Investigating the influences of mathematics teachers’ personal orientations and instrumental genesis on their mathematical digital knowledge for teaching

Investigating the influences of mathematics teachers’ personal orientations and instrumental genesis on their mathematical digital knowledge for teaching | 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 Investigating the influences of mathematics teachers’ personal orientations and instrumental genesis on their mathematical digital knowledge for teaching Christian Kwame Kpotosu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8450960/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 The practical implementation of technology in the mathematics curriculum for senior high schools is contingent upon teachers’ dispositions, encompassing their perceptions, beliefs, and attitudes toward technology use, as well as their instrumental orientation. Despite widespread investments in digital technologies for schooling, mathematics teachers’ use of technology often remains pedagogically limited, raising questions about how digital teaching knowledge develops. Drawing on the instrumental approach and the Mathematical Digital Knowledge for Teaching (MDKT) framework, this study examined how teachers’ personal orientations toward technology and their instrumental genesis shape MDKT. Survey data were collected from senior high school mathematics teachers in Ghana and analysed using partial least squares structural equation modelling. Results show that teachers’ personal orientations have significant positive effects on both instrumental genesis and MDKT. Instrumental genesis also strongly predicts MDKT, indicating that sustained appropriation of digital tools is central to developing integrated mathematical digital teaching knowledge. The model explains sustained variance in MDKT, suggesting that digital teaching competence emerges from the interaction between orientations and tool use rather than from access or technical skill alone. The findings extend prior descriptive work and highlight mechanisms critical for supporting meaningful technology integration in mathematics education. Instrumental geneses Mathematical digital knowledge personal orientations Technology Figures Figure 1 Figure 2 INTRODUCTION Understanding how incorporating digital resources into educational practices can help achieve learning objectives in a specific subject requires a combination of subject expertise and experience with technology in teaching. In this sense, Prensky [ 10 ] concluded that teachers today are more likely to be digital natives than previous generations. Therefore, it is reasonable to assume that members of this demographic have a favourable impression of and faith in technology and a high level of digital competence [ 9 ] on an individual basis. However, mathematics instructors are facing new challenges in selecting, evaluating, and incorporating technological resources due to the abundance of technology tools [ 16 ]. For instance, in addition to traditional classroom settings, several online platforms (including Coursera, Math is Fun, Khan Academy, Alison.com, and Edx, among others) have recently emerged to meet the demand for digital content resources in mathematics. Also, digital content resources such as videos, animations, images, interactive games, graphics, and infographics enable mathematics teachers to integrate real-world concepts and representations into their lessons. These reasons justify the importance of mathematics teachers possessing the skills to effectively utilise technology in the classroom to communicate mathematical concepts to their students [ 9 ]. Consequently, the National Council of Teachers of Mathematics [ 8 ] specifically emphasises the importance of mathematics and the necessity for teachers to stay up to date with technological knowledge in teacher education and professional development programmes to develop lessons that make good use of technology and incorporate digital tools into daily teaching. This stance by NCTM reveals that it is essential for teachers to acknowledge the benefits of technology in improving students’ understanding of mathematics, continuously improve their technological skills for teaching, and develop teaching materials that effectively use digital tools. Therefore, proficient teachers with strong digital skills will have fully grasped the various aspects of the digital competencies required to incorporate technology into teaching mathematics. To contribute to this conversation, Tabach and Trgalová [ 14 ], in their journey to develop a context-specific digital framework, argue that mathematical digital knowledge for teaching involves a teacher’s grasp of utilising digital technology to teach mathematics successfully. This knowledge involves a variety of skills and competencies, from utilising digital tools to improve teaching methods to creating and presenting engaging mathematical content using digital platforms. Having these digital competencies enables teachers to effectively utilise digital tools and resources to improve student learning and equip students for the digital landscape they will face. However, the current competence frameworks focus on general digital competencies rather than the specific mathematical digital competencies needed for teaching mathematics with technology. Tabach and Trgalová [ 15 ] thereby developed the Mathematical Digital Knowledge for Teaching (MDKT) framework to conceptualise the knowledge mathematics teachers require to integrate digital technologies into their instructional practice meaningfully. The MDKT extends beyond generic digital competencies to account for the disciplinary specificity of mathematics teaching. Grounded in research on teachers’ technological knowledge, MDKT captures interrelated domains such as personal orientations, instrumental genesis, and mathematical digital knowledge for teaching. These domains offer a mathematics-specific lens for examining teachers’ work with digital tools. Empirical studies using the MDKT framework only described teachers’ perceived digital competencies for teaching mathematics with technology. For instance, Trgalová and Tabach [ 15 ] in a bi-national survey of mathematics teachers in France and Israel reported that most teachers demonstrated intermediate levels of competence in creating and modifying digital resources and in planning technology-supported lessons. Similarly, findings from Ntow and Kpotosu [ 9 ] revealed that mathematics teachers in Ghana reported high levels of knowledge of digital content and curriculum, knowledge of digital content and students, and specialised digital content knowledge, but only moderate levels of knowledge of digital content and teaching. While these studies provide valuable baseline evidence about teachers’ perceived MDKT profiles, they treated MDKT primarily at the surface level, leaving unanswered questions about why certain domains are more developed than others. Tabach and Trgalová [ 15 ] argue that the fragmented development of these domains is influenced by mathematics teachers’ personal orientations and their dual instrumental genesis. Similarly, the instrumental approach by Rabardel [ 11 ] holds that teachers’ utilisation of ICT involves a dual instrumental genesis, both personal and professional. Tabach and Trgalová [ 14 ] averred that professional instrumental genesis leads to the development of a professional tool for the teacher’s teaching work, while personal instrumental genesis leads to the creation of a personal tool for mathematical activities. Empirically, Haspekian [ 6 ] found that teachers’ personal instrumental genesis negatively affected their professional instrumental genesis. Alqahtani and Powell [ 1 ] found that teachers effectively incorporated geometric tools into their instructional strategies, thereby enhancing students' mathematical problem-solving abilities. Yao [ 18 ] found a significant relationship between the development of instrumental genesis and the acquisition of geometric knowledge. Also, Ratnayake, Adler, and Thomas [ 12 ] found that, due to teachers’ limited experience with digital technology in teaching, their personal and professional development in this area may have been insufficient. The results of the aforementioned empirical studies suggest that relationships among personal instrumental genesis, professional instrumental genesis, and mathematical digital knowledge for teaching are likely to be systematic rather than incidental. Consequently, mathematics teachers’ instrumental genesis is an important component of teachers’ digital competence. Furthermore, to effectively utilise technology, mathematics teachers must consider both the cognitive and affective aspects of technology adoption. This has prompted scholars to explore the impact of mathematics teachers’ cognitive and emotional factors on their technology proficiency. For instance, Benning et al. [ 3 ] showed that using GeoGebra allowed teachers to put their technology integration skills, personal beliefs, pedagogical beliefs, confidence, and willingness to use technology in their teaching into practice. Zambak and Tyminski [ 19 ] found that future teachers’ beliefs influence the development of specialised content knowledge. Ardiç [ 2 ] found that mathematics teachers’ perspectives on technology positively influenced the integration of technology into teaching methods. These studies suggest that teachers’ cognitive and affective orientations toward technology usage are closely related to how technological knowledge and practices are enacted in teaching mathematics. While these studies have demonstrated that beliefs, confidence, and perspectives shape teachers’ technology integration and specialised content knowledge, the relational pathways through which these orientations connect to instrumental genesis and mathematical digital knowledge for teaching with technology remain insufficiently examined. Therefore, this study tests a set of theoretically grounded hypotheses that examine the directional influences of teachers’ personal orientations on their instrumental genesis and, in turn, on their mathematical digital knowledge for teaching to address this gap. CONCEPTUAL FRAMEWORK The conceptual framework for this study is adapted from the mathematical digital knowledge for teaching framework developed by Tabach and Trgalová [ 15 ]. In this study, personal orientations were specified through teachers’ beliefs, attitudes, and perceptions towards technology usage, instrumental genesis was represented by personal and professional instrumental genesis, and mathematical digital knowledge for teaching was operationalised through knowledge of digital content and curriculum, knowledge of digital content and teaching, knowledge of digital content and students, and specialised digital content knowledge. All latent constructs were modelled as reflective higher-order constructs. This specification aligns with the theoretical assumptions underlying the instrumental approach [ 11 ] and the MDKT framework [ 15 ], which conceptualise these dimensions as interrelated manifestations of broader professional competencies rather than independent formative components. The MDKT framework represents an integrated knowledge system rather than a checklist of independent competencies. The four dimensions describe how MDKT is enacted across instructional domains, not additive components that independently form the construct. Empirically, these dimensions are expected to covary, and changes in teachers’ overall levels of digital knowledge should be reflected across all four domains as found by Ntow and Kpotosu [ 9 ]. Teachers are required to understand their students’ levels of digital literacy and preferences, as this knowledge can inform the selection and creation of digital content that effectively engages students. Furthermore, the teacher needs to be able to incorporate digital resources into their instructional strategies. One crucial aspect is that teachers possess the knowledge and skills to effectively design instructional sessions that optimise student engagement and facilitate learning through the integration of technology. Hence, teachers must know about the alignment between digital tools and the broader curriculum objectives. This knowledge enables teachers to utilise technology in a manner that enhances, rather than hinders, the desired learning outcomes. In this study, attitudes, beliefs, and perceptions regarding technology use are referred to as teachers’ personal orientations. The interplay between these constructs implies that teachers' personal orientations towards technology can influence their mathematical digital knowledge for teaching and their instrumental genesis of its utility and potential effects. This is because their attitudes, beliefs, and perceptions play a crucial role in determining their inclination and capacity to utilise digital tools in the classroom. The literature conceptualises attitudes as teachers’ general affective orientations, feelings, and predispositions toward the use of digital technology in mathematics classrooms, including their levels of comfort, enthusiasm, and willingness to engage with technological tools for instruction [ 13 , 2 ]. These affective orientations have been shown to shape teachers’ openness to integrating technology beyond routine or administrative uses. In contrast, beliefs refer to teachers’ more stable and deeply held convictions about the instructional value, pedagogical relevance, and effectiveness of digital technologies for supporting students’ mathematical understanding and learning processes [ 19 ]. Such beliefs influence how teachers interpret the role of technology in mathematics teaching and whether they view it as a transformative, supplementary, or peripheral to core instructional practices. Perceptions, on the other hand, capture teachers’ subjective interpretations and sense-making regarding the potential impact of technology on their instructional decisions and on students’ engagement and learning experiences in mathematics classrooms [ 13 ]. These perceptions are shaped by teachers’ prior experiences with technology use and contextual factors, and they often mediate how beliefs and attitudes are enacted. Moreover, Ntow and Kpotosu [ 9 ] found that teachers with a solid grounding in personal digital competencies are more inclined to transfer and effectively utilise them in their professional sphere. Teachers who are highly comfortable and proficient with technology in their personal lives may be more inclined to investigate and incorporate digital tools into their pedagogical approaches. Conversely, teachers with limited proficiency in personal digital skills may encounter difficulties when endeavouring to integrate technology meaningfully in their instructional settings. It can, therefore, be inferred that teachers who exhibit high levels of personal and professional instrumental genesis are more inclined to possess the requisite digital competencies for incorporating technology into their teaching of mathematics. Teachers who possess a high level of competence in utilising digital tools for both personal and professional endeavours are likely to have a greater capacity to harness technology within their instructional methodologies. On the other hand, teachers with a low level of instrumental genesis may encounter difficulties when attempting to leverage digital technology to enhance their mathematics instruction. The following hypotheses guided the study: \(\:{H}_{0}1\) There is no statistically significant influence of mathematics teachers’ personal orientations on their mathematical digital knowledge for teaching. \(\:{H}_{0}2\) There is no statistically significant influence of mathematics teachers’ personal orientations on their instrumental genesis. \(\:{H}_{0}3\) There is no statistically significant effect of mathematics teachers’ instrumental genesis on their mathematical digital knowledge for teaching. METHODS The target population for this study was all senior high school (SHS) mathematics teachers from the ten public SHSs in the Cape Coast Metropolis. However, data were collected from 178 mathematics teachers in the Cape Coast Metropolis using the census. The instrument used for data collection was a closed-ended questionnaire consisting of four sections (A-D), designed using a 5-point Likert scale (1 = Strongly Disagree and 5 = Strongly Agree). The first section (Section A) collects data on the teachers’ demographic characteristics. 13 items were used to collect data on teachers’ personal orientations (attitudes, beliefs, and perceptions) towards technology use, adapted from Ertmer et al. [ 4 ], Liang et al. [ 7 ], and Benning et al. [ 3 ]. Twenty items (14 for personal instrumental genesis and 6 for professional instrumental genesis) were used to collect data on teachers' instrumental genesis (personal and professional). This section consisted of items adapted from Trgalová and Tabach [ 17 ] and modified to suit the purpose of this current study. The modification involved removing some items to measure teachers’ professional instrumental genesis, as not all were relevant to the Ghanaian context. Thus, Ghanaian senior high school classrooms do not provide opportunities for mathematics teachers to allow students to use digital technologies in their mathematics classrooms. For example, teachers do not require students to document their collaborative efforts using digital technologies. The last section included 30 items from Ntow and Kpotosu [ 9 ] to elicit teachers' responses on their mathematical digital knowledge (knowledge of digital content and curriculum, knowledge of digital content and students, knowledge of digital content and teaching, and specialised digital content knowledge). The use of closed-ended questionnaires in this study provided an efficient and reliable means of collecting quantitative data for statistical analysis. Closed-ended questionnaires provide consistency in data collection and reduce the risk of interpretation bias. Again, closed-ended questionnaires were used in this study, in which respondents were presented with a fixed set of response options to reduce the possibility of interpretation bias and response variation. Content validity was assessed by presenting the questionnaire to three experts in mathematics education to examine the items and evaluate whether they represent a comprehensive and representative sample of the domains being measured. Prior to data collection, an application for ethical clearance was submitted to the researcher’s Institutional Review Board. The protocol was approved by the University of Cape Coast Institutional Review Board (UCCIRB/CES/2023/63) in accordance with the ethical guidelines for human subjects research. During data collection, informed written consent was obtained from all participants, and they were informed that participation in the study was voluntary and that anyone who wished to withdraw was free to do so without any problems. Again, the teachers who needed further clarification on the questionnaire items were addressed promptly. The data were verified and revised to guarantee the accuracy of the responses. The questionnaires were coded to facilitate data input, processing, and interpretation. The data were analysed using inferential statistics, including simple and multiple linear regressions, at the 0.05 significance level, using the Partial Least Squares Structural Equation Model (PLS-SEM). RESULTS Measurement Model Evaluation Prior to testing the hypothesised impacts among teachers’ personal orientations, instrumental genesis, and mathematical digital knowledge for teaching, the measurement model was evaluated to establish indicator reliability, internal consistency, convergent validity, and discriminant validity, following established guidelines for PLS-SEM [ 5 ]. Indicator reliability (Table 1 ) was assessed using outer loadings; all retained indicators met the recommended threshold of 0.70. Internal consistency reliability was established through Cronbach’s alpha, composite reliability, and rho_A coefficients, all of which exceeded the minimum acceptable value of 0.70 while remaining below 0.95, indicating satisfactory reliability without evidence of redundancy. Convergent validity was confirmed, as the average variance extracted (AVE) for each construct exceeded the 0.50 criterion, indicating that each construct accounted for more than half of the variance in its indicators. Table 1 Reliability and convergent validity Latent Variable Dimension/Indicator Outer Loading Cronach’s α ρA Composite Reliability (CR) AVE Personal Orientations 0.9179 0.9199 0.9481 0.8591 Beliefs 0.9081 Attitudes 0.9446 Perceptions 0.9276 Instrumental Genesis 0.8650 0.8691 0.9367 0.8809 Personal Instrumental Genesis 0.9437 Professional Instrumental Genesis 0.9334 Mathematical Digital Knowledge for Teaching 0.9337 0.9363 0.9528 0.8349 Knowledge of Digital Content and Curriculum 0.8845 Knowledge of Digital Content and Teaching 0.9406 Knowledge of Digital Content and Students 0.9472 Specialised Digital Content Knowledge 0.8804 Source: PLS-SEM outputs Discriminant validity was evaluated using both the Fornell-Larcker criterion (Table 2 ) and the heterotrait (HTMT) ratio (Table 3 ). Fornell-Larcker results showed that the square root of each construct’s AVE exceeded its correlations with other constructs. HTMT values were below the conservative threshold of 0.85, providing further evidence that the constructs were empirically distinct. Together, these results indicate that the measurement model demonstrates adequate reliability and validity and is suitable for subsequent structural model analysis. Table 2 Discriminant validity - Heterotrait (HTMT) ratio Constructs HTMT Personal orientations ⇔ Mathematical digital knowledge for teaching 0.8248 Personal orientations ⇔ Instrumental genesis 0.8492 Instrumental genesis ⇔ Mathematical digital knowledge for teaching 0.9341 Source: PLS-SEM outputs Table 3 Discriminant validity - Fornell-Larcker results Construct Instrumental Genesis Mathematical Digital Knowledge for Teaching Personal Orientations Personal Orientations (PO) 0.7612 0.7676 0.9269 Instrumental Genesis (IG) 0.9385 - - Mathematical Digital Knowledge for Teaching (MDKT) 0.8391 0.9317 - Source: PLS-SEM outputs Structural model evaluation and hypothesis testing results Following the establishment of the measurement model adequacy, the structural model (Table 4 ) was evaluated to examine the hypothesised impacts among personal orientations, instrumental genesis, and mathematical digital knowledge for teaching. Collinearity diagnostics indicated no concerns, with all variance inflation factor (VIF) values below the recommended threshold, suggesting that estimated path coefficients were not biased by multicollinearity. The model's explanatory power was assessed using coefficients of determination (R 2 ), and the practical relevance of each impact model was examined using effect sizes (f 2 ). Statistical significance was evaluated using a 0.05 significance level. The model demonstrated substantial explanatory power, accounting for 73.81% of the variance in mathematical digital knowledge for teaching and 57.50% of the variance in instrumental genesis, indicating that the proposed predictors jointly offer a strong explanation of teachers’ digital teaching knowledge. Table 4 Structural model evaluation and hypotheses testing results Hypothesis/Structural path VIF β S. E t p f 2 R 2 Personal orientations → Mathematical digital knowledge for teaching 2.3777 0.3065 0.0695 4.4097 ≤ 0.05 0.7676 0.7381 Personal orientations → Instrumental genesis 1.0000 0.7612 0.0471 16.1641 ≤ 0.05 0.7612 0.5750 Instrumental genesis → Mathematical digital knowledge for teaching 2.3777 0.6057 0.0715 8.4729 ≤ 0.05 0.6057 Source: PLS-SEM outputs The results indicated in Table 4 and Fig. 2 indicated that mathematics teachers’ personal orientations exhibited a statistically significant and positive effect (β = 0.3065, p ≤ 0.05) on their mathematical digital knowledge for teaching, indicating that teachers’ beliefs, attitudes, and perceptions toward technology are meaningfully associated with their capacity to integrate digital content and pedagogy, students, and curriculum in mathematics teaching. The large effect size (f 2 = 0.7676) further suggests that personal orientations are not merely peripheral dispositions but substantive contributors to the development of mathematical digital knowledge for teaching. This finding reinforces the view that teachers’ affective-cognitive dispositions shape the quality of their digital teaching knowledge. Personal orientations also showed a strong positive influence on instrumental genesis (β = 0.7612, p ≤ 0.05), with a large effect size (f 2 = 0.7612), highlighting the central role of teachers’ orientations in shaping how digital artefacts are appropriated and transformed into instruments for mathematical activity and instruction. This result suggests that favourable orientations toward technology significantly accelerate the processes through which teachers develop both personal and professional uses of digital tools, lending empirical support to theoretical claims within the instrumental approach that users’ dispositions and intentions deeply condition appropriation. Finally, instrumental genesis demonstrated a strong and statistically significant effect on the mathematical digital knowledge for teaching (β = 0.6057, p ≤ 0.05, f 2 = 0.6057), indicating that teachers’ processes of transforming digital artefacts into instructional instruments are closely linked to the development of integrated digital knowledge for teaching mathematics. The magnitude of this effect highlights instrumental genesis as a key mechanism through which orientations translate into pedagogically meaningful digital knowledge. These findings suggest that mathematical digital knowledge for teaching emerges not simply from access to technology or technical skill acquisition, but from the interplay between teachers’ orientations and their sustained engagement in instrumentalising digital tools for teaching and learning. DISCUSSION This study examined how mathematics teachers’ personal orientations toward technology and their instrumental genesis jointly shape the development of mathematical digital knowledge for teaching. Using PLS-SEM, the analysis revealed a structurally coherent model with strong explanatory power, accounting for substantial variance in both instrumental genesis and in digital knowledge for teaching mathematics. The findings thus move beyond descriptive accounts of teachers’ digital competencies by identifying the mechanisms by which orientations and the tool-appropriation process contribute to the development of integrated digital knowledge for mathematics teaching. The first hypothesis examined the direct influence of personal orientations on mathematics teachers' digital knowledge for teaching. The significant positive relationship observed indicates that teachers’ beliefs, attitudes, and perceptions toward technology are directly associated with their integrated knowledge of digital content and teaching, students, and curriculum. This finding resonates with studies showing that teachers’ orientations condition the development of specialised, pedagogically grounded digital knowledge rather than merely technical proficiency [ 15 ]. Importantly, this result helps explain patterns reported by Ntow and Kpotosu [ 9 ] in the first phase of this research, where Ghanaian mathematics teachers reported high levels of digital knowledge of content and curriculum, students, and specialised digital content knowledge, yet comparatively moderate knowledge of digital content and teaching. The present findings suggest that such uneven knowledge profiles may stem from orientations that prioritise content manipulation and resource creation over instructional transformation. Thus, mathematics teachers’ digital knowledge for teaching appears to be shaped not only by what teachers can do with technology, but by how they conceptualise its role in mathematics teaching and learning. The second hypothesis tested whether teachers’ personal orientations, operationalised through beliefs, attitudes, and perceptions, predict their instrumental genesis. The results indicate a strong and statistically significant relationship, suggesting that orientations toward technology are foundational to how teachers’ appropriate digital artefacts for mathematical activity and instruction. This finding aligns with recent empirical work by Ardiç [ 2 ], which demonstrates that teachers’ beliefs and attitudes influence not only technology adoption but also the depth of pedagogical engagement with digital tools. This present finding, therefore, helps explain why some teachers move beyond basic use towards instrumental development, while others do not. From a theoretical standpoint, this result supports the instrumental approach’s claim that instrumental genesis is not a purely technical process but is mediated by users’ intentions, meanings, and dispositions [ 11 ]. Teachers who view technology as pedagogically valuable are more likely to invest effort in transforming artefacts into teaching instruments, whereas unfavourable or ambivalent orientations may constrain such development. In the Ghanaian context, this relationship is particularly salient given national initiatives that have prioritised access to digital devices, such as the one-teacher-one-laptop policy. While such policies expand access to materials, the present findings suggest that access alone is insufficient; teachers’ orientations play a decisive role in determining whether digital tools become pedagogically functional instruments. The third hypothesis tested whether instrumental genesis predicts mathematical digital knowledge for teaching, and the results revealed a strong positive effect. This finding indicates that teachers’ processes of appropriating and adapting digital tools are closely tied to the development of integrated digital teaching knowledge. From a theoretical perspective, this relationship reinforces the instrumental approach’s claim that knowledge emerges through sustained, goal-oriented interaction with artefacts as they are transformed into instruments for specific practices [ 11 ]. Empirically, this result is consistent with studies highlighting the role of design, experimentation, and reflective use of digital tools in developing teachers’ pedagogical digital knowledge [ 19 , 12 ]. In the Ghanaian educational system, where teachers often have access to digital tools but limited opportunities for sustained pedagogical experimentation, this finding highlights the importance of professional learning environments that support instrumental genesis rather than one-off training sessions. Without such opportunities, mathematics teachers’ digital knowledge risks remaining fragmented or disconnected from instructional practice. This study contributes to mathematics education research by empirically elaborating the mathematical digital knowledge form teaching framework through the lens of the instrumental approach. The results highlight the need to conceptualise digital competence not as a static set of skills, but as an orientation-dependent and practice-mediated knowledge system. These findings suggest that efforts to strengthen mathematics teachers’ digital competencies must simultaneously attend to orientations, opportunities for instrumentalisation, and the integrated nature of mathematical digital knowledge for teaching. CONCLUSION This study advances mathematics education research by empirically articulating how mathematics teachers’ personal orientations toward technology, their personal and professional instrumental genesis, and their mathematical digital knowledge for teaching are systematically related. Anchored in the MDKT framework, the findings demonstrate that teachers’ digital competencies cannot be adequately understood as a static set of skills or knowledge domains. Instead, it emerges through interrelated affective, cognitive, and instrumental processes. By showing that teachers’ orientations significantly relate to both personal and professional instrumental genesis, and that these instrumental geneses, in turn, are associated with MDKT, the study offers empirical support for a relational and process-oriented account of teachers’ digital knowledge for development in mathematics. This contribution extends prior MDKT research, which has largely remained descriptive, by providing evidence of coherent pathways linking dispositions, tool appropriation, and domain-specific digital knowledge. These results suggest that the effectiveness of technology integration in mathematics classrooms depends less on digital readiness alone and more on how teachers appropriate tools within teaching practices. In this sense, the study reframes digital competence as a developmental construct shaped by orientations and professional activity, thereby offering a theoretically integrated perspective relevant to both mathematics education research and policy. RECOMMENDATIONS Based on these findings, future professional development and policy initiatives should prioritise pedagogically grounded engagements with digital tools that support teachers’ professional instrumental genesis, rather than focusing solely on technical proficiency or access. For researchers, longitudinal and classroom-based studies are needed to trace how changes in teachers’ orientations and instrumental genesis correspond to shifts in enacted MDKT over time. Policy makers and teacher educators should design sustained, practice-oriented professional learning structures that connect digital tools to task design, student thinking, and instructional decision-making in mathematics. Such efforts are likely to foster more transferable forms of mathematical digital knowledge for teaching. Declarations Funding The author did not receive support from any organisation for the submitted work. Conflict s of interest The author has no relevant financial or non-financial interests to disclose. Ethics statement The protocol was approved by the University of Cape Coast Institutional Review Board (UCCIRB/CES/2023/63) in accordance with the ethical guidelines for human subjects research. Consent to participate Informed written consent was obtained from all participants. Participation in the study was voluntary, and all teachers who did not consent were not included without any consequences. Consent to publish The author agrees that the manuscript should be published in its current form. Acknowledgement I acknowledge my supervisor, Dr Forster D. Ntow, for supervising my MPhil thesis from which I wrote this manuscript. I also appreciate all the teachers who took the time to respond to the survey. Data availability statement Data for this study will be made available upon reasonable request. 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Integrating mathematics teaching with digital resources: Where to begin? Australian Primary Mathematics Classroom, 23 (2), 14–19. Trgalová, J., & Tabach, M. (2020). Bi-national survey on mathematics teachers’ digital competences. In H.-G. Weigand, A. Clark-Wilson, A. Donevska-Todorova, E. Faggiano, N. Grønbaek, et al. (Eds.), Proceedings of the Fifth ERME topic conference (ETC 5) on mathematics education in the digital age (MEDA) (pp. 117–124). ERME. https://hal.science/hal-02500112 Yao, X. (2020). Preservice mathematics teachers' instrumental genesis and their development of geometric knowledge in a dynamic geometry environment. International Journal for Technology in Mathematics Education , 27 (4).191–206. https://doi.org/10.1564/tme_v27.4.02 Zambak, V. S., & Tyminski, A. M. (2017). A case study on specialised content knowledge development with dynamic geometry software: The analysis of influential factors and technology beliefs of three pre-service middle grades mathematics teachers. Mathematics Teacher Education and Development , 19 (1), 82–106. Additional Declarations No competing interests reported. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8450960","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":585043993,"identity":"7ce90b29-fc2d-43e8-bad2-fc12596ca261","order_by":0,"name":"Christian Kwame Kpotosu","email":"data:image/png;base64,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","orcid":"","institution":"University of Cape Coast","correspondingAuthor":true,"prefix":"","firstName":"Christian","middleName":"Kwame","lastName":"Kpotosu","suffix":""}],"badges":[],"createdAt":"2025-12-25 21:08:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8450960/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8450960/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101988180,"identity":"ae62a6f4-436d-411f-9771-20c88eb94358","added_by":"auto","created_at":"2026-02-05 18:53:09","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":335011,"visible":true,"origin":"","legend":"\u003cp\u003eConceptual Framework\u003c/p\u003e\n\u003cp\u003eSource: Adapted from Tabach and Trgalová [15]\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8450960/v1/0fa9f44a218d2f7b7ba5fbc7.jpeg"},{"id":101988185,"identity":"b5602ad2-f59c-4672-a6ca-c7cd377ac329","added_by":"auto","created_at":"2026-02-05 18:53:14","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":38427,"visible":true,"origin":"","legend":"\u003cp\u003eStructural model\u003c/p\u003e\n\u003cp\u003eSource: PLS-SEM outputs\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8450960/v1/cec0aa0b5a96e6ee666a8c70.png"},{"id":104430073,"identity":"1770b2bf-1926-478e-8bad-3fc49beedff0","added_by":"auto","created_at":"2026-03-11 15:27:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1015152,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8450960/v1/38931f72-750d-43b0-bef0-48a71f76c45b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Investigating the influences of mathematics teachers’ personal orientations and instrumental genesis on their mathematical digital knowledge for teaching","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eUnderstanding how incorporating digital resources into educational practices can help achieve learning objectives in a specific subject requires a combination of subject expertise and experience with technology in teaching. In this sense, Prensky [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] concluded that teachers today are more likely to be digital natives than previous generations. Therefore, it is reasonable to assume that members of this demographic have a favourable impression of and faith in technology and a high level of digital competence [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] on an individual basis.\u003c/p\u003e \u003cp\u003eHowever, mathematics instructors are facing new challenges in selecting, evaluating, and incorporating technological resources due to the abundance of technology tools [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. For instance, in addition to traditional classroom settings, several online platforms (including Coursera, Math is Fun, Khan Academy, Alison.com, and Edx, among others) have recently emerged to meet the demand for digital content resources in mathematics. Also, digital content resources such as videos, animations, images, interactive games, graphics, and infographics enable mathematics teachers to integrate real-world concepts and representations into their lessons. These reasons justify the importance of mathematics teachers possessing the skills to effectively utilise technology in the classroom to communicate mathematical concepts to their students [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eConsequently, the National Council of Teachers of Mathematics [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] specifically emphasises the importance of mathematics and the necessity for teachers to stay up to date with technological knowledge in teacher education and professional development programmes to develop lessons that make good use of technology and incorporate digital tools into daily teaching. This stance by NCTM reveals that it is essential for teachers to acknowledge the benefits of technology in improving students\u0026rsquo; understanding of mathematics, continuously improve their technological skills for teaching, and develop teaching materials that effectively use digital tools. Therefore, proficient teachers with strong digital skills will have fully grasped the various aspects of the digital competencies required to incorporate technology into teaching mathematics.\u003c/p\u003e \u003cp\u003eTo contribute to this conversation, Tabach and Trgalov\u0026aacute; [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], in their journey to develop a context-specific digital framework, argue that mathematical digital knowledge for teaching involves a teacher\u0026rsquo;s grasp of utilising digital technology to teach mathematics successfully. This knowledge involves a variety of skills and competencies, from utilising digital tools to improve teaching methods to creating and presenting engaging mathematical content using digital platforms. Having these digital competencies enables teachers to effectively utilise digital tools and resources to improve student learning and equip students for the digital landscape they will face. However, the current competence frameworks focus on general digital competencies rather than the specific mathematical digital competencies needed for teaching mathematics with technology.\u003c/p\u003e \u003cp\u003eTabach and Trgalov\u0026aacute; [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] thereby developed the Mathematical Digital Knowledge for Teaching (MDKT) framework to conceptualise the knowledge mathematics teachers require to integrate digital technologies into their instructional practice meaningfully. The MDKT extends beyond generic digital competencies to account for the disciplinary specificity of mathematics teaching. Grounded in research on teachers\u0026rsquo; technological knowledge, MDKT captures interrelated domains such as personal orientations, instrumental genesis, and mathematical digital knowledge for teaching. These domains offer a mathematics-specific lens for examining teachers\u0026rsquo; work with digital tools.\u003c/p\u003e \u003cp\u003eEmpirical studies using the MDKT framework only described teachers\u0026rsquo; perceived digital competencies for teaching mathematics with technology. For instance, Trgalov\u0026aacute; and Tabach [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] in a bi-national survey of mathematics teachers in France and Israel reported that most teachers demonstrated intermediate levels of competence in creating and modifying digital resources and in planning technology-supported lessons. Similarly, findings from Ntow and Kpotosu [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] revealed that mathematics teachers in Ghana reported high levels of knowledge of digital content and curriculum, knowledge of digital content and students, and specialised digital content knowledge, but only moderate levels of knowledge of digital content and teaching. While these studies provide valuable baseline evidence about teachers\u0026rsquo; perceived MDKT profiles, they treated MDKT primarily at the surface level, leaving unanswered questions about why certain domains are more developed than others. Tabach and Trgalov\u0026aacute; [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] argue that the fragmented development of these domains is influenced by mathematics teachers\u0026rsquo; personal orientations and their dual instrumental genesis.\u003c/p\u003e \u003cp\u003eSimilarly, the instrumental approach by Rabardel [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] holds that teachers\u0026rsquo; utilisation of ICT involves a dual instrumental genesis, both personal and professional. Tabach and Trgalov\u0026aacute; [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] averred that professional instrumental genesis leads to the development of a professional tool for the teacher\u0026rsquo;s teaching work, while personal instrumental genesis leads to the creation of a personal tool for mathematical activities.\u003c/p\u003e \u003cp\u003eEmpirically, Haspekian [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] found that teachers\u0026rsquo; personal instrumental genesis negatively affected their professional instrumental genesis. Alqahtani and Powell [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] found that teachers effectively incorporated geometric tools into their instructional strategies, thereby enhancing students' mathematical problem-solving abilities. Yao [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] found a significant relationship between the development of instrumental genesis and the acquisition of geometric knowledge. Also, Ratnayake, Adler, and Thomas [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] found that, due to teachers\u0026rsquo; limited experience with digital technology in teaching, their personal and professional development in this area may have been insufficient. The results of the aforementioned empirical studies suggest that relationships among personal instrumental genesis, professional instrumental genesis, and mathematical digital knowledge for teaching are likely to be systematic rather than incidental. Consequently, mathematics teachers\u0026rsquo; instrumental genesis is an important component of teachers\u0026rsquo; digital competence.\u003c/p\u003e \u003cp\u003eFurthermore, to effectively utilise technology, mathematics teachers must consider both the cognitive and affective aspects of technology adoption. This has prompted scholars to explore the impact of mathematics teachers\u0026rsquo; cognitive and emotional factors on their technology proficiency. For instance, Benning et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] showed that using GeoGebra allowed teachers to put their technology integration skills, personal beliefs, pedagogical beliefs, confidence, and willingness to use technology in their teaching into practice. Zambak and Tyminski [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] found that future teachers\u0026rsquo; beliefs influence the development of specialised content knowledge. Ardi\u0026ccedil; [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] found that mathematics teachers\u0026rsquo; perspectives on technology positively influenced the integration of technology into teaching methods.\u003c/p\u003e \u003cp\u003eThese studies suggest that teachers\u0026rsquo; cognitive and affective orientations toward technology usage are closely related to how technological knowledge and practices are enacted in teaching mathematics. While these studies have demonstrated that beliefs, confidence, and perspectives shape teachers\u0026rsquo; technology integration and specialised content knowledge, the relational pathways through which these orientations connect to instrumental genesis and mathematical digital knowledge for teaching with technology remain insufficiently examined. Therefore, this study tests a set of theoretically grounded hypotheses that examine the directional influences of teachers\u0026rsquo; personal orientations on their instrumental genesis and, in turn, on their mathematical digital knowledge for teaching to address this gap.\u003c/p\u003e"},{"header":"CONCEPTUAL FRAMEWORK","content":"\u003cp\u003eThe conceptual framework for this study is adapted from the mathematical digital knowledge for teaching framework developed by Tabach and Trgalov\u0026aacute; [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e]. In this study, personal orientations were specified through teachers\u0026rsquo; beliefs, attitudes, and perceptions towards technology usage, instrumental genesis was represented by personal and professional instrumental genesis, and mathematical digital knowledge for teaching was operationalised through knowledge of digital content and curriculum, knowledge of digital content and teaching, knowledge of digital content and students, and specialised digital content knowledge. All latent constructs were modelled as reflective higher-order constructs. This specification aligns with the theoretical assumptions underlying the instrumental approach [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e] and the MDKT framework [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e], which conceptualise these dimensions as interrelated manifestations of broader professional competencies rather than independent formative components.\u003c/p\u003e\n\u003cp\u003eThe MDKT framework represents an integrated knowledge system rather than a checklist of independent competencies. The four dimensions describe how MDKT is enacted across instructional domains, not additive components that independently form the construct. Empirically, these dimensions are expected to covary, and changes in teachers\u0026rsquo; overall levels of digital knowledge should be reflected across all four domains as found by Ntow and Kpotosu [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]. Teachers are required to understand their students\u0026rsquo; levels of digital literacy and preferences, as this knowledge can inform the selection and creation of digital content that effectively engages students. Furthermore, the teacher needs to be able to incorporate digital resources into their instructional strategies. One crucial aspect is that teachers possess the knowledge and skills to effectively design instructional sessions that optimise student engagement and facilitate learning through the integration of technology. Hence, teachers must know about the alignment between digital tools and the broader curriculum objectives. This knowledge enables teachers to utilise technology in a manner that enhances, rather than hinders, the desired learning outcomes.\u003c/p\u003e\n\u003cp\u003eIn this study, attitudes, beliefs, and perceptions regarding technology use are referred to as teachers\u0026rsquo; personal orientations. The interplay between these constructs implies that teachers\u0026apos; personal orientations towards technology can influence their mathematical digital knowledge for teaching and their instrumental genesis of its utility and potential effects. This is because their attitudes, beliefs, and perceptions play a crucial role in determining their inclination and capacity to utilise digital tools in the classroom.\u003c/p\u003e\n\u003cp\u003eThe literature conceptualises attitudes as teachers\u0026rsquo; general affective orientations, feelings, and predispositions toward the use of digital technology in mathematics classrooms, including their levels of comfort, enthusiasm, and willingness to engage with technological tools for instruction [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e]. These affective orientations have been shown to shape teachers\u0026rsquo; openness to integrating technology beyond routine or administrative uses. In contrast, beliefs refer to teachers\u0026rsquo; more stable and deeply held convictions about the instructional value, pedagogical relevance, and effectiveness of digital technologies for supporting students\u0026rsquo; mathematical understanding and learning processes [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]. Such beliefs influence how teachers interpret the role of technology in mathematics teaching and whether they view it as a transformative, supplementary, or peripheral to core instructional practices. Perceptions, on the other hand, capture teachers\u0026rsquo; subjective interpretations and sense-making regarding the potential impact of technology on their instructional decisions and on students\u0026rsquo; engagement and learning experiences in mathematics classrooms [\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e]. These perceptions are shaped by teachers\u0026rsquo; prior experiences with technology use and contextual factors, and they often mediate how beliefs and attitudes are enacted.\u003c/p\u003e\n\u003cp\u003eMoreover, Ntow and Kpotosu [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e] found that teachers with a solid grounding in personal digital competencies are more inclined to transfer and effectively utilise them in their professional sphere. Teachers who are highly comfortable and proficient with technology in their personal lives may be more inclined to investigate and incorporate digital tools into their pedagogical approaches. Conversely, teachers with limited proficiency in personal digital skills may encounter difficulties when endeavouring to integrate technology meaningfully in their instructional settings.\u003c/p\u003e\n\u003cp\u003eIt can, therefore, be inferred that teachers who exhibit high levels of personal and professional instrumental genesis are more inclined to possess the requisite digital competencies for incorporating technology into their teaching of mathematics. Teachers who possess a high level of competence in utilising digital tools for both personal and professional endeavours are likely to have a greater capacity to harness technology within their instructional methodologies. On the other hand, teachers with a low level of instrumental genesis may encounter difficulties when attempting to leverage digital technology to enhance their mathematics instruction. The following hypotheses guided the study:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{0}1\\)\u003c/span\u003e\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere is no statistically significant influence of mathematics teachers\u0026rsquo; personal orientations on their mathematical digital knowledge for teaching.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{0}2\\)\u003c/span\u003e\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere is no statistically significant influence of mathematics teachers\u0026rsquo; personal orientations on their instrumental genesis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{0}3\\)\u003c/span\u003e\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere is no statistically significant effect of mathematics teachers\u0026rsquo; instrumental genesis on their mathematical digital knowledge for teaching.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003eThe target population for this study was all senior high school (SHS) mathematics teachers from the ten public SHSs in the Cape Coast Metropolis. However, data were collected from 178 mathematics teachers in the Cape Coast Metropolis using the census.\u003c/p\u003e\u003cp\u003eThe instrument used for data collection was a closed-ended questionnaire consisting of four sections (A-D), designed using a 5-point Likert scale (1 = Strongly Disagree and 5 = Strongly Agree). The first section (Section A) collects data on the teachers’ demographic characteristics. 13 items were used to collect data on teachers’ personal orientations (attitudes, beliefs, and perceptions) towards technology use, adapted from Ertmer et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], Liang et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], and Benning et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Twenty items (14 for personal instrumental genesis and 6 for professional instrumental genesis) were used to collect data on teachers' instrumental genesis (personal and professional). This section consisted of items adapted from Trgalová and Tabach [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] and modified to suit the purpose of this current study. The modification involved removing some items to measure teachers’ professional instrumental genesis, as not all were relevant to the Ghanaian context. Thus, Ghanaian senior high school classrooms do not provide opportunities for mathematics teachers to allow students to use digital technologies in their mathematics classrooms. For example, teachers do not require students to document their collaborative efforts using digital technologies. The last section included 30 items from Ntow and Kpotosu [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] to elicit teachers' responses on their mathematical digital knowledge (knowledge of digital content and curriculum, knowledge of digital content and students, knowledge of digital content and teaching, and specialised digital content knowledge).\u003c/p\u003e\u003cp\u003eThe use of closed-ended questionnaires in this study provided an efficient and reliable means of collecting quantitative data for statistical analysis. Closed-ended questionnaires provide consistency in data collection and reduce the risk of interpretation bias. Again, closed-ended questionnaires were used in this study, in which respondents were presented with a fixed set of response options to reduce the possibility of interpretation bias and response variation. Content validity was assessed by presenting the questionnaire to three experts in mathematics education to examine the items and evaluate whether they represent a comprehensive and representative sample of the domains being measured.\u003c/p\u003e\u003cp\u003ePrior to data collection, an application for ethical clearance was submitted to the researcher’s Institutional Review Board. The protocol was approved by the University of Cape Coast Institutional Review Board (UCCIRB/CES/2023/63) in accordance with the ethical guidelines for human subjects research. During data collection, informed written consent was obtained from all participants, and they were informed that participation in the study was voluntary and that anyone who wished to withdraw was free to do so without any problems. Again, the teachers who needed further clarification on the questionnaire items were addressed promptly.\u003c/p\u003e\u003cp\u003eThe data were verified and revised to guarantee the accuracy of the responses. The questionnaires were coded to facilitate data input, processing, and interpretation. The data were analysed using inferential statistics, including simple and multiple linear regressions, at the 0.05 significance level, using the Partial Least Squares Structural Equation Model (PLS-SEM).\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eMeasurement Model Evaluation\u003c/h2\u003e \u003cp\u003ePrior to testing the hypothesised impacts among teachers\u0026rsquo; personal orientations, instrumental genesis, and mathematical digital knowledge for teaching, the measurement model was evaluated to establish indicator reliability, internal consistency, convergent validity, and discriminant validity, following established guidelines for PLS-SEM [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIndicator reliability (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) was assessed using outer loadings; all retained indicators met the recommended threshold of 0.70. Internal consistency reliability was established through Cronbach\u0026rsquo;s alpha, composite reliability, and rho_A coefficients, all of which exceeded the minimum acceptable value of 0.70 while remaining below 0.95, indicating satisfactory reliability without evidence of redundancy. Convergent validity was confirmed, as the average variance extracted (AVE) for each construct exceeded the 0.50 criterion, indicating that each construct accounted for more than half of the variance in its indicators.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eReliability and convergent validity\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=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLatent Variable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDimension/Indicator\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOuter Loading\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCronach\u0026rsquo;s α\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eρA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eComposite Reliability (CR)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAVE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePersonal Orientations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9199\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9481\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.8591\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBeliefs\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9081\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 \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\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAttitudes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9446\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 \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\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePerceptions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9276\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 \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\"\u003e \u003cp\u003eInstrumental Genesis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.8650\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8691\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9367\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.8809\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePersonal Instrumental Genesis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9437\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 \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\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eProfessional Instrumental Genesis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9334\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 \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\"\u003e \u003cp\u003eMathematical Digital Knowledge for Teaching\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9337\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9363\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9528\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.8349\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKnowledge of Digital Content and Curriculum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8845\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 \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\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKnowledge of Digital Content and Teaching\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9406\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 \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\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKnowledge of Digital Content and Students\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9472\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 \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\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpecialised Digital Content Knowledge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8804\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 \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\"\u003eSource: PLS-SEM outputs\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eDiscriminant validity was evaluated using both the Fornell-Larcker criterion (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and the heterotrait (HTMT) ratio (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Fornell-Larcker results showed that the square root of each construct\u0026rsquo;s AVE exceeded its correlations with other constructs. HTMT values were below the conservative threshold of 0.85, providing further evidence that the constructs were empirically distinct. Together, these results indicate that the measurement model demonstrates adequate reliability and validity and is suitable for subsequent structural model analysis.\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\u003eDiscriminant validity - Heterotrait (HTMT) ratio\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstructs\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHTMT\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePersonal orientations \u0026hArr; Mathematical digital knowledge for teaching\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8248\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePersonal orientations \u0026hArr; Instrumental genesis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8492\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInstrumental genesis \u0026hArr; Mathematical digital knowledge for teaching\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.9341\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"2\"\u003eSource: PLS-SEM outputs\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \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\u003eDiscriminant validity - Fornell-Larcker results\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=\"char\" char=\".\" 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\u003eConstruct\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInstrumental Genesis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMathematical Digital Knowledge for Teaching\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePersonal Orientations\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePersonal Orientations (PO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7612\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.7676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9269\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInstrumental Genesis (IG)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.9385\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMathematical Digital Knowledge for Teaching (MDKT)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.8391\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9317\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eSource: PLS-SEM outputs\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eStructural model evaluation and hypothesis testing results\u003c/h3\u003e\n\u003cp\u003eFollowing the establishment of the measurement model adequacy, the structural model (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) was evaluated to examine the hypothesised impacts among personal orientations, instrumental genesis, and mathematical digital knowledge for teaching. Collinearity diagnostics indicated no concerns, with all variance inflation factor (VIF) values below the recommended threshold, suggesting that estimated path coefficients were not biased by multicollinearity. The model's explanatory power was assessed using coefficients of determination (R\u003csup\u003e2\u003c/sup\u003e), and the practical relevance of each impact model was examined using effect sizes (f\u003csup\u003e2\u003c/sup\u003e). Statistical significance was evaluated using a 0.05 significance level.\u003c/p\u003e \u003cp\u003eThe model demonstrated substantial explanatory power, accounting for 73.81% of the variance in mathematical digital knowledge for teaching and 57.50% of the variance in instrumental genesis, indicating that the proposed predictors jointly offer a strong explanation of teachers\u0026rsquo; digital teaching knowledge.\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\u003eStructural model evaluation and hypotheses testing results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHypothesis/Structural path\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVIF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eS. E\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003et\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ep\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003ef\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u003csup\u003e2\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\u003ePersonal orientations \u0026rarr; Mathematical digital knowledge for teaching\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.3777\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.4097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u0026le;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.7676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.7381\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePersonal orientations \u0026rarr; Instrumental genesis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7612\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0471\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e16.1641\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u0026le;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.7612\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.5750\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInstrumental genesis \u0026rarr; Mathematical digital knowledge for teaching\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.3777\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0715\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.4729\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u0026le;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.6057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003eSource: PLS-SEM outputs\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\u003cp\u003eThe results indicated in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e indicated that mathematics teachers\u0026rsquo; personal orientations exhibited a statistically significant and positive effect (β\u0026thinsp;=\u0026thinsp;0.3065, p\u0026thinsp;\u0026le;\u0026thinsp;0.05) on their mathematical digital knowledge for teaching, indicating that teachers\u0026rsquo; beliefs, attitudes, and perceptions toward technology are meaningfully associated with their capacity to integrate digital content and pedagogy, students, and curriculum in mathematics teaching. The large effect size (f\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.7676) further suggests that personal orientations are not merely peripheral dispositions but substantive contributors to the development of mathematical digital knowledge for teaching. This finding reinforces the view that teachers\u0026rsquo; affective-cognitive dispositions shape the quality of their digital teaching knowledge.\u003c/p\u003e \u003cp\u003ePersonal orientations also showed a strong positive influence on instrumental genesis (β\u0026thinsp;=\u0026thinsp;0.7612, p\u0026thinsp;\u0026le;\u0026thinsp;0.05), with a large effect size (f\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.7612), highlighting the central role of teachers\u0026rsquo; orientations in shaping how digital artefacts are appropriated and transformed into instruments for mathematical activity and instruction. This result suggests that favourable orientations toward technology significantly accelerate the processes through which teachers develop both personal and professional uses of digital tools, lending empirical support to theoretical claims within the instrumental approach that users\u0026rsquo; dispositions and intentions deeply condition appropriation.\u003c/p\u003e \u003cp\u003eFinally, instrumental genesis demonstrated a strong and statistically significant effect on the mathematical digital knowledge for teaching (β\u0026thinsp;=\u0026thinsp;0.6057, p\u0026thinsp;\u0026le;\u0026thinsp;0.05, f\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.6057), indicating that teachers\u0026rsquo; processes of transforming digital artefacts into instructional instruments are closely linked to the development of integrated digital knowledge for teaching mathematics. The magnitude of this effect highlights instrumental genesis as a key mechanism through which orientations translate into pedagogically meaningful digital knowledge. These findings suggest that mathematical digital knowledge for teaching emerges not simply from access to technology or technical skill acquisition, but from the interplay between teachers\u0026rsquo; orientations and their sustained engagement in instrumentalising digital tools for teaching and learning.\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eThis study examined how mathematics teachers\u0026rsquo; personal orientations toward technology and their instrumental genesis jointly shape the development of mathematical digital knowledge for teaching. Using PLS-SEM, the analysis revealed a structurally coherent model with strong explanatory power, accounting for substantial variance in both instrumental genesis and in digital knowledge for teaching mathematics. The findings thus move beyond descriptive accounts of teachers\u0026rsquo; digital competencies by identifying the mechanisms by which orientations and the tool-appropriation process contribute to the development of integrated digital knowledge for mathematics teaching.\u003c/p\u003e \u003cp\u003eThe first hypothesis examined the direct influence of personal orientations on mathematics teachers' digital knowledge for teaching. The significant positive relationship observed indicates that teachers\u0026rsquo; beliefs, attitudes, and perceptions toward technology are directly associated with their integrated knowledge of digital content and teaching, students, and curriculum. This finding resonates with studies showing that teachers\u0026rsquo; orientations condition the development of specialised, pedagogically grounded digital knowledge rather than merely technical proficiency [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eImportantly, this result helps explain patterns reported by Ntow and Kpotosu [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] in the first phase of this research, where Ghanaian mathematics teachers reported high levels of digital knowledge of content and curriculum, students, and specialised digital content knowledge, yet comparatively moderate knowledge of digital content and teaching. The present findings suggest that such uneven knowledge profiles may stem from orientations that prioritise content manipulation and resource creation over instructional transformation. Thus, mathematics teachers\u0026rsquo; digital knowledge for teaching appears to be shaped not only by what teachers can do with technology, but by how they conceptualise its role in mathematics teaching and learning.\u003c/p\u003e \u003cp\u003eThe second hypothesis tested whether teachers\u0026rsquo; personal orientations, operationalised through beliefs, attitudes, and perceptions, predict their instrumental genesis. The results indicate a strong and statistically significant relationship, suggesting that orientations toward technology are foundational to how teachers\u0026rsquo; appropriate digital artefacts for mathematical activity and instruction. This finding aligns with recent empirical work by Ardi\u0026ccedil; [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], which demonstrates that teachers\u0026rsquo; beliefs and attitudes influence not only technology adoption but also the depth of pedagogical engagement with digital tools. This present finding, therefore, helps explain why some teachers move beyond basic use towards instrumental development, while others do not.\u003c/p\u003e \u003cp\u003eFrom a theoretical standpoint, this result supports the instrumental approach\u0026rsquo;s claim that instrumental genesis is not a purely technical process but is mediated by users\u0026rsquo; intentions, meanings, and dispositions [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Teachers who view technology as pedagogically valuable are more likely to invest effort in transforming artefacts into teaching instruments, whereas unfavourable or ambivalent orientations may constrain such development. In the Ghanaian context, this relationship is particularly salient given national initiatives that have prioritised access to digital devices, such as the one-teacher-one-laptop policy. While such policies expand access to materials, the present findings suggest that access alone is insufficient; teachers\u0026rsquo; orientations play a decisive role in determining whether digital tools become pedagogically functional instruments.\u003c/p\u003e \u003cp\u003eThe third hypothesis tested whether instrumental genesis predicts mathematical digital knowledge for teaching, and the results revealed a strong positive effect. This finding indicates that teachers\u0026rsquo; processes of appropriating and adapting digital tools are closely tied to the development of integrated digital teaching knowledge. From a theoretical perspective, this relationship reinforces the instrumental approach\u0026rsquo;s claim that knowledge emerges through sustained, goal-oriented interaction with artefacts as they are transformed into instruments for specific practices [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eEmpirically, this result is consistent with studies highlighting the role of design, experimentation, and reflective use of digital tools in developing teachers\u0026rsquo; pedagogical digital knowledge [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. In the Ghanaian educational system, where teachers often have access to digital tools but limited opportunities for sustained pedagogical experimentation, this finding highlights the importance of professional learning environments that support instrumental genesis rather than one-off training sessions. Without such opportunities, mathematics teachers\u0026rsquo; digital knowledge risks remaining fragmented or disconnected from instructional practice.\u003c/p\u003e \u003cp\u003eThis study contributes to mathematics education research by empirically elaborating the mathematical digital knowledge form teaching framework through the lens of the instrumental approach. The results highlight the need to conceptualise digital competence not as a static set of skills, but as an orientation-dependent and practice-mediated knowledge system. These findings suggest that efforts to strengthen mathematics teachers\u0026rsquo; digital competencies must simultaneously attend to orientations, opportunities for instrumentalisation, and the integrated nature of mathematical digital knowledge for teaching.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eThis study advances mathematics education research by empirically articulating how mathematics teachers\u0026rsquo; personal orientations toward technology, their personal and professional instrumental genesis, and their mathematical digital knowledge for teaching are systematically related. Anchored in the MDKT framework, the findings demonstrate that teachers\u0026rsquo; digital competencies cannot be adequately understood as a static set of skills or knowledge domains. Instead, it emerges through interrelated affective, cognitive, and instrumental processes. By showing that teachers\u0026rsquo; orientations significantly relate to both personal and professional instrumental genesis, and that these instrumental geneses, in turn, are associated with MDKT, the study offers empirical support for a relational and process-oriented account of teachers\u0026rsquo; digital knowledge for development in mathematics. This contribution extends prior MDKT research, which has largely remained descriptive, by providing evidence of coherent pathways linking dispositions, tool appropriation, and domain-specific digital knowledge.\u003c/p\u003e \u003cp\u003eThese results suggest that the effectiveness of technology integration in mathematics classrooms depends less on digital readiness alone and more on how teachers appropriate tools within teaching practices. In this sense, the study reframes digital competence as a developmental construct shaped by orientations and professional activity, thereby offering a theoretically integrated perspective relevant to both mathematics education research and policy.\u003c/p\u003e\u003ch1\u003eRECOMMENDATIONS\u003c/h1\u003e\n\u003cp\u003eBased on these findings, future professional development and policy initiatives should prioritise pedagogically grounded engagements with digital tools that support teachers\u0026rsquo; professional instrumental genesis, rather than focusing solely on technical proficiency or access. For researchers, longitudinal and classroom-based studies are needed to trace how changes in teachers\u0026rsquo; orientations and instrumental genesis correspond to shifts in enacted MDKT over time. Policy makers and teacher educators should design sustained, practice-oriented professional learning structures that connect digital tools to task design, student thinking, and instructional decision-making in mathematics. Such efforts are likely to foster more transferable forms of mathematical digital knowledge for teaching.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThe author did not receive support from any organisation for the submitted work.\u003c/p\u003e\n\u003ch2\u003eConflict\u003cem\u003es\u003c/em\u003e of interest\u003c/h2\u003e\n\u003cp\u003eThe author has no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003ch2\u003eEthics statement\u003c/h2\u003e\n\u003cp\u003eThe protocol was approved by the University of Cape Coast Institutional Review Board (UCCIRB/CES/2023/63) in accordance with the ethical guidelines for human subjects research.\u003c/p\u003e\n\u003ch2\u003eConsent to participate\u003c/h2\u003e\n\u003cp\u003eInformed written consent was obtained from all participants. Participation in the study was voluntary, and all teachers who did not consent were not included without any consequences.\u003c/p\u003e\n\u003ch2\u003eConsent to publish\u003c/h2\u003e\n\u003cp\u003eThe author agrees that the manuscript should be published in its current form.\u003c/p\u003e\n\u003ch2\u003eAcknowledgement\u003c/h2\u003e\n\u003cp\u003eI acknowledge my supervisor, Dr Forster D. Ntow, for supervising my MPhil thesis from which I wrote this manuscript. I also appreciate all the teachers who took the time to respond to the survey.\u003c/p\u003e\n\u003ch2\u003eData availability statement\u003c/h2\u003e\n\u003cp\u003eData for this study will be made available upon reasonable request. Please contact the corresponding author, Christian Kwame Kpotosu, at [email protected] to obtain access to the raw data analysed in the study.\u003c/p\u003e\n\u003ch2\u003eDual publication\u003c/h2\u003e\n\u003cp\u003eNo\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlqahtani, M. M., \u0026amp; Powell, A. B. (2017). Teachers\u0026rsquo; instrumental genesis and their geometrical understanding in a dynamic geometry environment. \u003cem\u003eDigital Experiences in Mathematics Education\u003c/em\u003e, \u003cem\u003e3\u003c/em\u003e, 9\u0026ndash;38. https://doi.org/10.1007/s40751-016-0025-5 \u003c/li\u003e\n\u003cli\u003eArdi\u0026ccedil;, M. A. (2021). Opinions and attitudes of secondary school mathematics teachers towards technology. \u003cem\u003eParticipatory Educational Research\u003c/em\u003e, \u003cem\u003e8\u003c/em\u003e(3), 136\u0026ndash;155.\u003c/li\u003e\n\u003cli\u003eBenning, I., Linsell, C., \u0026amp; Ingram, N. (2018). 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Teachers\u0026rsquo; instrumental geneses when integrating spreadsheet software. In: Clark-Wilson, A., Robutti, O., Sinclair, N. (eds)\u003cem\u003e The Mathematics Teacher in the Digital Era. Mathematics Education in the Digital Era, (vol 2, pp. 241\u003c/em\u003e\u0026ndash;\u003cem\u003e275). \u003c/em\u003eSpringer, Dordrecht. https://doi.org/10.1007/978-94-007-4638-1_11\u003cem\u003e \u003c/em\u003e\u003c/li\u003e\n\u003cli\u003eLiang, T., Su, Y., \u0026amp; Chen, C. (2016). A study of teachers\u0026rsquo; technology acceptance in the use of digital learning materials. \u003cem\u003eEducational Technology \u0026amp; Society, 19\u003c/em\u003e(2), 64\u0026ndash;76.\u003c/li\u003e\n\u003cli\u003eNational Council of Teachers of Mathematics (2011). \u003cem\u003eTechnology in teaching and learning mathematics. A position on the National Council of Teachers of Mathematics\u003c/em\u003e. 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ICT standards for teachers: Toward a frame defining mathematics teachers\u0026rsquo; digital knowledge. In \u003cem\u003eProceedings of the 5th ERME Topic Conference. Mathematics Education in the Digital Age\u003c/em\u003e (pp. 273\u0026ndash;280). https://www.math.ku.dk/english/research/conferences/2018/meda/proceedings/MEDA_2018_Proceedings.pdf \u003c/li\u003e\n\u003cli\u003eTabach, M., \u0026amp; Trgalov\u0026aacute;, J. (2020). Teaching mathematics in the digital era: Standards and beyond. In \u003cem\u003eSTEM Teachers and Teaching in the Digital Era\u003c/em\u003e (pp. 221\u0026ndash;242). Springer, Cham. https://doi.org/10.1007/978-3-030-19741-4_8\u003c/li\u003e\n\u003cli\u003eThomas, A., \u0026amp; Edson, A. J. (2018). Integrating mathematics teaching with digital resources: Where to begin? \u003cem\u003eAustralian Primary Mathematics Classroom, 23\u003c/em\u003e(2), 14\u0026ndash;19.\u003c/li\u003e\n\u003cli\u003eTrgalov\u0026aacute;, J., \u0026amp; Tabach, M. (2020). Bi-national survey on mathematics teachers\u0026rsquo; digital competences. In H.-G. Weigand, A. Clark-Wilson, A. Donevska-Todorova, E. Faggiano, N. Gr\u0026oslash;nbaek, et al. (Eds.), \u003cem\u003eProceedings of the Fifth ERME topic conference (ETC 5) on mathematics education in the digital age (MEDA)\u003c/em\u003e (pp. 117\u0026ndash;124). ERME. https://hal.science/hal-02500112 \u003c/li\u003e\n\u003cli\u003eYao, X. (2020). Preservice mathematics teachers\u0026apos; instrumental genesis and their development of geometric knowledge in a dynamic geometry environment. \u003cem\u003eInternational Journal for Technology in Mathematics Education\u003c/em\u003e, \u003cem\u003e27\u003c/em\u003e(4).191\u0026ndash;206. https://doi.org/10.1564/tme_v27.4.02 \u003c/li\u003e\n\u003cli\u003eZambak, V. S., \u0026amp; Tyminski, A. M. (2017). A case study on specialised content knowledge development with dynamic geometry software: The analysis of influential factors and technology beliefs of three pre-service middle grades mathematics teachers. \u003cem\u003eMathematics Teacher Education and Development\u003c/em\u003e, \u003cem\u003e19\u003c/em\u003e(1), 82\u0026ndash;106.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","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":"Instrumental geneses, Mathematical digital knowledge, personal orientations, Technology","lastPublishedDoi":"10.21203/rs.3.rs-8450960/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8450960/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe practical implementation of technology in the mathematics curriculum for senior high schools is contingent upon teachers\u0026rsquo; dispositions, encompassing their perceptions, beliefs, and attitudes toward technology use, as well as their instrumental orientation. Despite widespread investments in digital technologies for schooling, mathematics teachers\u0026rsquo; use of technology often remains pedagogically limited, raising questions about how digital teaching knowledge develops. Drawing on the instrumental approach and the Mathematical Digital Knowledge for Teaching (MDKT) framework, this study examined how teachers\u0026rsquo; personal orientations toward technology and their instrumental genesis shape MDKT. Survey data were collected from senior high school mathematics teachers in Ghana and analysed using partial least squares structural equation modelling. Results show that teachers\u0026rsquo; personal orientations have significant positive effects on both instrumental genesis and MDKT. Instrumental genesis also strongly predicts MDKT, indicating that sustained appropriation of digital tools is central to developing integrated mathematical digital teaching knowledge. The model explains sustained variance in MDKT, suggesting that digital teaching competence emerges from the interaction between orientations and tool use rather than from access or technical skill alone. The findings extend prior descriptive work and highlight mechanisms critical for supporting meaningful technology integration in mathematics education.\u003c/p\u003e","manuscriptTitle":"Investigating the influences of mathematics teachers’ personal orientations and instrumental genesis on their mathematical digital knowledge for teaching","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-05 18:53:03","doi":"10.21203/rs.3.rs-8450960/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":"28cfada5-3a92-4dbc-aeb4-cebc96734848","owner":[],"postedDate":"February 5th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-11T15:26:55+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-05 18:53:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8450960","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8450960","identity":"rs-8450960","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}