance. Effect size analysis endorsed the positive effect of GGS-POGIL on productive disposition. While effective, challenges like teacher training and access to technology indicate the need for professional development and infrastructure support. These findings confirm the role of technology-enhanced inquiry learning in developing positive mathematical attitudes and offer recommendations for educators and policymakers. Future studies should investigate the long-term effects and scalability of GGS-POGIL in a range of educational settings in resource-limited settings. Educational Philosophy and Theory Productive disposition liking for mathematics confidence in mathematics valuing mathematics GeoGebra Guided Inquiry Figures Figure 1 Introduction The role of mathematics education in building cognitive and emotional attitudes of students has found numerous research publications, writing that mathematics education is significant (Rohman et al., 2023 ; Hutajulu et al., 2019 ; Kilpatrick et al., 2001). Another important element in the development of mathematical proficiency is productive disposition because it is defined as the stable tendency of the learner to view mathematics as useful and worthwhile (Chua, 2021). It is not just the knowledge of the concepts but also involves such issues as the pleasure of studying math, the belief in mathematical skills, and the perception of mathematics as something significant and practical in the real life (Ayalew, 2019 ; Kilpatrick et al., 2001). Nevertheless, conventional approaches to teaching mathematics and that of geometry, in particular, have not resulted in some of the key elements of productive disposition of mathematics learning and require pedagogical re-consideration (Dereje, 2023 ; Baye et al., 2021 ), living with status-quo practices. Geometry learning is a challenge among the Ethiopian secondary school students because it is an abstract subject and the pedagogical system frequently encourages memorizing and learning by rote, rather than conceptual learning (Gurmu et al., 2024 ; Eshetu et al., 2022 ). Studies have reported that traditional instruction methods do not engage students, diminish their drive and self-efficacy towards mathematics, which constitute important elements in order to be productively disposed (Ayalew, 2019 ). Other dynamism enforced in the learning environment like inquiry-based approaches that are technologically integrated, have become a comparatively proactive substitute to transform and not to stay in the past following these ongoing challenges (Romero Albaladejo and Garccia Lopez, 2024; Bekene and Machaba, 2022 ). Process-Oriented Guided Inquiry Learning (POGIL), is created to engage students in organized problem-solving tasks that encourage conceptual knowledge as well as collaborative learning (Andriani et al., 2019 ; Muhammad and Purwanto, 2020). The same applies to the example of GeoGebra software (GGS). It is noted that an interactive visualization is an effective form of engaging students in a better perception of geometry concepts (Simbolon and Siahaan, 2021; Ansong et al., 2021). There are signs that, in the case of the combination of GeoGebra and POGIL, the students do not only gain a deeper insight into the mathematical structures but also reinforce their productive disposition by improving their confidence, enjoyment, and interest in mathematics (Hosseini et al., 2022; Rodriguez-Nieto et al., 2021). Nonetheless, the research by Deranje and his colleagues (2022) is antithetical to prior research and suggested further study of the situation in Ethiopia. Although the global community is starting to see progress in the area of educational technology and teaching methods, the overall impact of GGS and POGIL on fruitful dispositions in learners has not been well-documented (Rodríguez-Nieto et al., 2021 ) and especially in Ethiopia (Gurmu et al., 2024 ). Individual research on POGIL and GeoGebra has brought out informative advantages. Their integrated action and the promised scaffold that they would introduce in improving productive disposition of students in mathematics, though, is of critical importance to study. The research will be conducted to explore the interactive and combination effects of GGS-POGIL on productive dispositions in geometry learning among students in secondary schools in terms of enjoying, feeling confident, and value of mathematics. In this regard, the operationally defined productive disposition in this study is the drive of the students to feel that math is useful and worth studying, to feel confident in their capability of completing a mathematical task, and to like and get a satisfaction in the study of mathematics. This study is relevant to the urban Ethiopian secondary schools where students are said to have shown decreasing interest in geometry because of the application of traditional teaching methods that do not involve the participants in educational activities (Ayalew, 2019 ). The results of this research can be used in this literature area since they are based on the comparisons of the various impacts of GGS & POGIL combination, POGIL alone, and traditional teaching methods on the productive disposition of the students. Another aspect of appreciative learning about the role of technology-based inquiry learning in the development of positive dispositions can be of interest in the curriculum changes towards the engagement of students in math and the attainment of improved performances; and also fill gaps in research that are evident. Statement of the Problem: There has long been a history of deep-seated problems in mathematics education in Ethiopia and the root causes of the problems remain to this day. The learning of geometry is one of the strands that has been associated with a lot of problems, with the performance of students being a dismal one. Literature also indicates that students experience issues with the conceptual comprehension of the subject, are influenced by demotivating and emotional facts and they still do not like the geometrical concepts and consequently do not perform well in examinations although geometry is effective in the practical situation (Kpotosu et al., 2024). The productive attitude that included the pleasure that students enjoyed mathematics, their belief in their mathematical potential, and the sense of the importance of the subject matter was one of the aspects that did not fit in the existing instructional paradigms (Rohmah et al., 2020 ; Rohendi and Dulpaja, 2013 ; Kilpatrick et al., 2001). This issue was particularly acute in Addis Ababa secondary schools where the students are said to be passive, uninterested, and have poor outcomes (Tesfamicael & Ayalew, 2021 ; Ayalew, 2019 ). The continued application of conventional pedagogical methods that are inefficient towards enhancing active learning among learners and providing an instructional setting that would facilitate the development of a positive productive mind towards mathematics are one of the key factors that precondition this critical issue (Gurmu et al., 2024 ; Dereje, 2023 ). Memorization and lectural forms of pedagogy, which are predominantly employed by teachers, do not offer learners the feeling of enjoyment or confidence. Also, the enormous majority of students did not consider mathematics as a topic that could be applied to life issues, which made their deficit of interest and disengagement (Melese, 2017 ; Safi and Desai, 2017 ). This disconnection uncovered the need to adopt new teaching methods to engage students intellectually and emotionally in learning so that they can learn more, become interested in mathematics over the long run (Kilpatrick et al., 2001; Rohendi and Dulpaja, 2013 ), and research has also proven that the adoption of technology tools has a positive effect on student engagement, motivation, and conceptual learning (Mahmoud, 2023). Studies of recent years emphasized the potential of Process-Oriented Guided Inquiry Learning (POGIL) paired with dynamic mathematics software to transform the way mathematics is taught (Rodríguez-Nieto et al., 2021 ; Romero Albaladejo and García López, 2024 ), which this research attempts to access. Such techniques have been discovered to enhance understanding of abstract mathematical concepts, generate more interest among students and have positive effect on learning attitudes with regards to mathematics. Nevertheless, little has been researched on the application of these methods in Ethiopia especially on their effects on productive disposition of students as regards to geometry (Baye et al., 2021 ; Gurmu et al., 2024 ). The viability of this integrated strategy-GeoGebra Software blend POGIL (GGS-POGIL) in the solutions of the deficient areas in the engagement and performance of students led to additional empirical research. The urgent need to address these weaknesses was highlighted by the new assessment statistics that have shown frighteningly low rates of engagement and student achievement in Ethiopian high schools. In their research, Abera and his co-authors mentioned that 32.5 percent of students had mastered simple mathematical concepts (Abate et al., 2023), and over 60 percent of students failed to reach the desired level in nationwide mathematics exams (Ayalew, 2019 ). In addition, Ethiopian secondary school pupils possessed weak conceptualization in geometry with less than 35 percent of the students being proficient in the key areas (Dereje et al., 2023). Ethiopian Third National Learning Assessment (ETNLA) also noted that the average national mean score of Grade 10 students in mathematics only reaches to 11.9% which is significantly lower than the national education policy targets (NEAEA, 2017). The reliance on poor pedagogical activities has also increased failure rates in math performance, thus responding to the high problem, and these result in student dispositions issues (Baye et al., 2021 ). The current research aimed to evaluate the effectiveness of the pairing of GeoGebra Software and Process-Oriented Guided Inquiry Learning (GGS-POGIL) to improve productive disposition of the students in studying geometry. The study investigates the impact of the integrated strategy on certain features of active disposition, including, enjoyment of mathematics by students, confidence in mathematics, and relevance of the subject. By a comparison of teaching methods like GGS-POGIL, POGIL-only, and conventional teaching methods, this study attempts to offer empirical validity on the best teaching methods which can be used in facilitating productive dispositions of students in mathematics. It is expected that results of this study will help in developing evidence-based instructional strategies in an attempt to enhance productive disposition of students in Ethiopian secondary schools in Addis Ababa. Objectives: The general objective of this study was to investigate the effectiveness of integrating GeoGebra software with Process Oriented Guided Inquiry Learning in enhancing students’ productive disposition toward learning geometry. In particular, the study sought to: Investigate the effect of integrated POGIL with GeoGebra approach on the overall students’ productive disposition in geometry. Assess the effect of this integrated approach on the different components of productive disposition, namely, students' enjoyment of mathematics, confidence in math abilities, and perceived importance of the subject. Research Questions In attempting to meet these objectives, the research centered on the following research questions: Is there the positive gain in positive productive disposition of students who experience geometry instruction through an integrated POGIL and GGS than students who experience traditional instruction or POGIL-only instruction? Which of the productive disposition dimensions, enjoyment of math, confidence in math ability, and perceived importance of math, are most impacted by the combined POGIL and GGS method in the context of geometry instruction? Significance of the Study: The study under consideration is immensely important as it considers the potential benefits of the combination of Process-Oriented Guided Inquiry Learning (POGIL) and GeoGebra software (GGS) in promoting a constructive attitude of students to mathematics, and specifically to geometry. The study presents advice to teachers and policymakers in Ethiopia and other countries by targeting those factors that constitute productive disposition; enjoyment of learning mathematics, self-confidence, mathematics ability, and liking mathematics. It also fills the gap in the existing literature on mathematics education in Ethiopia where students might usually face some difficulties related to engagement and self-efficacy. Demonstrating that the adoption of POGIL-GGS creates a positive productive disposition can also provide the educators with practical examples that can be used by to encourage mathematical motivation and success. Moreover, the research contributes to the creation of curriculum design and methods of teaching, as well, by studying how this combined method impacts the students in their enjoyment of math, self-confidence, and the perception of the importance of the studied material. These aspects could be enhanced to facilitate increased motivation, less anxiety and appreciation of mathematics. The results of this research may also extend well beyond the Ethiopian situation to provide a model that may be used across the board in all the educational institutions in other developing countries plagued with the same problem in the field of mathematics education. Revealing the successful examples of teaching, the study supports the global project to impose mathematics education with the use of creative pedagogy. Theoretical Framework The theoretical framework that drives this study is a combination of two theoretical perspectives that relate process-oriented guided inquiry learning (POGIL) pedagogical innovation with the technological capabilities of GeoGebra software to promoting productive disposition in geometry among the students. The framework integrates constructivist and sociocultural theories of learning, a model of mathematical proficiency proposed by Kilpatrick et al. (2001) and Technological Pedagogical Content Knowledge (TPACK) model (Mishra and Koehler, 2006 ) to describe how and why the integrated GGS-POGIL approach would be hypothesized to facilitate affective involvement of students in mathematics. Constructivist theory (Schoenfeld, 2007 ) has it that the learner is the active entity in the process of building knowledge (by interacting with the surrounding world, reflecting and problem solving) as opposed to an entity that is passive receivers of information. This is consistent with the fundamental structure of POGIL, in which students are provided with a guided, structured inquiry where they are expected to construct their own meaning and achieve conceptual clarity by way of guided inquiry. POGIL engages students as active participants towards learning beyond merely a deeper learning experience but also a sense of ownership and agency in mathematics. To supplement this, the sociocultural theory proposed by Vygotsky (1978) highlights the social aspect of learning, in which knowledge is co-created in a conversation, in collaboration and mediated interaction with the tools and others. POGIL's small group structure reflects this tenet where a community of inquiry is formed in which students negotiate meaning, express reasoning, and scaffold one another's understanding in their zone of proximal development. When combined, these theories offer a solid pedagogical-underlying justification why POGIL is likely to improve the cognitive and affective outcomes: such as confidence, enjoyment, and spirit of collaboration. Technology integration in education cannot be executed without technical aptitude, it needs to be synergistic, to combine technology, pedagogy and content. This intersection is conceptualized in the TPACK framework (Mishra and Koehler, 2006 ) in the form of Technological Pedagogical Content Knowledge: that specialty knowledge that teachers must have in order to meaningfully incorporate technology into teaching the subject matter. Here, GeoGebra is known as the technological knowledge (TK), whereas POGIL is known as the pedagogical knowledge (PK) of the content knowledge (CK) of geometry. TS-POGIL integration is a feasible implementation of TPACK, in which the dynamic visualization features of GeoGebra could be used to enhance the inquiry cycle of POGIL allowing students to interactively manipulate geometric objects, make real time hypothesis tests, and visually observe relationships. This combination lowers the level of abstraction, facilitates spatial reasoning and renders geometry more interactive and approachable thus encouraging engagement and clarity of conceptualization. Kilpatrick et al. (2001) define mathematical proficiency as a combination of five interconnected strands, that is, conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. The latter (productive disposition) refers to a habitual inclination of the student to consider mathematics as sensible, useful and worthwhile and trusting in his ability and self-perseverance in solving problems. Productive disposition is an affective motivation and an educational product that is vital in order to achieve the long-term success and sustain motivation in mathematics. There are three sub-constructs which are operationalized in this study in accordance to Kilpatrick model, productive disposition: 1. Like learning mathematics: interpretation of liking to study the subject. 2. Confidence in mathematics: believing in individual mathematical ability. 3. Valuing mathematics: perception of its relevance and applicability in real-life. The use of these dimensions is measured with the help of the Productive Disposition Questionnaire (PDQ), which is the main tool that will be used to measure the effectiveness of the intervention. Integrated Conceptual Framework: In order to integrate these theoretical lenses and diagrammatically present the hypothetical correlation between the constructs of the study, the researcher suggests the following composite conceptual model (Fig. 1 ). As it is presented, the GGS-POGIL intervention has a theoretical base in constructivist, sociocultural and TPACK principles. It fulfills the cognitive requirements of geometry and especially spatial reasoning based on the pedagogy-technology synergy to promote the process of mediating learning in active exploration, peer collaboration, and dynamic visualization. Such processes, in their turn, have been conjectured to have a positive impact on productive disposition of students, which is quantified in its three affective dimensions. The framework therefore presents a logical sequence between theory-based intervention into improved affective results, which exists as a clear foundation of empirical research and teaching methodology. Cognitive Demands of Geometry Learning : The spatial reasoning is also closely connected with the understanding of geometrical ideas as a cognitive ability when a person can visualize and change objects (Khalil et al., 2019 ). This ability plays a great role in comprehending the geometry associations as it supports in the study of relationships and transformations between shapes. The enhanced understanding is achieved through visualization through which the learners are able to interact effectively with the geometric figures and properties and, therefore, develop an effective conceptualization of concepts like congruence and symmetry. However, the conventional teaching strategies negatively affect the development of the spatial reasoning skill, as the strategies emphasize memorization more than the actual engagement and thus lead to the superficial knowledge and the inability to relate concepts to real-world contexts (Bwalya, 2019 ; Negara et al., 2022 ). Learning theories of cognitive development, in particular, the stages of Piaget, acknowledge the shift of concrete to abstract thinking in geometry learning (Rohman et al., 2023 ). Piaget assumes that learners progress through manipulation of physical objects to abstract thoughts of geometric ideas and learners are taught through experiential learning. Constructivist theories underline the importance of experiential learning, and they encourage teachers to create the conditions that would help students to experience the actual interaction with geometric concepts (Hutajulu et al., 2019 ). Spatial thinking may be promoted and intellectual progress may be encouraged in the geometry field through facilitating group work and problem-solving activities. Productive Disposition as a Critical Factor: Kilpatrick et al. (2001) identified five strands of mathematical proficiency including conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. Among these strands, productive disposition is core in encouraging students to learn geometry since, positive disposition prompts curiosity and makes them more motivated thus developing resilience in approaching challenging problems. Conversely, a negative productive attitude would deter engagement and achievements in geometry since learners will doubt their talents or the subject can be irrelevant (Hutajulu et al., 2019 ; Rohendi and Dulpaka, 2013). Innovative learning methods and tools are required to facilitate the development of the conceptual learning and desirable disposition. The use of technology, e.g., GeoGebra, enhances the knowledge of geometry through interactive exploration and dynamic visualization (Bwalya, 2019 ; Khalil et al., 2019 ; Niam and Asikin, 2020 ). GeoGebra enhances the conceptualization of the students by allowing them to operate geometrical objects and view their characteristics in real time. In addition, processes like Process-Oriented Guided Inquiry Learning (POGIL) ensure that the learners engage actively and cooperate with one another to improve their engagement levels. Overall, these theoretical foundations imply the need to develop the skills of spatial sense and foster the positive and constructive attitude, which would place students in a situation to feel confident and skilled in geometry. Challenges in Geometry Instruction: The subject of geometry is faced with the severe issues due to the abstract form of study that in most cases leads to a lack of interest and motivation among the students. Numerous students do not understand how the concepts of geometry can be applied to their lives, so there is a lack of interest in this subject (Bwalya, 2019 ; Khalil et al., 2019 ). Traditional approaches to teaching and learning only exacerbate this issue, where memorization and procedural practice is taught at the expense of developing a deeper conceptual understanding. These approaches do not generally provide students with an opportunity to explore the concept of geometry in meaningful sense, and in this regard, they do not enable students to appreciate the role geometry plays in real life (Rohman et al., 2023 ). This leads to the development by many students of negative attitudes about geometry as a subject that is theoretical and has no connection with real life situations hence lowering their interest to learn further. The teaching of geometry also becomes complicated in the Ethiopian educational system by a number of structural and resource-related problems. Melese ( 2017 ) notes that the lack of appropriate teaching materials and resources reduces the level of teaching and learning. Besides, excessive classrooms reduce the ability of teachers to provide students with individual attention and this has a negative impact on the engagement of students in the study and mastery of geometric concepts. The use of the conventional pedagogical practices that focus on lecture-based instruction inhibits the delivery of interactive and experiential learning. Such experiences play an essential role in the growth of spatial thinking and a profound conceptual vision of geometry (Hutajulu et al., 2019 ). In this regard, specific interventions to address the issue of cognitive challenges and affective challenges are required to develop a productive learning environment that encourages engagement and motivation in learning geometry. Traditional teacher-centered approaches in teaching geometry involve more of procedural learning and memorization, thus limiting the knowledge of the students on the concepts of geometry. In this scenario, the teachers tend to lean towards the direct teaching approach where the students are forced to learn the procedures and formulas without really analyzing the concepts behind those. Such an educational approach prevents the cultivation of critical thinking skills and reduces student engagement because students are engaged in mechanical tasks that do not seem to have any real-life interaction (Rohman et al., 2023 ). Research indicates that students who have been taught a curriculum that places more focus on memorization stand a chance of developing negative attitudes towards geometry and seeing it as either irrelevant or highly demanding (Hutajulu et al., 2019 ). This is because these negative attitudes can lead to a vicious cycle of poor performance and lack of self-efficacy whereby not passing the concepts of geometry on the first attempt will further erode self-confidence and interest and this will prove that pedagogical changes are required to make geometry more positively perceived. Innovative Approaches: POGIL and GGS GeoGebra Software (GGS): GeoGebra has become one of the most significant instruments of geometry teaching today, with the visualization being dynamic and incorporating several branches of mathematics including algebra, geometry, and calculus. The interactive computer software will help students to manipulate geometric objects and explore mathematical concepts in an interactive and visual manner. It is shown by research that GeoGebra is useful in enhancing conceptual knowledge and interest of students in geometry. To highlight, it was observed in studies that the learners who used GeoGebra achieved significant improvement in mastering the concepts of geometry compared to learners who completed a more traditional learning experience (Bwalya, 2019 ; Khalil et al., 2019 ; Melese, 2017 ). Moreover, the program also cultivates the culture of learning that is characterized by inquiry and exploration and results in the active engagement of students with mathematical concepts due to their being active receivers of information. Through GeoGebra, the students develop a more favorable attitude towards mathematics i.e. their increased ownership of the learning experience and increased their motivation to learn more about the topic. It is also stated that the utilization of GeoGebra enhanced the feelings of visualization, motivation, engagement, and conceptual understanding in the Ethiopian setting (Abate et al., 2023; Dereje et al., 2023; Gurmu et al., 2024 ). Process Oriented Guided Inquiry Learning (POGIL): Another new strategy of teaching geometry focusing on active learning and collaboration between students is the POGIL approach. To facilitate the learning of mathematical concepts using the guided inquiry approach, POGIL encourages a highly organized and yet pliable classroom environment where students can discover mathematical concepts with and through groups to become owners of their learning processes. The teaching model has demonstrated positive outcomes in the development of the problem-solving abilities, conceptual knowledge, and general interest of geometry in students. The studies have shown that students who were taught POGIL based instruction reported higher levels of engagement and a superior level of understanding geometric concepts than students who were taught using standard lecture-based instruction (Andriani et al., 2019 ). Not only does POGIL enable mathematical success of the learners through its promotion of collaborative methodology and elicitation of higher order thinking, but also learners being armed with useful tools in which to surmount mathematics challenges with preparedness and enthusiasm, ultimately, can be said to have achieved success as far as improving attitude towards learning of geometry is concerned. The use of GeoGebra and POGIL in teaching geometry shows a shift to more interactive and student-centered classes, which are required to help establish meaningful engagement and enhance mathematical competencies. Methodology Research Design: This study used, a quasi-experimental design method to examine the efficacy of incorporating GGS and POGIL on ensuring productive disposition towards studying geometry on students. The research design was based on a pretest- posttest, non-equivalent groups design including one group that was instructed in the traditional way (Comparison group), another one was in POGIL-only way (POGIL group), and the third group was taught in the integrated manner using the GGS and POGIL (GGS-POGIL group) (See Table 1). Table 1 Pretest-posttest non-equivalent group quasi-experimental design Group Pretest Treatment Posttest GGS-POGIL group O 1 T 1 O 2 POGIL group O 1 T 2 O 2 Comparison group O 1 O 2 O 1 : Pretest for all groups O 2 : Posttest for all groups T 1 : Teaching with GGS integrated POGIL T 2 : Teaching with POGIL Research Design: This study used, a quasi-experimental design method to examine the efficacy of incorporating GGS and POGIL on ensuring productive disposition towards studying geometry on students. The research design was based on a pretest- posttest, non-equivalent groups design including one group that was instructed in the traditional way (Comparison group), another one was in POGIL-only way (POGIL group), and the third group was taught in the integrated manner using the GGS and POGIL (GGS-POGIL group) (See Table 1). Participants and Sampling: The sample of this research was the Grade 10 students in the secondary schools in the capital city of Ethiopia, Addis Ababa. Purposive sampling method was employed in order to select three schools that were willing to take part in the research and had the proper infrastructure in terms of technology that would facilitate the use of GGS. They were three conditions of instruction namely, Traditional instruction, POGIL-only instruction, and integrated GGS and POGIL instruction. In the three schools three intact classes were selected on a random basis (one per school). Experimental groups were divided into two classes, whereas, the comparison group was issued. The overall group of the sample consisted of 149 students of whom 50 students would be in the GGS-POGIL group, 49 students in the POGIL group, and 50 students in the Comparison Group. Instrumentation: The method of gathering the data was the Productive Disposition Questionnaire (PDQ) that was modified based on Trends in International Mathematics and Science Study TIMSS (2015). The questionnaire was constructed to reflect the various aspects of the attitude of the students to mathematics as the liking of the mathematics learning topic, confidence, and the usefulness of mathematics to the students in their lives. Every question in the questionnaire was graded out of five through a Likert scale questionnaire and this enabled the research participants to elaborate their answers. The reliability and validity of the PDQ to the Ethiopian context were established by carrying out an expert review on the face and content validity and a pilot study on a sample of 40 Grade 11 students who were randomly selected among schools that were not part of the intervention. Reliability was considered as the internal consistency of productive disposition questionnaire and its dimension and the alpha of Cronbach was 0.82, and was greater than the value of 0.7. This was agreeable and the questionnaire was valid to gather additional information. Procedures : The first step into the process of data collection involved the Professional Development Course (PDC) training of chosen teachers, therefore making them have the necessary experience and skills needed to successfully implement instructional interventions. An assortment of detailed teaching resources consisting of teacher manuals, lesson plans, student activity sheets and GeoGebra guides were created and distributed to intervention teachers creating the backbone of delivery of instruction and application of GeoGebra lab activities. After that there was an initial assessment performed using the Productive Disposition Questionnaire (PDQ) on all three groups to ascertain a preceding assessment of their productive disposition in learning geometry. This served as a pre-test. The intervention lasted eight weeks in which the school teachers administered instructional interventions based on the teaching materials provided. The interventions included a mixture of integrated GGS/ POGIL teaching of POGIL Group, pure POGIL teaching of POGIL Group, and standard instruction of Comparison Group. The students in the POGIL group intervention course experienced inquiry-based learning in the small group discussion, practical exploration of geometric concepts and teacher facilitated guided inquiry within a small group. In the same case the POGIL group intervention issue-based class (GGS-POGIL) students were provided with POGIL only instruction during real time class and a combination POGIL approach with the help of GGS to visualize and explore geometric concepts in ICT laboratories. Comparing students, on the contrary, were taught geometry using standard teaching methods without focused direction on POGIL and GGS. The three groups were administered a posttest involving the Productive Disposition Questionnaire after the intervention so that to identify any change in productive disposition towards learning geometry. To compare the differences between and within the groups, inferential statistical tests, parametric (e.g., ANOVA and ANCOVA) and non-parametric (e.g., Kruskal-Wallis) were performed to analyze the data. In order to take a closer look at these differences, a few comparisons with post hoc pair wise analysis were done, which provided a richer analysis of specific group differences and helped in overall interpretation of the research findings. Results Pretest Result: The pretest was aimed at testing the difference in bases of productive disposition of students on education in geometry especially their liking of mathematics learning, their confidence in mathematics ability and perceived value of mathematics in GGS-POGIL, POGIL and Comparison groups. In deciding the appropriate statistical tests, significant assumptions: i. e., independent observations, normal distribution, and homogeneity of variance were checked. Independent observations were determined considering the fact that different groups were used to collect the data. Instead, the Kolmogorov-Smirnov test and Shapiro-Wilk test assessed the normality assumption and it was found that Overall Productive Disposition (p = 0.483) and Students Confident in Mathematics abilities (p = 0.051) passed the test whereas Students Like Learning Mathematics (p = 0.023) and Students Value Mathematics (p = 0.040) failed the test. The homogeneity of variance test, used to test the homogenous variances in the overall productive disposition (p = 0.074), as well as those in Students Confident in Mathematics abilities (p = 0.725), but not those in Students Like Learning Mathematics (p = 0.041) and Students Value Mathematics (p = 0.003), showed homogenous variances respectively. Based on the results, the parametric tests (e.g., ANOVA) were applied to those variables that fit the assumptions and the non -parametric tests (e.g., Kruskal- Wallis) applied to the variables that did not fit the assumption. Students Liking for Learning Geometry Pretest: To compare the differences among the three groups based on the liking of mathematics among students, Krushal-Wallis test was applied. As demonstrated in Table 2 , the test found out that the responses of students in three groups had a statistically significant difference (H = 9.623, df = 2, p = .008). In other words, before the intervention the groups had an interest of learning mathematics to varying levels. The rank mean demonstrates that GGS-POGIL group had the highest rank mean (85.98), next was the Comparison group (78.77), and the lowest rank mean was found in the POGIL one (59.95). This indicates that the learners in the GGS-POGIL and Comparison groups apportioned more than their counterparts in POGIL group to like mathematics learning. Table 2 Independent Samples Kruskal-Wallis Test summary of groups on Students Like Learning Mathematics and Value Mathematics pretest in learning geometry. Variable Ranks Test Statistics a,b Group N Mean Rank Kruskal-Wallis H df Asymp. Sig. Students like learning mathematics pretest GGS-POGIL group 50 85.98 9.623 2 .008 POGIL group 49 59.95 Comparison group 50 78.77 Total 149 Students value mathematics pretest GGS-POGIL group 50 59.22 10.213 2 .006 POGIL group 49 81.44 Comparison group 50 84.47 Total 149 a. Kruskal Wallis Test b. Grouping Variable: Group These differences were made more clear by a pair wise comparison of Table 3 by Dunn. The finding showed that the POGIL group had significant difference with GGS- POGIL group (Test Statistic = 26.031, p = .003, Adj. Sig. =.008). This means that students in the GGS-POGIL group enjoyed learning mathematics as opposed to those in POGIL group. Nonetheless, the result of the POGIL group, compared with Comparison group (Test Statistic = -18.821, p = .030, Adj. Sig. =.089), did not turn out to be statistically significant when multiple tests were corrected. Further, no meaningful differences were drawn between the GGS-POGIL and Comparison groups (p = .402), and thus, suggesting that the three groups were similar in the level of liking mathematics before the intervention though, the three groups were not at the same level, and this means that using pretest as covariate was necessary. Table 3 Duns test Pairwise Comparisons of Groups on Students Like Learning Mathematics and Value Mathematics Pretest. Variable Sample 1-Sample 2 Test Statistic Std. Error Std. Test Statistic Sig. Adj. Sig. a Like Learning Mathematics Pretest POGIL group-Comparison group -18.821 8.655 -2.175 .030 .089 POGIL group-GGS-POGIL group 26.031 8.655 3.008 .003 .008 Comparison group-GGS-POGIL group 7.210 8.611 .837 .402 1.000 Value Mathematics Pretest GGS-POGIL group – POGIL group -22.219 8.663 -2.565 .010 .031 GGS-POGIL group – Comparison group -25.250 8.619 -2.930 .003 .010 POGIL group – Comparison group -3.031 8.663 − .350 .726 1.000 Each row tests the null hypothesis that the Sample 1 and Sample 2 distributions are the same. Asymptotic significances (2-sided tests) are displayed. The significance level is .05. a. Significance values have been adjusted by the Bonferroni correction for multiple tests. Students Value Math Pretest: The interest of students towards mathematics also became a consideration of the study. Table 2 used Kruskal-Wallis test to determine that the groups have a significant difference between them (H = 10.213, df = 2, p = .006). Comparisons and POGIL batches had greater average rank (81.44 and 84.47, respectively) than the GGS-POGIL (59.22). This finding indicates that pre-intervention students in POGIL and Comparison groups attached more importance to mathematics than the students in GGS-POGIL group. This was confirmed by Dunn in his couple of comparisons in Table 3 . The difference between the GGS-POGIL group and POGIL group (Test Statistic = -22.219, p = .010, Adj. Sig. = .031) and with the Comparison group (Test Statistic = -25.250, p = .003, Adj. Sig. =.010) was significantly different. This demonstrates that before the intervention, Comparison and POGIL students ranked mathematics higher in comparison to GGS-POGIL students. There was no significant difference in the Comparison and POGIL groups (p = .726) so similar was the perception of the value of mathematics in both groups prior to the starting of an intervention study. Pre-Test Measure of Mathematical Confidence and Overall Productive Disposition : One-way ANOVA was employed in order to determine the confidence of students in mathematics, in addition to overall positive attitude towards running geometry as a learning task. The outcomes, as cited in Table 4 , revealed that the groups were not significantly differentiated on the premise of the confidence of the students in mathematics skills (F = 2.073, p = .129) and their general amicable attitude (F = .688, p = .504). This means that initially the groups were identical regarding the two variables in terms of which no group had a particular advantage or a disadvantage regarding the confidence and the general productive disposition. Table 4 Summary of Groups of One-Way Analysis of Variance (ANOVA) of Confidence of Students in Mathematics and the General Productive Disposition in Geometry Learning. SS df MS F P Students confident in mathematics pretest Between Groups 1.372 2 .686 2.073 .129 Within Groups 48.297 146 .331 Total 49.669 148 Overall Productive Disposition pretest Between Groups .289 2 .145 .688 .504 Within Groups 30.695 146 .210 Total 30.984 148 * The mean difference is significant at the 0.05 level. The results of the pretest showed a problem of significant differences in the groups in terms of liking mathematics and the importance of mathematics with GGS-POGIL group having fewer positive dispositions in terms of valuing mathematics in comparison to POGIL and Comparison groups. Nevertheless, the results also showed no great differences regarding the confidence of the students to mathematics or overall productive attitude which shows that there was a comparability between the groups before the intervention. These results highlight the significance of the upcoming intervention in possibly changing the attitudes of the students toward learning mathematics in aspects such as increasing their liking mathematics learning and how they engage mathematics learning. Posttest Results Evaluation of the Assumptions : The ultimate objective of the posttest analysis was to test the effect of GGS-POGIL, POGIL and other traditional methods on the productive disposition of learning geometry using the secondary school students due to their liking, confidence, and valuing of mathematics. Statistical tests to determine the assumptions of normality and homogeneous variance and independence of observations were completed before performing the statistical tests. Observational independence was ensured because there were different group assignments. Kolmogorov-Smirnoff test and Shapiro-Wilk test demonstrated that the assumptions about the normality were breached by such variables as Students like learning mathematics and Students value mathematics (p .05). The test of the homogeneity of variance used by Levene showed that the variances of all variables were similar within each group, and the values of the p-tests (p >. 05) were not significant. According to these results, within-group pretest- posttest tests were performed by means of the Wilcoxon Signed rank test when variables were not normally distributed whereas the Kruskal-Wallis test was applied to evaluate the difference between groups. In the case of variables that fit the parametric requirements, there was one-way ANOVA to compare total productive disposition in terms of instructional methods. Analysis of Posttest Data on Students' Productive Disposition in Learning Geometry This study factored into the research the question of whether there existed any relationship between three instruction models and productive disposition in learning geometry: GeoGebra-based Process-Oriented Guided Inquiry Learning (GGS-POGIL), POGIL-only, and traditional instruction. The productive attitude included the liking to study math, mathematical confidence, and the value of mathematics. This was measured by the use of tests that were taken before and after the intervention. The posttest results were compared to the results of the pretest and showed the effectiveness of both of the instruction styles. Posttest Results for Students' Liking for Learning Mathematics: Table 5 Wilcoxon Signed-Rank Test demonstrated a statistically significant change in the extent to which students liked learning mathematics at the end of intervention. There was also a test value of z- -4.540 and an asymptotic significant (p-value) of.000, indicating that most probably the positive change was not randomly done by the chance. Among 144 students that were tested, 96 students said that they like mathematics less, whereas 48 students said that they like mathematics more. This demonstrates that the liking of students to the subject was highly influenced by the programs. This finding is significantly unlike in the pretest which showed no significant likes of students towards mathematics (Tables 2 and 3 ). Consequently, as it can be seen, GGS-POGIL turned out to be effective in creating a considerable effect of student enjoyment in learning geometry. Comparing the groups after hoc with the use of Tukey HSD (Table 6 ), it is possible to note that GGS-POGIL group received much higher scores than POGIL group and the comparison group on the enjoyment of learning mathematics. The average differences showed a clear difference: the GGS-POGIL ranged at 22.227 below the POGIL group (p = .021) and 24.255 below the comparison group on average (p = .010). The POGIL group was not significantly different than the comparison group (mean difference = 2.027, p = .967). This outcome demonstrates the additional advantages of the work with GeoGebra with the POGIL technique. The posttest results have shown a better engagement and enjoyment of mathematics compared to the pretest results with both groups having an equal liking on mathematics (Tables 2 and 3 ). Besides that, the Non-Parametric ANCOVA (Quade’s Test), presented in Table 7 indicated the significant effect of the GGS-POGIL technique on the enjoyment of learning mathematics in students with F-value of 5.364 and p-value of.006. The model proposed that posttest scores variance (6.8 percent) was explained by the fact that technology and guided inquiry were used. This implies that the application of such methodologies had a positive influence on the liking to learn mathematics amongst the students which was not realized using the pretest data (Table 4 ). The outcome demonstrates that GeoGebra, POGIL can be used to make students more enthusiastic and active in mathematics. Also indicated by the posttest result, GGS-POGIL strategy improved the affinities of the students in learning math as opposed to POGIL or traditional teaching. This can be further explained by the comparison of the pretest and posttest results to understand the effectiveness of using GeoGebra in a learning setting that stimulates guided inquiry as this improves the learning process by making learning fun and engaging. According to this study, there should be a need to develop new methods of teaching that allow students to connect mathematics to the positive spirit that they have, and through which their learning experience may be enhanced. Table 5 Wilcoxon Signed-Rank Test of Pretest and Posttest of Component of productive disposition of students in learning geometry. Ranks Test Statistics a Variable Rank Types N Mean Rank Sum of Ranks z Asymp. Sig. (2-tailed) Students’ Like Learning Mathematics pretest - Students’ Like Learning Mathematics posttest Negative Ranks 96 78.07 7494.50 -4.540 b .000 Positive Ranks 48 61.36 2945.50 Ties 5 Students’ Confident in Mathematics Pretest - Students’ Confident in Mathematics Posttest Negative Ranks 115 77.25 8884.00 -7.534 b .000 Positive Ranks 28 50.43 1412.00 Ties 6 Students’ Value Mathematics Pretest – Students’ Value Mathematics Posttest Negative Ranks 92 79.90 7350.50 -3.519 b .000 Positive Ranks 56 65.63 3675.50 Ties 1 Notes : a. Wilcoxon Signed-Rank Test. b. Based on negative ranks. Rank Descriptions : • Negative Ranks: Indicates Posttest Pretest • Ties: Indicates Posttest = Pretest Table 6 Multiple Comparisons Post-hoc Tests (Tukey HSD) on Students' Like Learning Mathematics, Value Mathematics, and Overall Productive Disposition Posttest Variable (I) Group (J) Group Mean Difference (I-J) Sig. Students’ Like Leaning Mathematics Posttest GGS-POGIL group POGIL group 22.2271623 * .021 Comparison group 24.2545234 * .010 POGIL group Comparison group 2.0273611 .967 Students’ Value Mathematics Posttest GGS-POGIL group POGIL group -1.8018432 .976 Comparison group 12.0755049 .340 POGIL group Comparison group 13.8773481 .245 Overall Productive Disposition GGS-POGIL group POGIL group .19454 .304 Comparison group .44963 * .002 POGIL group Comparison group .25509 .132 *. The mean difference is significant at the 0.05 level. Table 7 Non-Parametric ANCOVA (Quade's Test) on Students’ Like Learning Mathematics and Value Mathematics Posttest Variable Source Type III Sum of Squares df Mean Square F Sig. Students’ Like Leaning Mathematics Posttest Corrected Model 18061.673 a 2 9030.836 5.364 .006 Intercept .304 1 .304 .000 .989 Group 18061.673 2 9030.836 5.364 .006 Error 245812.003 146 1683.644 Total 263873.676 149 Corrected Total 263873.676 148 a. R Squared = .068 (Adjusted R Squared = .056) Students’ Value Mathematics Posttest Corrected Model 5666.589 a 2 2833.294 1.539 .218 Intercept .183 1 .183 .000 .992 Group 5666.589 2 2833.294 1.539 .218 Error 268717.486 146 1840.531 Total 274384.075 149 Corrected Total 274384.075 148 a. R Squared = .021 (Adjusted R Squared = .007) Posttest Results for Students' Valuing Mathematics: The posttest outcome of perceived value of mathematics in students as shown in Table 5 identified a statistically significant change at the pretest level of value of mathematics among students (z = -3.519, p = less than 0.001). On the contrary, 92 students said that their valuation of mathematics declined whereas only 56 students said that mathematics increased in their valuation. This finding is the opposite to the comparatively positive pretest dispositions that had been noted before (Tables 2 and 3 ), indicating that the interventions were not equally productive in terms of their influence on the perception of mathematics relevance in students. The findings can also be explained through post-hoc comparisons (Table 6 ). The GGS-POGIL group had statistically significant higher means compared to the comparison group (mean difference = 12.076), albeit not statistically significant to support the idea (p = .340). Likewise, there was no significant difference between the GGS-POGIL and POGIL-only ones ( *p* =.976). This means that there was no significant difference in the way GeoGebra and POGIL were used because of the valuation of mathematics developed by students compared with other modes of instruction. The non-parametric ANCOVA (Quades Test, Table 7 ) indicates the same findings and indicated that the difference in the valuing of mathematics according to instructional method was non-significant (F = 1.539, p = .218, R2 = .021). The small explain variance highlights the poor influences of the interventions on this affective dimension. Posttest Results for Students' Confidence in Mathematics : The confidence of students to mathematics was analyzed as well where it showed general change in direction after the instructional interventions, but there is significant variability in the direction. A statistically significant pretest-posttest difference was observed across all participants (z = -7.534 p = .001) according to Wilcoxon Signed-Rank Test (Table 5 ). Nonetheless, with increased scrutiny of rank distributions, 115 students indicated a drop in confidence and only 28 indicated an improvement, potentially indicating that the interventions did not equally drive self-efficacy and could have brought about cognitive/ affective difficulties on a group of learners. Comparisons between groups also helped to describe the effects of the instructional methods. The Kruskal-Wallis test revealed statistically significant differences in the posttest ranks in confidence between the three groups (H = 24.091, *p = 0.001) as shown in Table 8 . The means of rank were the highest in the GGS-POGIL group (89.85), then POGIL-only group (84.53), and the comparison group (50.81). This ordinal trend shows that both inquiry-based models, in particular, the technology-enhanced GGS- POGIL model, are more helpful to promote the mathematical confidence compared to the traditional instruction. Table 8 Independent-Samples Kruskal-Wallis Test Summary on Students’ Confidence in Mathematics Posttest Across Group Group N Mean Rank Kruskal-Wallis H df Asymp. Sig. GGS-POGIL group 50 89.85 24.091 2 .000 POGIL group 49 84.53 Comparison group 50 50.81 Total 149 Note. The Kruskal-Wallis H test indicates significant differences in confidence ranks across groups. These results indicate that even though GGS-POGIL was most effective in developing the comfort as compared to other groups, the high rate of students who developed with reduced confidence needs more research. Possible causes can be the combination of first overconfidence, the necessity of acquiring experience with inquiry-based and technology-mediated learning, and the different readiness of students. However, the relative effectiveness of the GGS-POGIL group highlights the possibility of combining dynamic visualization tools and guided inquiry to create mathematical confidence self-regarding learning in geometry. Table 9 Dunn’s Test Pairwise Comparisons on Students’ Confidence in Mathematics Posttest Sample 1-Sample 2 Test Statistic Std. Error Std. Test Statistic Sig. Adj. Sig. a Comparison group-POGIL group 33.721 8.662 3.893 .000 .000 Comparison group-GGS-POGIL group 39.040 8.618 4.530 .000 .000 POGIL group-GGS-POGIL group 5.319 8.662 .614 .539 1.000 Each row tests the null hypothesis that the Sample 1 and Sample 2 distributions are the same. Asymptotic significances (2-sided tests) are displayed. The significance level is .05. a. Significance values have been adjusted by the Bonferroni correction for multiple tests. More to the point, the pairwise comparisons provided by Dunn (Table 9 ) were more longitudinal and allowed concluding the fact that both the POGIL and GGS-POGIL groups performed significantly better than the comparison one regarding the posttest confidence ranks (both with a p-value of less than 0.001). Nevertheless, it was not found that the two experimental groups differed statistically significantly (*** p = .539, indicated that whereas integration of GeoGebra gave an numerical benefit of mean rank, its contribution of confidence over POGIL as an intervention was not significant in this sample). It is through these findings that the power of inquiry-based methods with or without technology should be highlighted as compared to conventional teaching in bringing mathematical confidence. However, the observation that most students in all groups had decreased self-confidence (will be shown by the Wilcoxon test) is where a vital sensitivity is needed, as the interventions were relatively effective, although not the ones that affected all learners. This is an indication that inquiry based and technology integrated teaching methods require differentiated instruction and continuous pedagogical reflection, in order to make sure that instructional methods are sensitive to student readiness levels and affective needs. Posttest Scores on Students' Productive Disposition: Findings of paired samples t-test in Table 10 reveal that every group had at least some improvement in productive disposition when there was comparison between pretest and posttest scores. GGS-POGIL group had the highest mean gained of.69 (SD = .71, t(49) = 6.861, p = .000), and the POGIL group had the mean gained of.42 (SD = .74, t(48) = 3.933, p = .000). Relative to the comparison group, the change in the latter was not significant, at only.15 (SD = .76, t(49) = 1.375, p = .175) on average. These findings indicate that the conventional approaches failed to make much positive impact on productive dispositions of students. Most saliently, the overall productive disposition in its component’s terms liking learning mathematics, valuing mathematics, and mathematics confidence - the GGS-POGIL group experienced significant increase in terms of liking learning mathematics only (mean difference of 22.23, p = .021) and not in the context of improving the valuing mathematics to a comparable extent (-1.80, p = .976) and mathematic confidence. This would mean that despite the fact that the interventions increased value of learning mathematics, the intervention made no overall approach to the overall perception of value of the subject and the confidence of students with mathematics abilities. The results of the paired samples test, which were provided after the analysis of one way ANOVA, the result of which is presented in Table 11 , further confirms the effectiveness of the instruction methods applied within the context of this study. The ANOVA test had an impressive F-value of 5.932 ( p = .003) which means that there is statistical significance of difference among the groups. Such findings indicate that the different pedagogical strategies employed played a significant role towards the overall productive disposition of the students with significant differences being expressed among the different groups. These outcomes are in line with the assumption that GGS-POGIL and POGIL methods significantly improved the general productive disposition of the students compared with that of the traditional instruction group. Table 10 Paired Samples t-Test on the Pretest and Posttest of Students’ Productive Disposition in Learning Geometry Variable Group Paired Differences T Df P M SD Overall Productive Disposition: Posttest-pretest GGS-POGIL group .69 .71 6.861 49 .000 POGIL group .42 .74 3.933 48 .000 Comparison group .15 .76 1.375 49 .175 Table 11 One-way ANOVA Summary of Groups on Productive Disposition Posttest in Learning Geometry SS df MS F P Overall Productive Disposition Between Groups 5.084 2 2.542 5.932 .003 Within Groups 62.573 146 .429 Total 67.657 148 * The mean difference is significant at the 0.05 level. Lastly, the results of the Tukey HSD post-hoc tests reported in Table 6 indicate the definite group effects concerning the total productive disposition. The comparison group had a significant mean difference of.44963 (p = .002) with the GGS-POGIL group indicating that their total productive disposition had increased significantly. However, the only statistical finding is that the differences between the post-intervention GGS-POGIL and POGIL groups were not significant (mean difference of.19454, p = .304). This can be construed to mean that though the integrated approach has a tendency of positively influencing the productive disposition of students in learning geometry, there is need to have more strategies that will be applied so as to bring about noticeable changes in all the groups. Overall, this evidence indicates the need to use new instructional strategies like GGS-POGIL and POGIL in the process of cultivating productive disposition towards learning geometry among students. Additionally, the results lead to continued development of teaching methods over the effective advancements of all items of productive disposition-viz., liking, valuation and confidence in mathematics. Table 12 Effect Sizes (Cohen's d) for Group Comparisons of Students’ Productive Disposition and its Components in learning geometry Variable GGS-POGIL vs. POGIL GGS-POGIL vs. Comparison POGIL vs. Comparison Liking for Mathematics 0.71 0.65 0.00 Confidence in Mathematics 0.16 0.88 0.70 Value of Mathematics -0.01 0.29 0.29 Productive Disposition 0.31 0.68 0.35 In Table 12 , it was found that GGS-POGIL group experienced the largest positive change in their productive disposition in geometry, particularly, confidence in mathematics (Cohen d = 0.88) and overall productive disposition (Cohen d = 0.68) over the conventional approach. There was also some small improvement in GGS-POGIL group in liking mathematics (Cohen d = 0.71) and valuing mathematics (Cohen d = 0.29). The positive impact of the POGIL group as compared to the comparison group also occurred but with less degree. These observations indicate that GeoGebra with POGIL could assist students to have higher integrated and better productive disposition in geometry education than in traditional approach. The study highlights the fact that GGS-POGIL use can render it achievable to make the students possess a more fruitful disposition in mathematics. Discussion The findings in this research give substantial proof that, integration of the GeoGebra Software (GGS) with the Process-Oriented Guided Inquiry Learning (POGIL) is comprehensive in influencing the productive disposition of the students towards learning geometry. To be more precise, the gains in mathematics liking, mathematical confidence, and mathematics value were truly impressive by the GGS-POGIL students, which were measured again in comparison to the POGIL and comparison groups. These results support the study which shows that technology-enhanced dynamical pedagogical activities can facilitate cognitive and affective involvement in mathematics education (Hosseini et al., 2022; Rodríguez-Nieto et al., 2021 ). Among the main findings of this research is that GGS-POGIL group had a greater disposition of liking mathematics. The finding aligns with the available literature that indicates that interactive learning setting promotes greater engagement and pleasure in students (Baye et al., 2021 ). Probably another factor that might have given students greater enjoyment is also the interactive and visual quality of GeoGebra, as this would enable students to manipulate geometric shapes interactively and explore mathematical relationships in a more intuitive manner (Ansong et al., 2021). Even the inquiry-based and collaborative features of POGIL could have been more engaging to the students because they provided an opportunity to engage in active learning and new conceptual insights (Andriani et al., 2019 ). The main result of this study is that there is a significant increase in the belief of the students in their confidence of mathematical ability in the GGS-POGIL group. It appears that the use of GeoGebra has provided the students with immediate visual feedback, which, conversely, has been shown to enhance mathematical self-efficacy (Hutkmri and Zakaria, 2014). In addition, it has been found that Process Oriented Guided Inquiry Learning (POGIL) strengthens logical thinking and problem-solving, thus complementing the confidence of students in their ability to work on difficult mathematical problems (Irwanto et al., 2018). The results however indicate that the students who underwent POGIL only recorded average increases in their confidence, although, lesser than in the GGS-POGIL group, meaning that, technology use is essential in strengthening student confidence. The third aspect of productive disposition, i.e. the perceived usefulness of mathematics by the learners also recorded a significant gain among the GGS-POGIL group. The observation aligns with the previous studies that have shown that technology-based learning scenarios help pupils to value the practical relevance and applicability of mathematical concepts (Bedada and Machaba, 2022). Through GeoGebra, students were in a position to relate abstract geometric ideas with real- world visual models, therefore enhancing their appreciation of mathematics as a necessary problem-solving device. The study also reported that the members of the comparison group were more affected with a positive opinion of mathematics at the start than their counterparts namely members of the GGS-POGIL group. What this means is that traditional methods of teaching may still be deemed as ideal by a given group of learners, maybe due to their usedness to traditional, assessment-based learning models (Abate et al., 2023). The discrepant findings of the previous research reveal that in spite of the fact that GeoGebra facilitates immersion and conceptualization, its effects on the student motivation and productive attitude can be rather fluctuating. To illustrate, the studies show that scholars, who are technology-unskilled, may experience some challenges when working with GeoGebra at first, and that can further demotivate and lower the confidence levels among them (Adelabu et al., 2022). Furthermore, certain studies have established that the success of inquiry-based teaching methods such as POGIL highly relies on the performance and willingness of teachers (Awofala et al., 2022 ). This underscores the need to properly train teachers and design instructional methods in the incorporation of such methods. Despite these potential constraints, there is an overall compatibility of the findings of this study with the global tendencies in favor of the introduction of technology and inquiry-based pedagogies in the learning of mathematics. GeoGebra and POGIL complementarism provides a strategy that is backed by research to address the issue of attitude and orientation to mathematics among the students in settings where learning geometry poses a major challenge to many students. The next step in research should be studying the long-term outcomes of this pedagogical practice and the way it can be extended to other learning environments, e.g. schools in rural or resource-limited areas. On the whole, this paper highlights the power of change in incorporating GeoGebra and POGIL to facilitate the positive attitude of students to mathematics by their productiveness. In the midst of difficulties in implementation, the achievement of this research studies will mark the need to keep on innovating the process of teaching mathematics to make students enjoy mathematics, feel confident, and appreciate mathematics. Conclusion The integration of the GeoGebra Software (GGS) and Process-Oriented Guided Inquiry Learning (POGIL) makes math more enjoyable and more confident, as well as more valuable, to students. The interactivity of GeoGebra and the teamwork orientation of POGIL help to learn and solve more problems. Although it is necessary to resolve technological problems at the outset and facilitate the teachers, it is possible to maximize benefits in a structured implementation. The possible usefulness of technology-supported inquiry learning in mathematics education in this study is reported and should be the subject of long-term impact research and generalization to other areas. Recommendations : The technology-based inquiry learning needs to be incorporated into curriculum by the practitioners and GeoGebra Software (GGS) and Process-Oriented Guided Inquiry Learning (POGIL) should be adopted by schools to enhance the enthusiasm, confidence, and understanding of geometry among students. Implementation can only be achieved when teachers are taught well and so it is important to train them on technology-driven inquiry techniques and development professionally using different modalities. The governments among others should also donate money towards the provision of proper infrastructure including computer laboratories and internet connections to the digital resources. The long-term performance of GGS-POGIL on mathematical competency must be measured, and its performance in the case of other learning settings are explored, such as the case of low-resource schools. Declarations Acknowledgements: I acknowledge my main advisor Dr. Kassa Micheal, and co-advisor Dr. Mulugeta Woldemichael for their consistent guidance and review of this manuscript. Funding: This research did not receive any specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Author contributions: All authors review the manuscript. Competing interests : no competing interests between authors. Ethical Approval: The ethical approval of this study was also taken before the intervention by the Institutional Review Committee of the Addis Ababa University, College of Education and Behavioral Studies. The study was carried out under the strict compliance of the National Research Ethics Review Guideline of Ethiopia and keeps the ethical standards stipulated in the Declaration of Helsinki. The basic ethical principles included justice, autonomy, beneficence, and non-maleficence that were upheld throughout the research process. Consent to participate: All participants signed an informed consent before data collection. Since all the student participants were aged 17 or older, the parental or the guardian consent was not needed. The participants were completely aware of the purpose of the study, procedures, and their rights, which included: Voluntary enrolment coupled with the right to quit without penalty. Confidentiality and anonymity (no identities of respondents will be disclosed) Debriefing processes at the interview to have proper representation of their ideas. It will give them an opportunity to proofread and confirm their responses. Regularity of length of classes (45 minutes per period) at intervention times. The college management was also granted permission to carry out the study. Consent to Publish: Participants consented to the publication of anonymized, aggregated research findings. No personally identifiable information is included in the manuscript. Data Availability Statement (DAS): The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. Code Availability: not applicable References Andriani S, Nurlaelah E, Yulianti K (2019) The effect of process oriented guided inquiry learning (POGIL) model toward students’ logical thinking ability in mathematics. 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Int J Secondary Educ 5(5):56. https://doi.org/10.11648/j.ijsedu.20170505.11 Mishra, Koehler MJ (2006) Technological Pedagogical Content Knowledge: A Framework for Teacher Knowledge PUNYA MISHRA. Teachers Coll Record 108(6):1017–1054 Negara HRP, Wahyudin, Nurlaelah E, Herman T (2022) Improving Students’ Mathematical Reasoning Abilities Through Social Cognitive Learning Using GeoGebra. Int J Emerg Technol Learn 17(18):118–135. https://doi.org/10.3991/ijet.v17i18.32151 Niam MA, Asikin M, AND MATHEMATICS (STEM)-BASED MATHEMATICS TEACHING MATERIALS TO INCREASE MATHEMATICAL CONNECTION ABILITY (2020) THE DEVELOPMENT OF SCIENCE, TECHNOLOGY, ENGINEERING. MaPan 8(1):153. https://doi.org/10.24252/mapan.2018v8n1a12 Rodriguez JMG, Hunter KH, Scharlott LJ, Becker NM (2020) A Review of Research on Process Oriented Guided Inquiry Learning: Implications for Research and Practice. J Chem Educ 97(10):3506–3520. https://doi.org/10.1021/acs.jchemed.0c00355 Rodríguez-Nieto CA, Rodríguez-Vásquez FM, García-García J (2021) Exploring University Mexican Students’ Quality of Intra-Mathematical Connections When Solving Tasks About Derivative Concept. Eurasia J Math Sci Technol Educ 17(9):1–21. https://doi.org/10.29333/ejmste/11160 Rohendi D, Dulpaja J (2013) Journal of Education and Practice www.iiste.org ISSN (Vol. 4, Issue 4). Online. www.iiste.org Rohmah S, Kusmayadi TA, Fitriana L (2020) Mathematical connections ability of junior high school students viewed from mathematical resilience. Journal of Physics: Conference Series , 1538 (1). https://doi.org/10.1088/1742-6596/1538/1/012106 Rohman K, Turmudi T, Budimansyah D, Syaodih E (2023) Development of a Productive Disposition Skills Instrument for Elementary School Students. Jurnal Elementaria Edukasia 6(2):650–660. https://doi.org/10.31949/jee.v6i2.5259 Romero Albaladejo IM, García López M (2024) del M. Mathematical attitudes transformation when introducing GeoGebra in the secondary classroom. Education and Information Technologies , 29 (8), 10277–10302. https://doi.org/10.1007/s10639-023-12085-w Safi F, Desai S (2017) Promoting Mathematical Connections Using Three-Dimensional Manipulatives. Math Teach Middle School 22(8):488–492. https://doi.org/10.5951/mathteacmiddscho.22.8.0488 Schoenfeld AH (2007) What is mathematical proficiency and how can it be assessed? In Assessing Mathematical Proficiency (pp. 59–74). Cambridge University Press. https://doi.org/10.1017/CBO9780511755378.008 Tesfamicael SA, Ayalew Y (2021) Mathematics Education in Ethiopia in the Era of COVID-19: Boosting Equitable Access for All Learners via Opportunity to Learning. Contemp Math Sci Educ 2(1):ep21005. https://doi.org/10.30935/conmaths/9680 Walker L, Warfa ARM (2017) Process oriented guided inquiry learning (POGIL®) marginally effects student achievement measures but substantially increases the odds of passing a course. PLoS ONE 12(10). https://doi.org/10.1371/journal.pone.0186203 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8671177","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":578959537,"identity":"334df11d-d829-4c5b-818c-440e8284d05c","order_by":0,"name":"Gizachew 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07:27:08","extension":"html","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":173870,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8671177/v1/1c18051c5d1ffb09a3fa8ac0.html"},{"id":100954446,"identity":"ee6c64ac-21a5-4744-b690-f7a6f363c5b9","added_by":"auto","created_at":"2026-01-23 07:25:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":263992,"visible":true,"origin":"","legend":"\u003cp\u003eConceptual framework of the study, a combination of constructivist, sociocultural, TPACK and mathematical proficiency theories.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8671177/v1/a831992c30aa28455b51bcda.png"},{"id":100955470,"identity":"dd04e8ce-cd3b-4d47-b6c1-8a64d37a11b6","added_by":"auto","created_at":"2026-01-23 07:28:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1704532,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8671177/v1/ee6a63bd-42b6-4d3e-9a61-2a567a18587c.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eEnhancing Secondary School Students' Productive Disposition using GeoGebra Software integrated Process Oriented Guided Inquiry Learning in Geometry\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe role of mathematics education in building cognitive and emotional attitudes of students has found numerous research publications, writing that mathematics education is significant (Rohman et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Hutajulu et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Kilpatrick et al., 2001). Another important element in the development of mathematical proficiency is productive disposition because it is defined as the stable tendency of the learner to view mathematics as useful and worthwhile (Chua, 2021). It is not just the knowledge of the concepts but also involves such issues as the pleasure of studying math, the belief in mathematical skills, and the perception of mathematics as something significant and practical in the real life (Ayalew, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Kilpatrick et al., 2001). Nevertheless, conventional approaches to teaching mathematics and that of geometry, in particular, have not resulted in some of the key elements of productive disposition of mathematics learning and require pedagogical re-consideration (Dereje, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Baye et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), living with status-quo practices.\u003c/p\u003e \u003cp\u003eGeometry learning is a challenge among the Ethiopian secondary school students because it is an abstract subject and the pedagogical system frequently encourages memorizing and learning by rote, rather than conceptual learning (Gurmu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Eshetu et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Studies have reported that traditional instruction methods do not engage students, diminish their drive and self-efficacy towards mathematics, which constitute important elements in order to be productively disposed (Ayalew, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Other dynamism enforced in the learning environment like inquiry-based approaches that are technologically integrated, have become a comparatively proactive substitute to transform and not to stay in the past following these ongoing challenges (Romero Albaladejo and Garccia Lopez, 2024; Bekene and Machaba, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eProcess-Oriented Guided Inquiry Learning (POGIL), is created to engage students in organized problem-solving tasks that encourage conceptual knowledge as well as collaborative learning (Andriani et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Muhammad and Purwanto, 2020). The same applies to the example of GeoGebra software (GGS). It is noted that an interactive visualization is an effective form of engaging students in a better perception of geometry concepts (Simbolon and Siahaan, 2021; Ansong et al., 2021). There are signs that, in the case of the combination of GeoGebra and POGIL, the students do not only gain a deeper insight into the mathematical structures but also reinforce their productive disposition by improving their confidence, enjoyment, and interest in mathematics (Hosseini et al., 2022; Rodriguez-Nieto et al., 2021). Nonetheless, the research by Deranje and his colleagues (2022) is antithetical to prior research and suggested further study of the situation in Ethiopia.\u003c/p\u003e \u003cp\u003eAlthough the global community is starting to see progress in the area of educational technology and teaching methods, the overall impact of GGS and POGIL on fruitful dispositions in learners has not been well-documented (Rodr\u0026iacute;guez-Nieto et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) and especially in Ethiopia (Gurmu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Individual research on POGIL and GeoGebra has brought out informative advantages. Their integrated action and the promised scaffold that they would introduce in improving productive disposition of students in mathematics, though, is of critical importance to study. The research will be conducted to explore the interactive and combination effects of GGS-POGIL on productive dispositions in geometry learning among students in secondary schools in terms of enjoying, feeling confident, and value of mathematics. In this regard, the operationally defined productive disposition in this study is the drive of the students to feel that math is useful and worth studying, to feel confident in their capability of completing a mathematical task, and to like and get a satisfaction in the study of mathematics.\u003c/p\u003e \u003cp\u003eThis study is relevant to the urban Ethiopian secondary schools where students are said to have shown decreasing interest in geometry because of the application of traditional teaching methods that do not involve the participants in educational activities (Ayalew, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe results of this research can be used in this literature area since they are based on the comparisons of the various impacts of GGS \u0026amp; POGIL combination, POGIL alone, and traditional teaching methods on the productive disposition of the students. Another aspect of appreciative learning about the role of technology-based inquiry learning in the development of positive dispositions can be of interest in the curriculum changes towards the engagement of students in math and the attainment of improved performances; and also fill gaps in research that are evident.\u003c/p\u003e\n\u003ch3\u003eStatement of the Problem:\u003c/h3\u003e\n\u003cp\u003eThere has long been a history of deep-seated problems in mathematics education in Ethiopia and the root causes of the problems remain to this day. The learning of geometry is one of the strands that has been associated with a lot of problems, with the performance of students being a dismal one. Literature also indicates that students experience issues with the conceptual comprehension of the subject, are influenced by demotivating and emotional facts and they still do not like the geometrical concepts and consequently do not perform well in examinations although geometry is effective in the practical situation (Kpotosu et al., 2024). The productive attitude that included the pleasure that students enjoyed mathematics, their belief in their mathematical potential, and the sense of the importance of the subject matter was one of the aspects that did not fit in the existing instructional paradigms (Rohmah et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Rohendi and Dulpaja, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kilpatrick et al., 2001). This issue was particularly acute in Addis Ababa secondary schools where the students are said to be passive, uninterested, and have poor outcomes (Tesfamicael \u0026amp; Ayalew, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ayalew, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe continued application of conventional pedagogical methods that are inefficient towards enhancing active learning among learners and providing an instructional setting that would facilitate the development of a positive productive mind towards mathematics are one of the key factors that precondition this critical issue (Gurmu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Dereje, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Memorization and lectural forms of pedagogy, which are predominantly employed by teachers, do not offer learners the feeling of enjoyment or confidence. Also, the enormous majority of students did not consider mathematics as a topic that could be applied to life issues, which made their deficit of interest and disengagement (Melese, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Safi and Desai, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). This disconnection uncovered the need to adopt new teaching methods to engage students intellectually and emotionally in learning so that they can learn more, become interested in mathematics over the long run (Kilpatrick et al., 2001; Rohendi and Dulpaja, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), and research has also proven that the adoption of technology tools has a positive effect on student engagement, motivation, and conceptual learning (Mahmoud, 2023).\u003c/p\u003e \u003cp\u003eStudies of recent years emphasized the potential of Process-Oriented Guided Inquiry Learning (POGIL) paired with dynamic mathematics software to transform the way mathematics is taught (Rodr\u0026iacute;guez-Nieto et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Romero Albaladejo and Garc\u0026iacute;a L\u0026oacute;pez, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), which this research attempts to access. Such techniques have been discovered to enhance understanding of abstract mathematical concepts, generate more interest among students and have positive effect on learning attitudes with regards to mathematics. Nevertheless, little has been researched on the application of these methods in Ethiopia especially on their effects on productive disposition of students as regards to geometry (Baye et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Gurmu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The viability of this integrated strategy-GeoGebra Software blend POGIL (GGS-POGIL) in the solutions of the deficient areas in the engagement and performance of students led to additional empirical research.\u003c/p\u003e \u003cp\u003eThe urgent need to address these weaknesses was highlighted by the new assessment statistics that have shown frighteningly low rates of engagement and student achievement in Ethiopian high schools. In their research, Abera and his co-authors mentioned that 32.5 percent of students had mastered simple mathematical concepts (Abate et al., 2023), and over 60 percent of students failed to reach the desired level in nationwide mathematics exams (Ayalew, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In addition, Ethiopian secondary school pupils possessed weak conceptualization in geometry with less than 35 percent of the students being proficient in the key areas (Dereje et al., 2023). Ethiopian Third National Learning Assessment (ETNLA) also noted that the average national mean score of Grade 10 students in mathematics only reaches to 11.9% which is significantly lower than the national education policy targets (NEAEA, 2017). The reliance on poor pedagogical activities has also increased failure rates in math performance, thus responding to the high problem, and these result in student dispositions issues (Baye et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe current research aimed to evaluate the effectiveness of the pairing of GeoGebra Software and Process-Oriented Guided Inquiry Learning (GGS-POGIL) to improve productive disposition of the students in studying geometry. The study investigates the impact of the integrated strategy on certain features of active disposition, including, enjoyment of mathematics by students, confidence in mathematics, and relevance of the subject. By a comparison of teaching methods like GGS-POGIL, POGIL-only, and conventional teaching methods, this study attempts to offer empirical validity on the best teaching methods which can be used in facilitating productive dispositions of students in mathematics. It is expected that results of this study will help in developing evidence-based instructional strategies in an attempt to enhance productive disposition of students in Ethiopian secondary schools in Addis Ababa.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eObjectives:\u003c/h2\u003e \u003cp\u003eThe general objective of this study was to investigate the effectiveness of integrating GeoGebra software with Process Oriented Guided Inquiry Learning in enhancing students\u0026rsquo; productive disposition toward learning geometry. In particular, the study sought to:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eInvestigate the effect of integrated POGIL with GeoGebra approach on the overall students\u0026rsquo; productive disposition in geometry.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAssess the effect of this integrated approach on the different components of productive disposition, namely, students' enjoyment of mathematics, confidence in math abilities, and perceived importance of the subject.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eResearch Questions\u003c/h3\u003e\n\u003cp\u003eIn attempting to meet these objectives, the research centered on the following research questions:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIs there the positive gain in positive productive disposition of students who experience geometry instruction through an integrated POGIL and GGS than students who experience traditional instruction or POGIL-only instruction?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eWhich of the productive disposition dimensions, enjoyment of math, confidence in math ability, and perceived importance of math, are most impacted by the combined POGIL and GGS method in the context of geometry instruction?\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e\n\u003ch3\u003eSignificance of the Study:\u003c/h3\u003e\n\u003cp\u003eThe study under consideration is immensely important as it considers the potential benefits of the combination of Process-Oriented Guided Inquiry Learning (POGIL) and GeoGebra software (GGS) in promoting a constructive attitude of students to mathematics, and specifically to geometry. The study presents advice to teachers and policymakers in Ethiopia and other countries by targeting those factors that constitute productive disposition; enjoyment of learning mathematics, self-confidence, mathematics ability, and liking mathematics. It also fills the gap in the existing literature on mathematics education in Ethiopia where students might usually face some difficulties related to engagement and self-efficacy. Demonstrating that the adoption of POGIL-GGS creates a positive productive disposition can also provide the educators with practical examples that can be used by to encourage mathematical motivation and success.\u003c/p\u003e \u003cp\u003eMoreover, the research contributes to the creation of curriculum design and methods of teaching, as well, by studying how this combined method impacts the students in their enjoyment of math, self-confidence, and the perception of the importance of the studied material. These aspects could be enhanced to facilitate increased motivation, less anxiety and appreciation of mathematics. The results of this research may also extend well beyond the Ethiopian situation to provide a model that may be used across the board in all the educational institutions in other developing countries plagued with the same problem in the field of mathematics education. Revealing the successful examples of teaching, the study supports the global project to impose mathematics education with the use of creative pedagogy.\u003c/p\u003e"},{"header":"Theoretical Framework","content":"\u003cp\u003eThe theoretical framework that drives this study is a combination of two theoretical perspectives that relate process-oriented guided inquiry learning (POGIL) pedagogical innovation with the technological capabilities of GeoGebra software to promoting productive disposition in geometry among the students. The framework integrates constructivist and sociocultural theories of learning, a model of mathematical proficiency proposed by Kilpatrick et al. (2001) and Technological Pedagogical Content Knowledge (TPACK) model (Mishra and Koehler, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) to describe how and why the integrated GGS-POGIL approach would be hypothesized to facilitate affective involvement of students in mathematics.\u003c/p\u003e \u003cp\u003eConstructivist theory (Schoenfeld, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) has it that the learner is the active entity in the process of building knowledge (by interacting with the surrounding world, reflecting and problem solving) as opposed to an entity that is passive receivers of information. This is consistent with the fundamental structure of POGIL, in which students are provided with a guided, structured inquiry where they are expected to construct their own meaning and achieve conceptual clarity by way of guided inquiry. POGIL engages students as active participants towards learning beyond merely a deeper learning experience but also a sense of ownership and agency in mathematics.\u003c/p\u003e \u003cp\u003eTo supplement this, the sociocultural theory proposed by Vygotsky (1978) highlights the social aspect of learning, in which knowledge is co-created in a conversation, in collaboration and mediated interaction with the tools and others. POGIL's small group structure reflects this tenet where a community of inquiry is formed in which students negotiate meaning, express reasoning, and scaffold one another's understanding in their zone of proximal development. When combined, these theories offer a solid pedagogical-underlying justification why POGIL is likely to improve the cognitive and affective outcomes: such as confidence, enjoyment, and spirit of collaboration.\u003c/p\u003e \u003cp\u003eTechnology integration in education cannot be executed without technical aptitude, it needs to be synergistic, to combine technology, pedagogy and content. This intersection is conceptualized in the TPACK framework (Mishra and Koehler, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) in the form of Technological Pedagogical Content Knowledge: that specialty knowledge that teachers must have in order to meaningfully incorporate technology into teaching the subject matter.\u003c/p\u003e \u003cp\u003eHere, GeoGebra is known as the technological knowledge (TK), whereas POGIL is known as the pedagogical knowledge (PK) of the content knowledge (CK) of geometry. TS-POGIL integration is a feasible implementation of TPACK, in which the dynamic visualization features of GeoGebra could be used to enhance the inquiry cycle of POGIL allowing students to interactively manipulate geometric objects, make real time hypothesis tests, and visually observe relationships. This combination lowers the level of abstraction, facilitates spatial reasoning and renders geometry more interactive and approachable thus encouraging engagement and clarity of conceptualization.\u003c/p\u003e \u003cp\u003eKilpatrick et al. (2001) define mathematical proficiency as a combination of five interconnected strands, that is, conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. The latter (productive disposition) refers to a habitual inclination of the student to consider mathematics as sensible, useful and worthwhile and trusting in his ability and self-perseverance in solving problems. Productive disposition is an affective motivation and an educational product that is vital in order to achieve the long-term success and sustain motivation in mathematics.\u003c/p\u003e \u003cp\u003eThere are three sub-constructs which are operationalized in this study in accordance to Kilpatrick model, productive disposition:\u003c/p\u003e\u003cp\u003e\u003cspan\u003e1. Like learning mathematics: interpretation of liking to study the subject.\u003cbr\u003e\u003c/span\u003e\u003cspan\u003e2. Confidence in mathematics: believing in individual mathematical ability.\u003cbr\u003e\u003c/span\u003e\u003cspan\u003e3. Valuing mathematics: perception of its relevance and applicability in real-life.\u003cbr\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eThe use of these dimensions is measured with the help of the Productive Disposition Questionnaire (PDQ), which is the main tool that will be used to measure the effectiveness of the intervention.\u003c/p\u003e\n\u003ch3\u003eIntegrated Conceptual Framework:\u003c/h3\u003e\n\u003cp\u003eIn order to integrate these theoretical lenses and diagrammatically present the hypothetical correlation between the constructs of the study, the researcher suggests the following composite conceptual model (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs it is presented, the GGS-POGIL intervention has a theoretical base in constructivist, sociocultural and TPACK principles. It fulfills the cognitive requirements of geometry and especially spatial reasoning based on the pedagogy-technology synergy to promote the process of mediating learning in active exploration, peer collaboration, and dynamic visualization. Such processes, in their turn, have been conjectured to have a positive impact on productive disposition of students, which is quantified in its three affective dimensions. The framework therefore presents a logical sequence between theory-based intervention into improved affective results, which exists as a clear foundation of empirical research and teaching methodology.\u003c/p\u003e \u003cp\u003e \u003cb\u003eCognitive Demands of Geometry Learning\u003c/b\u003e:\u003c/p\u003e \u003cp\u003eThe spatial reasoning is also closely connected with the understanding of geometrical ideas as a cognitive ability when a person can visualize and change objects (Khalil et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This ability plays a great role in comprehending the geometry associations as it supports in the study of relationships and transformations between shapes. The enhanced understanding is achieved through visualization through which the learners are able to interact effectively with the geometric figures and properties and, therefore, develop an effective conceptualization of concepts like congruence and symmetry. However, the conventional teaching strategies negatively affect the development of the spatial reasoning skill, as the strategies emphasize memorization more than the actual engagement and thus lead to the superficial knowledge and the inability to relate concepts to real-world contexts (Bwalya, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Negara et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eLearning theories of cognitive development, in particular, the stages of Piaget, acknowledge the shift of concrete to abstract thinking in geometry learning (Rohman et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Piaget assumes that learners progress through manipulation of physical objects to abstract thoughts of geometric ideas and learners are taught through experiential learning. Constructivist theories underline the importance of experiential learning, and they encourage teachers to create the conditions that would help students to experience the actual interaction with geometric concepts (Hutajulu et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Spatial thinking may be promoted and intellectual progress may be encouraged in the geometry field through facilitating group work and problem-solving activities.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eProductive Disposition as a Critical Factor:\u003c/h2\u003e \u003cp\u003eKilpatrick et al. (2001) identified five strands of mathematical proficiency including conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. Among these strands, productive disposition is core in encouraging students to learn geometry since, positive disposition prompts curiosity and makes them more motivated thus developing resilience in approaching challenging problems. Conversely, a negative productive attitude would deter engagement and achievements in geometry since learners will doubt their talents or the subject can be irrelevant (Hutajulu et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Rohendi and Dulpaka, 2013).\u003c/p\u003e \u003cp\u003eInnovative learning methods and tools are required to facilitate the development of the conceptual learning and desirable disposition. The use of technology, e.g., GeoGebra, enhances the knowledge of geometry through interactive exploration and dynamic visualization (Bwalya, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Khalil et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Niam and Asikin, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). GeoGebra enhances the conceptualization of the students by allowing them to operate geometrical objects and view their characteristics in real time. In addition, processes like Process-Oriented Guided Inquiry Learning (POGIL) ensure that the learners engage actively and cooperate with one another to improve their engagement levels. Overall, these theoretical foundations imply the need to develop the skills of spatial sense and foster the positive and constructive attitude, which would place students in a situation to feel confident and skilled in geometry.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eChallenges in Geometry Instruction:\u003c/h3\u003e\n\u003cp\u003eThe subject of geometry is faced with the severe issues due to the abstract form of study that in most cases leads to a lack of interest and motivation among the students. Numerous students do not understand how the concepts of geometry can be applied to their lives, so there is a lack of interest in this subject (Bwalya, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Khalil et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Traditional approaches to teaching and learning only exacerbate this issue, where memorization and procedural practice is taught at the expense of developing a deeper conceptual understanding. These approaches do not generally provide students with an opportunity to explore the concept of geometry in meaningful sense, and in this regard, they do not enable students to appreciate the role geometry plays in real life (Rohman et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This leads to the development by many students of negative attitudes about geometry as a subject that is theoretical and has no connection with real life situations hence lowering their interest to learn further.\u003c/p\u003e \u003cp\u003eThe teaching of geometry also becomes complicated in the Ethiopian educational system by a number of structural and resource-related problems. Melese (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) notes that the lack of appropriate teaching materials and resources reduces the level of teaching and learning. Besides, excessive classrooms reduce the ability of teachers to provide students with individual attention and this has a negative impact on the engagement of students in the study and mastery of geometric concepts. The use of the conventional pedagogical practices that focus on lecture-based instruction inhibits the delivery of interactive and experiential learning. Such experiences play an essential role in the growth of spatial thinking and a profound conceptual vision of geometry (Hutajulu et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In this regard, specific interventions to address the issue of cognitive challenges and affective challenges are required to develop a productive learning environment that encourages engagement and motivation in learning geometry.\u003c/p\u003e \u003cp\u003eTraditional teacher-centered approaches in teaching geometry involve more of procedural learning and memorization, thus limiting the knowledge of the students on the concepts of geometry. In this scenario, the teachers tend to lean towards the direct teaching approach where the students are forced to learn the procedures and formulas without really analyzing the concepts behind those. Such an educational approach prevents the cultivation of critical thinking skills and reduces student engagement because students are engaged in mechanical tasks that do not seem to have any real-life interaction (Rohman et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Research indicates that students who have been taught a curriculum that places more focus on memorization stand a chance of developing negative attitudes towards geometry and seeing it as either irrelevant or highly demanding (Hutajulu et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This is because these negative attitudes can lead to a vicious cycle of poor performance and lack of self-efficacy whereby not passing the concepts of geometry on the first attempt will further erode self-confidence and interest and this will prove that pedagogical changes are required to make geometry more positively perceived.\u003c/p\u003e\n\u003ch3\u003eInnovative Approaches: POGIL and GGS\u003c/h3\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eGeoGebra Software (GGS):\u003c/h2\u003e \u003cp\u003eGeoGebra has become one of the most significant instruments of geometry teaching today, with the visualization being dynamic and incorporating several branches of mathematics including algebra, geometry, and calculus. The interactive computer software will help students to manipulate geometric objects and explore mathematical concepts in an interactive and visual manner. It is shown by research that GeoGebra is useful in enhancing conceptual knowledge and interest of students in geometry. To highlight, it was observed in studies that the learners who used GeoGebra achieved significant improvement in mastering the concepts of geometry compared to learners who completed a more traditional learning experience (Bwalya, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Khalil et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Melese, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Moreover, the program also cultivates the culture of learning that is characterized by inquiry and exploration and results in the active engagement of students with mathematical concepts due to their being active receivers of information. Through GeoGebra, the students develop a more favorable attitude towards mathematics i.e. their increased ownership of the learning experience and increased their motivation to learn more about the topic. It is also stated that the utilization of GeoGebra enhanced the feelings of visualization, motivation, engagement, and conceptual understanding in the Ethiopian setting (Abate et al., 2023; Dereje et al., 2023; Gurmu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eProcess Oriented Guided Inquiry Learning (POGIL):\u003c/h2\u003e \u003cp\u003eAnother new strategy of teaching geometry focusing on active learning and collaboration between students is the POGIL approach. To facilitate the learning of mathematical concepts using the guided inquiry approach, POGIL encourages a highly organized and yet pliable classroom environment where students can discover mathematical concepts with and through groups to become owners of their learning processes. The teaching model has demonstrated positive outcomes in the development of the problem-solving abilities, conceptual knowledge, and general interest of geometry in students. The studies have shown that students who were taught POGIL based instruction reported higher levels of engagement and a superior level of understanding geometric concepts than students who were taught using standard lecture-based instruction (Andriani et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Not only does POGIL enable mathematical success of the learners through its promotion of collaborative methodology and elicitation of higher order thinking, but also learners being armed with useful tools in which to surmount mathematics challenges with preparedness and enthusiasm, ultimately, can be said to have achieved success as far as improving attitude towards learning of geometry is concerned. The use of GeoGebra and POGIL in teaching geometry shows a shift to more interactive and student-centered classes, which are required to help establish meaningful engagement and enhance mathematical competencies.\u003c/p\u003e \u003c/div\u003e "},{"header":"Methodology","content":"\u003cdiv id=\"Sec13\"\u003e\n \u003ch2\u003eResearch Design:\u003c/h2\u003e\n \u003cp\u003eThis study used, a quasi-experimental design method to examine the efficacy of incorporating GGS and POGIL on ensuring productive disposition towards studying geometry on students. The research design was based on a pretest- posttest, non-equivalent groups design including one group that was instructed in the traditional way (Comparison group), another one was in POGIL-only way (POGIL group), and the third group was taught in the integrated manner using the GGS and POGIL (GGS-POGIL group) (See Table 1).\u003c/p\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 1\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003ePretest-posttest non-equivalent group quasi-experimental design\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eGroup\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePretest\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTreatment\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePosttest\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGGS-POGIL group\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eO\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePOGIL group\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eO\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eComparison group\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eO\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eO\u003csub\u003e1\u003c/sub\u003e: Pretest for all groups\u003c/p\u003e\n \u003cp\u003eO\u003csub\u003e2\u003c/sub\u003e: Posttest for all groups\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eT\u003csub\u003e1\u003c/sub\u003e: Teaching with GGS integrated POGIL\u003c/p\u003e\n \u003cp\u003eT\u003csub\u003e2\u003c/sub\u003e: Teaching with POGIL\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003ch2\u003eResearch Design:\u003c/h2\u003e\n\u003cp\u003eThis study used, a quasi-experimental design method to examine the efficacy of incorporating GGS and POGIL on ensuring productive disposition towards studying geometry on students. The research design was based on a pretest- posttest, non-equivalent groups design including one group that was instructed in the traditional way (Comparison group), another one was in POGIL-only way (POGIL group), and the third group was taught in the integrated manner using the GGS and POGIL (GGS-POGIL group) (See Table 1).\u003c/p\u003e\n\u003ch2\u003eParticipants and Sampling:\u003c/h2\u003e\n\u003cp\u003eThe sample of this research was the Grade 10 students in the secondary schools in the capital city of Ethiopia, Addis Ababa. Purposive sampling method was employed in order to select three schools that were willing to take part in the research and had the proper infrastructure in terms of technology that would facilitate the use of GGS. They were three conditions of instruction namely, Traditional instruction, POGIL-only instruction, and integrated GGS and POGIL instruction. In the three schools three intact classes were selected on a random basis (one per school). Experimental groups were divided into two classes, whereas, the comparison group was issued. The overall group of the sample consisted of 149 students of whom 50 students would be in the GGS-POGIL group, 49 students in the POGIL group, and 50 students in the Comparison Group.\u003c/p\u003e\n\u003ch2\u003eInstrumentation:\u003c/h2\u003e\n\u003cp\u003eThe method of gathering the data was the Productive Disposition Questionnaire (PDQ) that was modified based on Trends in International Mathematics and Science Study TIMSS (2015). The questionnaire was constructed to reflect the various aspects of the attitude of the students to mathematics as the liking of the mathematics learning topic, confidence, and the usefulness of mathematics to the students in their lives. Every question in the questionnaire was graded out of five through a Likert scale questionnaire and this enabled the research participants to elaborate their answers. The reliability and validity of the PDQ to the Ethiopian context were established by carrying out an expert review on the face and content validity and a pilot study on a sample of 40 Grade 11 students who were randomly selected among schools that were not part of the intervention. Reliability was considered as the internal consistency of productive disposition questionnaire and its dimension and the alpha of Cronbach was 0.82, and was greater than the value of 0.7. This was agreeable and the questionnaire was valid to gather additional information.\u003c/p\u003e\n\u003ch2\u003e\u003cstrong\u003eProcedures\u003c/strong\u003e:\u003c/h2\u003e\n\u003cp\u003eThe first step into the process of data collection involved the Professional Development Course (PDC) training of chosen teachers, therefore making them have the necessary experience and skills needed to successfully implement instructional interventions. An assortment of detailed teaching resources consisting of teacher manuals, lesson plans, student activity sheets and GeoGebra guides were created and distributed to intervention teachers creating the backbone of delivery of instruction and application of GeoGebra lab activities. After that there was an initial assessment performed using the Productive Disposition Questionnaire (PDQ) on all three groups to ascertain a preceding assessment of their productive disposition in learning geometry. This served as a pre-test.\u003c/p\u003e\n\u003cp\u003eThe intervention lasted eight weeks in which the school teachers administered instructional interventions based on the teaching materials provided. The interventions included a mixture of integrated GGS/ POGIL teaching of POGIL Group, pure POGIL teaching of POGIL Group, and standard instruction of Comparison Group. The students in the POGIL group intervention course experienced inquiry-based learning in the small group discussion, practical exploration of geometric concepts and teacher facilitated guided inquiry within a small group. In the same case the POGIL group intervention issue-based class (GGS-POGIL) students were provided with POGIL only instruction during real time class and a combination POGIL approach with the help of GGS to visualize and explore geometric concepts in ICT laboratories. Comparing students, on the contrary, were taught geometry using standard teaching methods without focused direction on POGIL and GGS.\u003c/p\u003e\n\u003cp\u003eThe three groups were administered a posttest involving the Productive Disposition Questionnaire after the intervention so that to identify any change in productive disposition towards learning geometry. To compare the differences between and within the groups, inferential statistical tests, parametric (e.g., ANOVA and ANCOVA) and non-parametric (e.g., Kruskal-Wallis) were performed to analyze the data. In order to take a closer look at these differences, a few comparisons with post hoc pair wise analysis were done, which provided a richer analysis of specific group differences and helped in overall interpretation of the research findings.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003ePretest Result:\u003c/h2\u003e \u003cp\u003eThe pretest was aimed at testing the difference in bases of productive disposition of students on education in geometry especially their liking of mathematics learning, their confidence in mathematics ability and perceived value of mathematics in GGS-POGIL, POGIL and Comparison groups. In deciding the appropriate statistical tests, significant assumptions: i. e., independent observations, normal distribution, and homogeneity of variance were checked. Independent observations were determined considering the fact that different groups were used to collect the data. Instead, the Kolmogorov-Smirnov test and Shapiro-Wilk test assessed the normality assumption and it was found that Overall Productive Disposition (p\u0026thinsp;=\u0026thinsp;0.483) and Students Confident in Mathematics abilities (p\u0026thinsp;=\u0026thinsp;0.051) passed the test whereas Students Like Learning Mathematics (p\u0026thinsp;=\u0026thinsp;0.023) and Students Value Mathematics (p\u0026thinsp;=\u0026thinsp;0.040) failed the test. The homogeneity of variance test, used to test the homogenous variances in the overall productive disposition (p\u0026thinsp;=\u0026thinsp;0.074), as well as those in Students Confident in Mathematics abilities (p\u0026thinsp;=\u0026thinsp;0.725), but not those in Students Like Learning Mathematics (p\u0026thinsp;=\u0026thinsp;0.041) and Students Value Mathematics (p\u0026thinsp;=\u0026thinsp;0.003), showed homogenous variances respectively. Based on the results, the parametric tests (e.g., ANOVA) were applied to those variables that fit the assumptions and the non -parametric tests (e.g., Kruskal- Wallis) applied to the variables that did not fit the assumption.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003eStudents Liking for Learning Geometry Pretest:\u003c/h2\u003e \u003cp\u003eTo compare the differences among the three groups based on the liking of mathematics among students, Krushal-Wallis test was applied. As demonstrated in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the test found out that the responses of students in three groups had a statistically significant difference (H\u0026thinsp;=\u0026thinsp;9.623, df\u0026thinsp;=\u0026thinsp;2, p =\u0026thinsp;.008). In other words, before the intervention the groups had an interest of learning mathematics to varying levels. The rank mean demonstrates that GGS-POGIL group had the highest rank mean (85.98), next was the Comparison group (78.77), and the lowest rank mean was found in the POGIL one (59.95). This indicates that the learners in the GGS-POGIL and Comparison groups apportioned more than their counterparts in POGIL group to like mathematics learning.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eIndependent Samples Kruskal-Wallis Test summary of groups on Students Like Learning Mathematics and Value Mathematics pretest in learning geometry.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eRanks\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eTest Statistics\u003csup\u003ea,b\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMean Rank\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eKruskal-Wallis H\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAsymp. Sig.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eStudents like learning mathematics pretest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e85.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e9.623\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e.008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e59.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e78.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e149\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eStudents value mathematics pretest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e59.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e10.213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e.006\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e81.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e84.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e149\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea. Kruskal Wallis Test\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cem\u003eb. Grouping Variable: Group\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThese differences were made more clear by a pair wise comparison of Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e by Dunn. The finding showed that the POGIL group had significant difference with GGS- POGIL group (Test Statistic\u0026thinsp;=\u0026thinsp;26.031, p =\u0026thinsp;.003, Adj. Sig. =.008). This means that students in the GGS-POGIL group enjoyed learning mathematics as opposed to those in POGIL group. Nonetheless, the result of the POGIL group, compared with Comparison group (Test Statistic = -18.821, p =\u0026thinsp;.030, Adj. Sig. =.089), did not turn out to be statistically significant when multiple tests were corrected. Further, no meaningful differences were drawn between the GGS-POGIL and Comparison groups (p =\u0026thinsp;.402), and thus, suggesting that the three groups were similar in the level of liking mathematics before the intervention though, the three groups were not at the same level, and this means that using pretest as covariate was necessary.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDuns test Pairwise Comparisons of Groups on Students Like Learning Mathematics and Value Mathematics Pretest.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSample 1-Sample 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTest Statistic\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStd. Error\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eStd. Test Statistic\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSig.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAdj. Sig.\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eLike Learning Mathematics Pretest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group-Comparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-18.821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.655\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.089\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group-GGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e26.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.655\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eComparison group-GGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.611\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.837\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eValue Mathematics Pretest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGGS-POGIL group \u0026ndash; POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-22.219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.663\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.565\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.031\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGGS-POGIL group \u0026ndash; Comparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-25.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.619\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.930\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.010\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group \u0026ndash; Comparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.663\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.726\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003eEach row tests the null hypothesis that the Sample 1 and Sample 2 distributions are the same.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cem\u003eAsymptotic significances (2-sided tests) are displayed. The significance level is .05.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea. Significance values have been adjusted by the Bonferroni correction for multiple tests.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\u003cp\u003eStudents Value Math Pretest:\u003c/p\u003e \u003cp\u003eThe interest of students towards mathematics also became a consideration of the study. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e used Kruskal-Wallis test to determine that the groups have a significant difference between them (H\u0026thinsp;=\u0026thinsp;10.213, df\u0026thinsp;=\u0026thinsp;2, p =\u0026thinsp;.006). Comparisons and POGIL batches had greater average rank (81.44 and 84.47, respectively) than the GGS-POGIL (59.22). This finding indicates that pre-intervention students in POGIL and Comparison groups attached more importance to mathematics than the students in GGS-POGIL group.\u003c/p\u003e \u003cp\u003eThis was confirmed by Dunn in his couple of comparisons in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The difference between the GGS-POGIL group and POGIL group (Test Statistic = -22.219, p =\u0026thinsp;.010, Adj. Sig. = .031) and with the Comparison group (Test Statistic = -25.250, p =\u0026thinsp;.003, Adj. Sig. =.010) was significantly different. This demonstrates that before the intervention, Comparison and POGIL students ranked mathematics higher in comparison to GGS-POGIL students. There was no significant difference in the Comparison and POGIL groups (p =\u0026thinsp;.726) so similar was the perception of the value of mathematics in both groups prior to the starting of an intervention study.\u003c/p\u003e \u003cp\u003e \u003cb\u003ePre-Test Measure of Mathematical Confidence and Overall Productive Disposition\u003c/b\u003e:\u003c/p\u003e \u003cp\u003eOne-way ANOVA was employed in order to determine the confidence of students in mathematics, in addition to overall positive attitude towards running geometry as a learning task. The outcomes, as cited in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, revealed that the groups were not significantly differentiated on the premise of the confidence of the students in mathematics skills (F\u0026thinsp;=\u0026thinsp;2.073, p =\u0026thinsp;.129) and their general amicable attitude (F =\u0026thinsp;.688, p =\u0026thinsp;.504). This means that initially the groups were identical regarding the two variables in terms of which no group had a particular advantage or a disadvantage regarding the confidence and the general productive disposition.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of Groups of One-Way Analysis of Variance (ANOVA) of Confidence of Students in Mathematics and the General Productive Disposition in Geometry Learning.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eStudents confident in mathematics pretest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBetween Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.372\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.686\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.129\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWithin Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e48.297\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.331\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e49.669\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eOverall Productive Disposition pretest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBetween Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.688\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.504\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWithin Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30.695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30.984\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e*\u003cem\u003eThe mean difference is significant at the 0.05 level.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe results of the pretest showed a problem of significant differences in the groups in terms of liking mathematics and the importance of mathematics with GGS-POGIL group having fewer positive dispositions in terms of valuing mathematics in comparison to POGIL and Comparison groups. Nevertheless, the results also showed no great differences regarding the confidence of the students to mathematics or overall productive attitude which shows that there was a comparability between the groups before the intervention. These results highlight the significance of the upcoming intervention in possibly changing the attitudes of the students toward learning mathematics in aspects such as increasing their liking mathematics learning and how they engage mathematics learning.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003ePosttest Results\u003c/h2\u003e \u003cdiv id=\"Sec21\" class=\"Section3\"\u003e \u003ch2\u003e\u003cb\u003eEvaluation of the Assumptions\u003c/b\u003e:\u003c/h2\u003e \u003cp\u003eThe ultimate objective of the posttest analysis was to test the effect of GGS-POGIL, POGIL and other traditional methods on the productive disposition of learning geometry using the secondary school students due to their liking, confidence, and valuing of mathematics. Statistical tests to determine the assumptions of normality and homogeneous variance and independence of observations were completed before performing the statistical tests. Observational independence was ensured because there were different group assignments. Kolmogorov-Smirnoff test and Shapiro-Wilk test demonstrated that the assumptions about the normality were breached by such variables as Students like learning mathematics and Students value mathematics (p \u0026lt;\u0026thinsp;.05). Nevertheless, \"Students confident in mathematics\" and \"Overall Productive Disposition\" were almost normal (p \u0026gt;\u0026thinsp;.05). The test of the homogeneity of variance used by Levene showed that the variances of all variables were similar within each group, and the values of the p-tests (p \u0026gt;. 05) were not significant. According to these results, within-group pretest- posttest tests were performed by means of the Wilcoxon Signed rank test when variables were not normally distributed whereas the Kruskal-Wallis test was applied to evaluate the difference between groups. In the case of variables that fit the parametric requirements, there was one-way ANOVA to compare total productive disposition in terms of instructional methods.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003eAnalysis of Posttest Data on Students' Productive Disposition in Learning Geometry\u003c/h2\u003e \u003cp\u003eThis study factored into the research the question of whether there existed any relationship between three instruction models and productive disposition in learning geometry: GeoGebra-based Process-Oriented Guided Inquiry Learning (GGS-POGIL), POGIL-only, and traditional instruction. The productive attitude included the liking to study math, mathematical confidence, and the value of mathematics. This was measured by the use of tests that were taken before and after the intervention. The posttest results were compared to the results of the pretest and showed the effectiveness of both of the instruction styles.\u003c/p\u003e \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e \u003ch2\u003ePosttest Results for Students' Liking for Learning Mathematics:\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e Wilcoxon Signed-Rank Test demonstrated a statistically significant change in the extent to which students liked learning mathematics at the end of intervention. There was also a test value of z- -4.540 and an asymptotic significant (p-value) of.000, indicating that most probably the positive change was not randomly done by the chance. Among 144 students that were tested, 96 students said that they like mathematics less, whereas 48 students said that they like mathematics more. This demonstrates that the liking of students to the subject was highly influenced by the programs. This finding is significantly unlike in the pretest which showed no significant likes of students towards mathematics (Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Consequently, as it can be seen, GGS-POGIL turned out to be effective in creating a considerable effect of student enjoyment in learning geometry.\u003c/p\u003e \u003cp\u003eComparing the groups after hoc with the use of Tukey HSD (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), it is possible to note that GGS-POGIL group received much higher scores than POGIL group and the comparison group on the enjoyment of learning mathematics. The average differences showed a clear difference: the GGS-POGIL ranged at 22.227 below the POGIL group (p = .021) and 24.255 below the comparison group on average (p =\u0026thinsp;.010). The POGIL group was not significantly different than the comparison group (mean difference\u0026thinsp;=\u0026thinsp;2.027, p =\u0026thinsp;.967). This outcome demonstrates the additional advantages of the work with GeoGebra with the POGIL technique. The posttest results have shown a better engagement and enjoyment of mathematics compared to the pretest results with both groups having an equal liking on mathematics (Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBesides that, the Non-Parametric ANCOVA (Quade\u0026rsquo;s Test), presented in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e indicated the significant effect of the GGS-POGIL technique on the enjoyment of learning mathematics in students with F-value of 5.364 and p-value of.006. The model proposed that posttest scores variance (6.8 percent) was explained by the fact that technology and guided inquiry were used. This implies that the application of such methodologies had a positive influence on the liking to learn mathematics amongst the students which was not realized using the pretest data (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The outcome demonstrates that GeoGebra, POGIL can be used to make students more enthusiastic and active in mathematics.\u003c/p\u003e \u003cp\u003eAlso indicated by the posttest result, GGS-POGIL strategy improved the affinities of the students in learning math as opposed to POGIL or traditional teaching. This can be further explained by the comparison of the pretest and posttest results to understand the effectiveness of using GeoGebra in a learning setting that stimulates guided inquiry as this improves the learning process by making learning fun and engaging. According to this study, there should be a need to develop new methods of teaching that allow students to connect mathematics to the positive spirit that they have, and through which their learning experience may be enhanced.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eWilcoxon Signed-Rank Test of Pretest and Posttest of Component of productive disposition of students in learning geometry.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eRanks\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eTest Statistics\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRank Types\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMean Rank\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSum of Ranks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ez\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAsymp. Sig. (2-tailed)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eStudents\u0026rsquo; Like Learning Mathematics pretest - Students\u0026rsquo; Like Learning Mathematics posttest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNegative Ranks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e78.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7494.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e-4.540\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePositive Ranks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e61.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2945.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eStudents\u0026rsquo; Confident in Mathematics Pretest - Students\u0026rsquo; Confident in Mathematics Posttest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNegative Ranks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e77.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8884.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e-7.534\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePositive Ranks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1412.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eStudents\u0026rsquo; Value Mathematics Pretest \u0026ndash; Students\u0026rsquo; Value Mathematics Posttest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNegative Ranks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e79.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7350.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e-3.519\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePositive Ranks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e65.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3675.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNotes\u003c/b\u003e: \u003cem\u003ea. Wilcoxon Signed-Rank Test.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cem\u003eb. Based on negative ranks.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eRank Descriptions\u003c/b\u003e:\u003c/p\u003e \u003cp\u003e\u0026bull; \u003cem\u003eNegative Ranks: Indicates Posttest\u0026thinsp;\u0026lt;\u0026thinsp;Pretest\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; \u003cem\u003ePositive Ranks: Indicates Posttest\u0026thinsp;\u0026gt;\u0026thinsp;Pretest\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; \u003cem\u003eTies: Indicates Posttest\u0026thinsp;=\u0026thinsp;Pretest\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMultiple Comparisons Post-hoc Tests (Tukey HSD) on Students' Like Learning Mathematics, Value Mathematics, and Overall Productive Disposition Posttest\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(I) Group\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(J) Group\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMean Difference (I-J)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSig.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eStudents\u0026rsquo; Like Leaning Mathematics Posttest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e22.2271623\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.021\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e24.2545234\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.010\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.0273611\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.967\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eStudents\u0026rsquo; Value Mathematics Posttest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.8018432\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.976\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e12.0755049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.340\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13.8773481\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.245\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eOverall Productive Disposition\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.19454\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.304\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.44963\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.25509\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.132\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003e*. \u003cem\u003eThe mean difference is significant at the 0.05 level.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNon-Parametric ANCOVA (Quade's Test) on Students\u0026rsquo; Like Learning Mathematics and Value Mathematics Posttest\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSource\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eType III Sum of Squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMean Square\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSig.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"6\" rowspan=\"7\"\u003e \u003cp\u003eStudents\u0026rsquo; Like Leaning Mathematics Posttest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCorrected Model\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18061.673\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9030.836\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.006\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.989\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18061.673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9030.836\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.006\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eError\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e245812.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1683.644\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e263873.676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e149\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCorrected Total\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e263873.676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e \u003cp\u003ea. R Squared = .068 (Adjusted R Squared = .056)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"6\" rowspan=\"7\"\u003e \u003cp\u003eStudents\u0026rsquo; Value Mathematics Posttest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCorrected Model\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5666.589\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2833.294\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.539\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.218\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.183\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.183\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.992\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5666.589\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2833.294\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.539\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.218\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eError\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e268717.486\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1840.531\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e274384.075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e149\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCorrected Total\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e274384.075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e \u003cp\u003ea. R Squared = .021 (Adjusted R Squared = .007)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003ePosttest Results for Students' Valuing Mathematics:\u003c/h2\u003e \u003cp\u003eThe posttest outcome of perceived value of mathematics in students as shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e identified a statistically significant change at the pretest level of value of mathematics among students (z = -3.519, p\u0026thinsp;=\u0026thinsp;less than 0.001). On the contrary, 92 students said that their valuation of mathematics declined whereas only 56 students said that mathematics increased in their valuation. This finding is the opposite to the comparatively positive pretest dispositions that had been noted before (Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), indicating that the interventions were not equally productive in terms of their influence on the perception of mathematics relevance in students.\u003c/p\u003e \u003cp\u003eThe findings can also be explained through post-hoc comparisons (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The GGS-POGIL group had statistically significant higher means compared to the comparison group (mean difference\u0026thinsp;=\u0026thinsp;12.076), albeit not statistically significant to support the idea (p =\u0026thinsp;.340). Likewise, there was no significant difference between the GGS-POGIL and POGIL-only ones ( *p* =.976). This means that there was no significant difference in the way GeoGebra and POGIL were used because of the valuation of mathematics developed by students compared with other modes of instruction.\u003c/p\u003e \u003cp\u003eThe non-parametric ANCOVA (Quades Test, Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) indicates the same findings and indicated that the difference in the valuing of mathematics according to instructional method was non-significant (F\u0026thinsp;=\u0026thinsp;1.539, p =\u0026thinsp;.218, R2 =\u0026thinsp;.021). The small explain variance highlights the poor influences of the interventions on this affective dimension.\u003c/p\u003e \u003cp\u003e \u003cb\u003ePosttest Results for Students' Confidence in Mathematics\u003c/b\u003e:\u003c/p\u003e \u003cp\u003eThe confidence of students to mathematics was analyzed as well where it showed general change in direction after the instructional interventions, but there is significant variability in the direction. A statistically significant pretest-posttest difference was observed across all participants (z = -7.534 p =\u0026thinsp;.001) according to Wilcoxon Signed-Rank Test (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Nonetheless, with increased scrutiny of rank distributions, 115 students indicated a drop in confidence and only 28 indicated an improvement, potentially indicating that the interventions did not equally drive self-efficacy and could have brought about cognitive/ affective difficulties on a group of learners.\u003c/p\u003e \u003cp\u003eComparisons between groups also helped to describe the effects of the instructional methods. The Kruskal-Wallis test revealed statistically significant differences in the posttest ranks in confidence between the three groups (H\u0026thinsp;=\u0026thinsp;24.091, *p\u0026thinsp;=\u0026thinsp;0.001) as shown in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. The means of rank were the highest in the GGS-POGIL group (89.85), then POGIL-only group (84.53), and the comparison group (50.81). This ordinal trend shows that both inquiry-based models, in particular, the technology-enhanced GGS- POGIL model, are more helpful to promote the mathematical confidence compared to the traditional instruction.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eIndependent-Samples Kruskal-Wallis Test Summary on Students\u0026rsquo; Confidence in Mathematics Posttest Across Group\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean Rank\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKruskal-Wallis H\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAsymp. Sig.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e89.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e24.091\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e84.53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e149\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003cem\u003eNote. The Kruskal-Wallis H test indicates significant differences in confidence ranks across groups.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThese results indicate that even though GGS-POGIL was most effective in developing the comfort as compared to other groups, the high rate of students who developed with reduced confidence needs more research. Possible causes can be the combination of first overconfidence, the necessity of acquiring experience with inquiry-based and technology-mediated learning, and the different readiness of students. However, the relative effectiveness of the GGS-POGIL group highlights the possibility of combining dynamic visualization tools and guided inquiry to create mathematical confidence self-regarding learning in geometry.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDunn\u0026rsquo;s Test Pairwise Comparisons on Students\u0026rsquo; Confidence in Mathematics Posttest\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample 1-Sample 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest Statistic\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStd. Error\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStd. Test Statistic\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSig.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAdj. Sig.\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComparison group-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e33.721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.662\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.893\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComparison group-GGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e39.040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.618\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.530\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePOGIL group-GGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.319\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.662\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.614\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.539\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003eEach row tests the null hypothesis that the Sample 1 and Sample 2 distributions are the same.\u003c/em\u003e\u003c/p\u003e \u003cp\u003e\u003cem\u003eAsymptotic significances (2-sided tests) are displayed. The significance level is .05.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea. Significance values have been adjusted by the Bonferroni correction for multiple tests.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eMore to the point, the pairwise comparisons provided by Dunn (Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e) were more longitudinal and allowed concluding the fact that both the POGIL and GGS-POGIL groups performed significantly better than the comparison one regarding the posttest confidence ranks (both with a p-value of less than 0.001). Nevertheless, it was not found that the two experimental groups differed statistically significantly (*** p =\u0026thinsp;.539, indicated that whereas integration of GeoGebra gave an numerical benefit of mean rank, its contribution of confidence over POGIL as an intervention was not significant in this sample).\u003c/p\u003e \u003cp\u003eIt is through these findings that the power of inquiry-based methods with or without technology should be highlighted as compared to conventional teaching in bringing mathematical confidence. However, the observation that most students in all groups had decreased self-confidence (will be shown by the Wilcoxon test) is where a vital sensitivity is needed, as the interventions were relatively effective, although not the ones that affected all learners. This is an indication that inquiry based and technology integrated teaching methods require differentiated instruction and continuous pedagogical reflection, in order to make sure that instructional methods are sensitive to student readiness levels and affective needs.\u003c/p\u003e \u003cdiv id=\"Sec25\" class=\"Section3\"\u003e \u003ch2\u003ePosttest Scores on Students' Productive Disposition:\u003c/h2\u003e \u003cp\u003eFindings of paired samples t-test in Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e reveal that every group had at least some improvement in productive disposition when there was comparison between pretest and posttest scores. GGS-POGIL group had the highest mean gained of.69 (SD =\u0026thinsp;.71, t(49)\u0026thinsp;=\u0026thinsp;6.861, p =\u0026thinsp;.000), and the POGIL group had the mean gained of.42 (SD =\u0026thinsp;.74, t(48)\u0026thinsp;=\u0026thinsp;3.933, p =\u0026thinsp;.000). Relative to the comparison group, the change in the latter was not significant, at only.15 (SD =\u0026thinsp;.76, t(49)\u0026thinsp;=\u0026thinsp;1.375, p =\u0026thinsp;.175) on average. These findings indicate that the conventional approaches failed to make much positive impact on productive dispositions of students. Most saliently, the overall productive disposition in its component\u0026rsquo;s terms liking learning mathematics, valuing mathematics, and mathematics confidence - the GGS-POGIL group experienced significant increase in terms of liking learning mathematics only (mean difference of 22.23, p =\u0026thinsp;.021) and not in the context of improving the valuing mathematics to a comparable extent (-1.80, p =\u0026thinsp;.976) and mathematic confidence. This would mean that despite the fact that the interventions increased value of learning mathematics, the intervention made no overall approach to the overall perception of value of the subject and the confidence of students with mathematics abilities.\u003c/p\u003e \u003cp\u003eThe results of the paired samples test, which were provided after the analysis of one way ANOVA, the result of which is presented in Table\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e11\u003c/span\u003e, further confirms the effectiveness of the instruction methods applied within the context of this study. The ANOVA test had an impressive F-value of 5.932 ( p =\u0026thinsp;.003) which means that there is statistical significance of difference among the groups. Such findings indicate that the different pedagogical strategies employed played a significant role towards the overall productive disposition of the students with significant differences being expressed among the different groups. These outcomes are in line with the assumption that GGS-POGIL and POGIL methods significantly improved the general productive disposition of the students compared with that of the traditional instruction group.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePaired Samples t-Test on the Pretest and Posttest of Students\u0026rsquo; Productive Disposition in Learning Geometry\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003ePaired Differences\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDf\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eOverall Productive Disposition: Posttest-pretest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGGS-POGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.861\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePOGIL group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.933\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eComparison group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.175\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOne-way ANOVA Summary of Groups on Productive Disposition Posttest in Learning Geometry\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eOverall Productive Disposition\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBetween Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.084\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.932\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.003\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWithin Groups\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e62.573\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.429\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e67.657\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e*\u003cem\u003eThe mean difference is significant at the 0.05 level.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eLastly, the results of the Tukey HSD post-hoc tests reported in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e indicate the definite group effects concerning the total productive disposition. The comparison group had a significant mean difference of.44963 (p =\u0026thinsp;.002) with the GGS-POGIL group indicating that their total productive disposition had increased significantly. However, the only statistical finding is that the differences between the post-intervention GGS-POGIL and POGIL groups were not significant (mean difference of.19454, p =\u0026thinsp;.304). This can be construed to mean that though the integrated approach has a tendency of positively influencing the productive disposition of students in learning geometry, there is need to have more strategies that will be applied so as to bring about noticeable changes in all the groups. Overall, this evidence indicates the need to use new instructional strategies like GGS-POGIL and POGIL in the process of cultivating productive disposition towards learning geometry among students. Additionally, the results lead to continued development of teaching methods over the effective advancements of all items of productive disposition-viz., liking, valuation and confidence in mathematics.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab12\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEffect Sizes (Cohen's d) for Group Comparisons of Students\u0026rsquo; Productive Disposition and its Components in learning geometry\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGGS-POGIL\u003c/p\u003e \u003cp\u003evs.\u003c/p\u003e \u003cp\u003ePOGIL\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGGS-POGIL\u003c/p\u003e \u003cp\u003evs.\u003c/p\u003e \u003cp\u003eComparison\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePOGIL\u003c/p\u003e \u003cp\u003evs. Comparison\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLiking for Mathematics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfidence in Mathematics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eValue of Mathematics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProductive Disposition\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn Table\u0026nbsp;\u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003e12\u003c/span\u003e, it was found that GGS-POGIL group experienced the largest positive change in their productive disposition in geometry, particularly, confidence in mathematics (Cohen d\u0026thinsp;=\u0026thinsp;0.88) and overall productive disposition (Cohen d\u0026thinsp;=\u0026thinsp;0.68) over the conventional approach. There was also some small improvement in GGS-POGIL group in liking mathematics (Cohen d\u0026thinsp;=\u0026thinsp;0.71) and valuing mathematics (Cohen d\u0026thinsp;=\u0026thinsp;0.29). The positive impact of the POGIL group as compared to the comparison group also occurred but with less degree.\u003c/p\u003e \u003cp\u003eThese observations indicate that GeoGebra with POGIL could assist students to have higher integrated and better productive disposition in geometry education than in traditional approach. The study highlights the fact that GGS-POGIL use can render it achievable to make the students possess a more fruitful disposition in mathematics.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe findings in this research give substantial proof that, integration of the GeoGebra Software (GGS) with the Process-Oriented Guided Inquiry Learning (POGIL) is comprehensive in influencing the productive disposition of the students towards learning geometry. To be more precise, the gains in mathematics liking, mathematical confidence, and mathematics value were truly impressive by the GGS-POGIL students, which were measured again in comparison to the POGIL and comparison groups. These results support the study which shows that technology-enhanced dynamical pedagogical activities can facilitate cognitive and affective involvement in mathematics education (Hosseini et al., 2022; Rodr\u0026iacute;guez-Nieto et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAmong the main findings of this research is that GGS-POGIL group had a greater disposition of liking mathematics. The finding aligns with the available literature that indicates that interactive learning setting promotes greater engagement and pleasure in students (Baye et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Probably another factor that might have given students greater enjoyment is also the interactive and visual quality of GeoGebra, as this would enable students to manipulate geometric shapes interactively and explore mathematical relationships in a more intuitive manner (Ansong et al., 2021). Even the inquiry-based and collaborative features of POGIL could have been more engaging to the students because they provided an opportunity to engage in active learning and new conceptual insights (Andriani et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe main result of this study is that there is a significant increase in the belief of the students in their confidence of mathematical ability in the GGS-POGIL group. It appears that the use of GeoGebra has provided the students with immediate visual feedback, which, conversely, has been shown to enhance mathematical self-efficacy (Hutkmri and Zakaria, 2014). In addition, it has been found that Process Oriented Guided Inquiry Learning (POGIL) strengthens logical thinking and problem-solving, thus complementing the confidence of students in their ability to work on difficult mathematical problems (Irwanto et al., 2018). The results however indicate that the students who underwent POGIL only recorded average increases in their confidence, although, lesser than in the GGS-POGIL group, meaning that, technology use is essential in strengthening student confidence.\u003c/p\u003e \u003cp\u003eThe third aspect of productive disposition, i.e. the perceived usefulness of mathematics by the learners also recorded a significant gain among the GGS-POGIL group. The observation aligns with the previous studies that have shown that technology-based learning scenarios help pupils to value the practical relevance and applicability of mathematical concepts (Bedada and Machaba, 2022). Through GeoGebra, students were in a position to relate abstract geometric ideas with real- world visual models, therefore enhancing their appreciation of mathematics as a necessary problem-solving device. The study also reported that the members of the comparison group were more affected with a positive opinion of mathematics at the start than their counterparts namely members of the GGS-POGIL group. What this means is that traditional methods of teaching may still be deemed as ideal by a given group of learners, maybe due to their usedness to traditional, assessment-based learning models (Abate et al., 2023).\u003c/p\u003e \u003cp\u003eThe discrepant findings of the previous research reveal that in spite of the fact that GeoGebra facilitates immersion and conceptualization, its effects on the student motivation and productive attitude can be rather fluctuating. To illustrate, the studies show that scholars, who are technology-unskilled, may experience some challenges when working with GeoGebra at first, and that can further demotivate and lower the confidence levels among them (Adelabu et al., 2022). Furthermore, certain studies have established that the success of inquiry-based teaching methods such as POGIL highly relies on the performance and willingness of teachers (Awofala et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This underscores the need to properly train teachers and design instructional methods in the incorporation of such methods.\u003c/p\u003e \u003cp\u003eDespite these potential constraints, there is an overall compatibility of the findings of this study with the global tendencies in favor of the introduction of technology and inquiry-based pedagogies in the learning of mathematics. GeoGebra and POGIL complementarism provides a strategy that is backed by research to address the issue of attitude and orientation to mathematics among the students in settings where learning geometry poses a major challenge to many students. The next step in research should be studying the long-term outcomes of this pedagogical practice and the way it can be extended to other learning environments, e.g. schools in rural or resource-limited areas.\u003c/p\u003e \u003cp\u003eOn the whole, this paper highlights the power of change in incorporating GeoGebra and POGIL to facilitate the positive attitude of students to mathematics by their productiveness. In the midst of difficulties in implementation, the achievement of this research studies will mark the need to keep on innovating the process of teaching mathematics to make students enjoy mathematics, feel confident, and appreciate mathematics.\u003c/p\u003e"},{"header":"Conclusion","content":" \u003cp\u003eThe integration of the GeoGebra Software (GGS) and Process-Oriented Guided Inquiry Learning (POGIL) makes math more enjoyable and more confident, as well as more valuable, to students. The interactivity of GeoGebra and the teamwork orientation of POGIL help to learn and solve more problems. Although it is necessary to resolve technological problems at the outset and facilitate the teachers, it is possible to maximize benefits in a structured implementation. The possible usefulness of technology-supported inquiry learning in mathematics education in this study is reported and should be the subject of long-term impact research and generalization to other areas.\u003c/p\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e\u003cb\u003eRecommendations\u003c/b\u003e:\u003c/h2\u003e \u003cp\u003eThe technology-based inquiry learning needs to be incorporated into curriculum by the practitioners and GeoGebra Software (GGS) and Process-Oriented Guided Inquiry Learning (POGIL) should be adopted by schools to enhance the enthusiasm, confidence, and understanding of geometry among students. Implementation can only be achieved when teachers are taught well and so it is important to train them on technology-driven inquiry techniques and development professionally using different modalities. The governments among others should also donate money towards the provision of proper infrastructure including computer laboratories and internet connections to the digital resources. The long-term performance of GGS-POGIL on mathematical competency must be measured, and its performance in the case of other learning settings are explored, such as the case of low-resource schools.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eI acknowledge my main advisor Dr. Kassa Micheal, and co-advisor Dr. Mulugeta Woldemichael for their consistent guidance and review of this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions:\u0026nbsp;\u003c/strong\u003eAll authors review the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e: \u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eno competing interests between authors.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe ethical approval of this study was also taken before the intervention by the Institutional Review Committee of the Addis Ababa University, College of Education and Behavioral Studies. The study was carried out under the strict compliance of the National Research Ethics Review Guideline of Ethiopia and keeps the ethical standards stipulated in the Declaration of Helsinki. The basic ethical principles included justice, autonomy, beneficence, and non-maleficence that were upheld throughout the research process.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to participate:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll participants signed an informed consent before data collection. Since all the student participants were aged 17 or older, the parental or the guardian consent was not needed. The participants were completely aware of the purpose of the study, procedures, and their rights, which included:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eVoluntary enrolment coupled with the right to quit without penalty.\u003c/li\u003e\n \u003cli\u003eConfidentiality and anonymity (no identities of respondents will be disclosed)\u003c/li\u003e\n \u003cli\u003eDebriefing processes at the interview to have proper representation of their ideas.\u003c/li\u003e\n \u003cli\u003eIt will give them an opportunity to proofread and confirm their responses.\u003c/li\u003e\n \u003cli\u003eRegularity of length of classes (45 minutes per period) at intervention times.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe college management was also granted permission to carry out the study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Publish:\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eParticipants consented to the publication of anonymized, aggregated research findings. No personally identifiable information is included in the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement (DAS):\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode Availability:\u0026nbsp;\u003c/strong\u003enot applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e \u003cli\u003e\u003cspan\u003eAndriani S, Nurlaelah E, Yulianti K (2019) The effect of process oriented guided inquiry learning (POGIL) model toward students\u0026rsquo; logical thinking ability in mathematics. \u003cem\u003eJournal of Physics: Conference Series\u003c/em\u003e, \u003cem\u003e1157\u003c/em\u003e(4). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1088/1742-6596/1157/4/042108\u003c/span\u003e\u003cspan address=\"10.1088/1742-6596/1157/4/042108\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAwofala AO, Lawal RF, Arigbabu AA, Fatade AO (2022) Mathematics productive disposition as a correlate of senior secondary school students\u0026rsquo; achievement in mathematics in Nigeria. 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PLoS ONE 12(10). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1371/journal.pone.0186203\u003c/span\u003e\u003cspan address=\"10.1371/journal.pone.0186203\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Addis Ababa University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Productive disposition, liking for mathematics, confidence in mathematics, valuing mathematics, GeoGebra, Guided Inquiry","lastPublishedDoi":"10.21203/rs.3.rs-8671177/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8671177/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigated the impacts of combining GeoGebra software and Process-Oriented Guided Inquiry Learning (GGS-POGIL) with the productive disposition of second level students towards geometry in Addis Ababa, Ethiopia in terms of enjoyment, confidence and felt value of mathematics. A quasi-experimental design with pre- and post-tests compared a GGS-POGIL group, a POGIL only group and Comparison group using the Productive Disposition Questionnaire. Results were that there was a significant increase in mathematics enjoyment and confidence in GGS-POGIL group compared to others (p\u0026thinsp;\u0026lt;\u0026thinsp;0.01), showing the combined effects of interactive visualization and inquiry-based learning. However, there was no significant improvement in student perceptions towards the importance of mathematics, which one might assume indicates a need for further strategies to indicate real world relevance. Effect size analysis endorsed the positive effect of GGS-POGIL on productive disposition. While effective, challenges like teacher training and access to technology indicate the need for professional development and infrastructure support. These findings confirm the role of technology-enhanced inquiry learning in developing positive mathematical attitudes and offer recommendations for educators and policymakers. Future studies should investigate the long-term effects and scalability of GGS-POGIL in a range of educational settings in resource-limited settings.\u003c/p\u003e","manuscriptTitle":"Enhancing Secondary School Students' Productive Disposition using GeoGebra Software integrated Process Oriented Guided Inquiry Learning in Geometry","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-23 07:19:12","doi":"10.21203/rs.3.rs-8671177/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8e57c100-74cc-4ff0-b30f-a5c9af75a148","owner":[],"postedDate":"January 23rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61602628,"name":"Educational Philosophy and Theory"}],"tags":[],"updatedAt":"2026-01-23T07:19:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-23 07:19:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8671177","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8671177","identity":"rs-8671177","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}