Teacher competence in inclusive mathematics education: Examining the effects of an innovative professional development program on teacher noticing

Teacher competence in inclusive mathematics education: Examining the effects of an innovative professional development program on teacher noticing | 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 Teacher competence in inclusive mathematics education: Examining the effects of an innovative professional development program on teacher noticing Anton Bastian, Johannes König, Natalie Ross, Isabelle Klee-Schramm, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5752892/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Aug, 2025 Read the published version in ZDM – Mathematics Education → Version 1 posted You are reading this latest preprint version Abstract This study investigated the effects of an innovative professional development program aimed at enhancing teacher noticing skills and professional knowledge in inclusive (mathematics) education in secondary algebra instruction. A total of 653 participants, comprising master’s students, teachers in preparatory service, and in-service teachers from Germany, participated in a pretest–posttest evaluation design that included a control group. The program comprised 18 hours of coursework that integrated novel teaching materials and video-based learning activities that combined both mathematics pedagogical and general pedagogical perspectives on teacher noticing and associated knowledge. The results indicated significant improvements in teachers’ noticing skills and professional knowledge for the intervention group across all investigated facets, particularly for teacher noticing under a pedagogical perspective and mathematics pedagogical knowledge, compared to a control group that exhibited no significant changes. Effect sizes ranged from small to medium, suggesting that the professional development program effectively improved participants’ knowledge of inclusive teaching and their abilities to perceive, interpret, and make decisions in inclusive contexts. Notably, master’s students exhibited the most substantial gains in all competencies, while in-service teachers primarily improved their teacher noticing from a pedagogical perspective. The findings underscore the importance of tailored professional development for fostering teacher noticing in inclusive mathematics education and yield valuable insights into the competencies necessary for inclusive (mathematics) education. Educational Psychology Special Education Inclusive education teacher noticing professional development teacher competence professional knowledge secondary algebra instruction Figures Figure 1 Figure 2 1 Introduction Since the United Nations General Assembly adopted the convention on the rights of persons with disabilities (United Nations, 2006 ), inclusive education and diversity-sensitive teaching have been identified as key challenges and goals for education systems worldwide. Teachers’ competencies play a crucial role in shaping educational practice and achieving an education that meets all students’ needs (European Agency for Development in Special Needs Education, 2012 ). To teach classes with diverse students who have varying content-specific and interdisciplinary skill levels and individual needs across a wide range of content with multiple representations and approaches, teachers require professional knowledge about subject-specific and general inclusive education and situation-specific skills to apply and translate their knowledge into successful classroom performance (Keppens et al., 2019 ; König et al., 2019 ). The conceptualization, measurement, and—particularly—development of teachers’ competencies for inclusive education is thus a central issue for education researchers and policy makers (Fränkel et al., 2023 ; König et al., 2019 ). Teachers require both general pedagogical and subject-specific perspectives on inclusive education to diagnose and support all students according to their individual needs (König et al., 2019 ; Moser Opitz, 2022 ) and to comprehensively conceptualize, measure, and develop teacher competencies for subject-specific inclusive education. Herein, therefore, we focus on inclusive mathematics education (IME), given the need for subject-specific professional development (PD) programs that prepare teachers for the challenges of inclusive education. However, subject-specific conceptualizations of IME are scarce, as are measurement instruments for teacher noticing and professional knowledge in IME and PD programs for secondary education in this area, despite the urgent need for such programs (Scherer et al., 2016 ; Weyers et al., 2023 ). Even fewer studies have examined the effectiveness of their PD program for IME to ensure evidence-based professional development measured with standardized assessments. The Teacher Education and Development Study - Inclusive Mathematics Education (TEDS-IME) project from the TEDS research program addresses this research gap on two levels: on a practical level by developing an innovative PD program that aims at the development of teacher noticing for IME and on a theoretical level by conceptualizing and assessing teacher noticing (and professional knowledge as an influencing factor) for IME using the example of secondary algebra instruction for all phases of teacher education in Germany—higher education at universities, practical teacher training (known as preparatory service or induction phase), and elective PD for in-service teachers. Below, we present the initial results of a pretest–posttest evaluation of a PD program. In particular, we explore (1) changes in the participants’ teacher noticing skills and professional knowledge compared to the control group and (2) influences, such as participants’ and PD characteristics, on these changes. 2 Literature survey, theoretical framework, and research questions 2.1 Inclusive (mathematics) education Current discourse conceptualizes inclusive education heterogeneously, based on legal, cultural, and social influences and resulting in different normative understandings of what constitutes inclusion (Grosche, 2015 ). Göransson and Nilholm ( 2014 ) identified four different conceptualizations of inclusion: (1) placing students with special needs in regular classrooms, (2) addressing these students’ social and academic needs, (3) addressing all students’ social and academic needs, and (4) the creation of specific communities. Piezunka et al. ( 2017 ) conceptualized a spectrum encompassing the non-discrimination of individuals with special needs, individualized support for all students to pragmatically develop student achievement or facilitate well-being, and inclusion as a utopia of noncategorical thinking. Both systematizations highlight the tension between narrower definitions focused on students with disabilities and broader definitions focusing on all students and their diverse individual backgrounds and the creation of inclusive communities. This tension is reflected in the current mathematics educational discourse, with studies on inclusion ranging from focusing on specific diagnoses or students with disabilities to examining the effects of interventions on students with differing prerequisites (Adeniji & Baker, 2023 ; Long et al., 2021 ). 2.2 Teacher competence for inclusive (mathematics) education Over the last two decades, researchers have reached the consensus that teacher competence may be understood as a multifaceted construct comprising a body of dispositions (professional knowledge and beliefs) and situation-specific skills mediating dispositions and classroom performance (Blömeke et al., 2015 ; Kaiser et al., 2017 ; Krauss et al., 2020 ). Mathematics education research often defines professional knowledge with reference to Shulman ( 1987 ), differentiating it into mathematics content knowledge (MCK), mathematics pedagogical content knowledge (MPCK), and general pedagogical knowledge (GPK) or comparable differentiations (Kaiser et al., 2017 ; Krauss et al., 2020 ). The teacher noticing construct, sometimes termed “professional vision,” was originally introduced to promote student-centered teaching by attending to and making sense of instructional events (Sherin et al., 2011 ; van Es & Sherin, 2002 ) and was later included as a situation-specific dimension in a framework of teacher competence by Blömeke et al. ( 2015 ) with the facets perception, interpretation, and decision-making in instructional settings. Although the specific definitions vary, conceptualizations of teacher noticing often include perceptual and interpretive facets and are increasingly complemented with a decision-oriented facet or even the decision’s enactment (Dindyal et al., 2021 ; König et al., 2022 ; Sherin et al., 2011 ; Thomas et al., 2020 ). Comprehensive competence frameworks specifically addressing inclusive education in general or IME in particular remain scarce, particularly for secondary education. Studies sometimes include a general conceptualization of teacher competence in the context of inclusive education without any adaption for its specific requirements (Pit-ten Cate et al., 2018 ). However, some competence catalogues and practice descriptions have been produced. Prediger and Buró ( 2024 ) identified 133 productive and unproductive practices in IME, structured within a framework of five demands: identifying learning prerequisites and assessing students’ abilities, differentiating learning goals, compensating for limited abilities, enhancing abilities, and organizing collaborative learning. König et al. ( 2019 ) review distinguishes four demands of inclusive education: diagnosis, intervention and support, management and organization, and counseling and communication, of which the first two are most relevant to teaching itself. Diagnosis entails recognizing students’ skills and possible learning difficulties in addition to (formative) assessment. It may be understood as an aspect of perceiving and interpreting classroom events and thus of teacher noticing (Heinrichs & Kaiser, 2018 ; König et al., 2019 ). Intervention and support include all pedagogical and methodological means for individualization and negotiating heterogeneity, their successful use, and the associated challenges for classroom management and lesson structure. Intervention can thus be regarded as part of the interpretation and decision-making facets of teacher noticing (König et al., submitted). Hence, as diagnostic competencies, such as diagnosis, and individual support can also be considered domains of teacher noticing, its development is particularly relevant to IME (Heinrichs & Kaiser, 2018 ; König et al., 2019 ; König et al., submitted; Leuders et al., 2018 ). However, no PD programs for IME specifically address teacher noticing. Overall, teacher noticing has rarely been linked to IME, and even less so using standardized assessment methods, as highlighted in the literature reviews by König et al. ( 2022 ) and Weyers et al. ( 2023 ). An exception is the work by Keppens et al. ( 2019 ) and colleagues, who conceptualized teacher noticing of teacher-student interactions and differentiated instruction as two aspects of inclusive education and developed two comparative judgment-based test instruments for primary and secondary education. They identified connections between high proficiency in teacher noticing for inclusive education in both investigated aspects and the implementation of inclusive teaching practices (Gheyssens et al., 2021 ). Other studies have adopted a more comprehensive conceptualization of inclusive education, focusing on the differences between teacher noticing in inclusive and special needs schools (Smit et al., 2024 ) or on the development of teacher noticing skills in co-teaching (Meadows & Caniglia, 2018 ) but without using standardized testing. Research that uses standardized testing to comprehensively examine teacher noticing for inclusive education in general, particularly for IME with the consideration of subject-specific aspects, remains a desideratum. 2.3 Professional development for inclusive (mathematics) education PD programs are essential interventions for translating research findings into classroom practice and impacting student achievement (Desimone, 2009 ; Prediger et al., 2022 ). However, PD for IME and inclusive education in general has hitherto focused on primary education, with few programs targeting secondary education. The project Mathilda - Learning to teach mathematics inclusively , aimed at developing teachers’ skills to teach a unit on understanding percentages inclusively considering the diverse needs of all students (Prediger et al., 2020 ), is a rare example. The program entailed collaborative coursework and testing of materials in teachers’ own teaching. Kuhl et al. (2022) demonstrated the PD program’s intervention effects at the student level through increased learning gains without considering possible teacher learning gains. To the best of our knowledge, PD programs for other core topics in the secondary mathematics curriculum and evidence-based evaluations of the effects of PD on teacher competence for IME are still lacking and possible influences on these programs’ effects have not been investigated. Overall, PD programs’ effects on teacher competence and especially teacher noticing and in-service teachers are seldom examined (Amador et al., 2021 ; König et al., 2023 ; König et al., 2022 ; Yoon et al., 2007 ). 2.4 Study framework Shaped by our research interest and the literature review, we define inclusive education with reference to Piezunka et al. ( 2017 ) as the best possible academic support for all students—considering their learning needs—to achieve the best possible individual learning outcome, thus adopting a broad understanding of inclusion with a focus on learning achievement. We focus on diagnosis and intervention as two main demands of IME and conceptualize them as part of teacher noticing (Kaiser et al., 2017 ; König et al., 2019 ). We analytically conceptualize teacher noticing as having three facets: perceiving instructional events, interpreting the perceived events, and making decisions about the events—for example, deciding on the lessons’ progress or proposing alternative instructional strategies (Kaiser et al., 2015 ). We understand teacher noticing for IME as combining a subject-specific perspective (M_PID-IT: teaching under a mathematics pedagogical perspective for inclusive teaching: perception, interpretation, decision-making) and a general pedagogical perspective (P_PID-IT: teaching under a general pedagogical perspective for inclusive teaching: perception, interpretation, decision-making) to facilitate comprehensive measurement and PD of teachers’ skills. Teacher noticing constitutes one part of teacher competence for IME. We also include professional knowledge as a foundational influencing factor for teacher noticing and thus diagnosis and intervention. Following Shulman ( 1987 ), we consider MPCK for inclusive teaching (MPCK-IT) and GPK for inclusive teaching (GPK-IT). For the PD program, we focus on algebra as a core secondary mathematics topic that poses several comprehension barriers for students. Additionally, possible student errors and difficulties as well as sustainable basic mental models have already been researched through subject-specific analysis (Korntreff & Prediger, 2021 ; Malle, 1993 ). However, despite its relevance for the students’ learning trajectories, few PD programs address this topic, particularly regarding inclusive teaching. To facilitate teachers’ learning, two demands of IME—diagnosis and intervention—are complemented by the identification of learning needs as a third demand and an important prerequisite for the others (König et al., 2019 ; Prediger & Buró, 2024 ). Four of the five prerequisites for successful learning as identified by Hasselhorn and Gold ( 2022 )—prior knowledge, selective attention and working memory, learning strategies and metacognitive regulation, and motivation and self-concept—are included as pedagogical categories and linked to algebra to combine subject-specific and interdisciplinary approaches. 2.5 Research questions Based on the research gaps identified in our literature review and theoretical framework, this study aims to develop measurement instruments for teacher noticing and professional knowledge for IME and to use these instruments to evaluate an innovative PD program for secondary IME in the field of algebra education from the TEDS-IME project. The study is guided by the following research questions: (1) To what extent do the facets of pre-service and in-service teachers’ noticing and professional knowledge change over the course of the PD program? a. Can the changes be validated in comparison to a control group? b. How do these changes differ between the three experience groups that participated in the PD program? (2) To what extent do participants’ characteristics, differential use of opportunities to learn, evaluation of the PD program, and prior knowledge and skills influence the change in skills? 3 Methodological approach 3.1 Study design In the TEDS-IME project, we developed an innovative PD program for IME focusing on algebra instruction and administered it to three experience groups corresponding to the teacher education phases—master students, teachers in preparatory service, and in-service teachers—in four German federal states. To evaluate the PD program, we tested the participants’ competencies in a pre–post-follow-up design using a control group to control for the program’s effects. Herein, we focus on the teacher noticing and professional knowledge tests at the pre- and posttest stages (see Fig. 1 ). The intervention group engaged in the program over four to six months and took the pretest survey at the program’s beginning and the posttest after the last content unit. Following a similar timeframe, teachers in the control group took a pretest and posttest survey with a reduced competence test consisting only of the teacher noticing tests, since it was necessary to reduce the testing time to convince teachers to participate without the incentive of a PD program. 3.2 Sample The sample comprises 653 pre-service and in-service teachers (master students: n = 241, teachers in preparatory service: n = 169, in-service teachers: n = 243) with 539 participants in the intervention group and 114 participants in the control group. Table 1 presents the descriptive statistics. The intervention and control groups show no differences in gender, age, and teaching experience duration but differ significantly with respect to teaching type, with more academic-track teachers in the control group and high school diploma grade, with a higher grade mean for the control group. Both variables are associated with higher levels of teacher competence (Kleickmann et al., 2013 ), favoring the control group. This must be considered when comparing the groups. For the intervention group, the three experience groups exhibit significant differences in age and teaching experience by design. Moreover, teaching type and high school diploma grade vary significantly, both in favor of the master students ( p < .001 and F (2, 624) = 336.3, p < .001; full descriptive statistics are provided in the electronic supplemental material (ESM)). This is also considered in the analysis and discussion. Table 1 Descriptive characteristics of the intervention and control group Variable Condition Test of group differences c Intervention group Control group Sample size 539 114 Gender (% female) 64.4 58.8 p = .565 Teaching type a (% academic) 44.1 68.1 p < .001 M SD M SD Age (in years) 32.6 10.1 30.9 11.3 t (154) = -1.45, p = .149 Teaching experience (in years) 5.1 7.5 6.1 10.2 t (140) = .95, p = .342 Grade (Abitur) b 2.10 .64 1.96 .64 t (165) = -2.02, p = .045 Note. a This variable was dichotomously coded in 0 – non-academic-track school and 1 – academic-track school (Gymnasium). b The German high school diploma that qualifies for university admission. Grades rage from 1 (best) to 4 (pass). c Fisher’s exact test was conducted for nominal data; t-tests were used for metric data. 3.3 Assessment instruments 3.3.1 Teacher noticing To measure teacher noticing for IME, we developed an innovative standardized video-based instrument that assesses teachers’ abilities to perceive, interpret, and make decisions in inclusive secondary algebra education from a mathematics pedagogical perspective (M_PID-IT) and a general pedagogical perspective (P_PID-IT) based on the established TEDS-FU video instrument (Kaiser et al., 2015 ; König et al., submitted). The instrument comprises four scripted (i.e., staged) video vignettes ranging from 2.45 to 4.00 minutes and covering a wide range of algebraic topics, including variables, algebraic terms, and equations as well as instructional phases, such as group exploration or review of students’ work. In addition, the classroom situations include students at varying levels of learning prerequisites, including those who lack prerequisites such as the necessary prior knowledge to achieve the lesson’s objectives and those who do have sufficient prerequisites. The video vignettes were developed in close collaboration with experienced teachers and experts in IME to simulate authentic typical classroom situations. Each participant worked on three randomly selected video vignettes administered in a random incomplete test design. For each vignette, participants first received contextual information about the class, such as grade level and school type, the current lesson, such as the lesson’s objective and topic, and the task addressed. They were then permitted to watch the vignette once to simulate a corresponding classroom situation. Participants responded to open-response and Likert-type rating scale items that test their skills in perception, interpretation, and decision-making. In total, the test comprised 63 items, divided into M_PID-IT ( n = 32) and P_PID-IT ( n = 31) items, and takes 60 minutes to complete. Each item was additionally related to diagnosis ( n = 27) or intervention ( n = 36). Extensive expert ratings were conducted with 47 experts to determine correct responses for each item and to ensure a high-quality instrument. For open-response items, we developed a comprehensive coding manual with sample responses from a pilot study and detailed descriptions of correct responses to ensure reliability and validity. Coders were extensively trained and achieved good overall interrater reliability in double coding of 10% of the answers to open-response items at T1 (κ: M = .77). All rating scale and open-response items were scored dichotomously. The ESM presents example items and an example vignette. 3.3.2 Professional knowledge To assess teachers’ knowledge of IME as an influencing factor of teacher noticing, we developed a two-dimensional instrument with items focusing on MPCK-IT or GPK-IT. MPCK-IT comprises questions on algebra pedagogy, such as basic mental models of variables and functions, and items on more general topics, including conceptual understanding or language-sensitive mathematics instruction. For GPK-IT, the items cover learning processes, diagnosis, classroom management, structuring, and individualization/differentiation. Overall, the items include selected and partially adapted items from previous studies, including the MPCK instrument from TEDS-M (Blömeke et al., 2014 ) and the GPK-IT test from König et al. ( 2019 ), as well as newly developed items. This resulted in 50 single- or multiple-choice items (MPCK-IT: n = 37, GPK-IT: n = 13) and a test duration of 25 minutes. All items were scored dichotomously. The ESM presents example items. 3.3.3 Further instruments Demographic data and personal characteristics, such as age, gender, experience duration, and teaching type, were collected at T1. At T2, we used an additional questionnaire with the intervention group to inquire about the number of opportunities to learn (OTL) to account for differences in participation frequency using a dichotomous scale and the intensity of OTL use using a four-point Likert scale (see ESM for examples). Scales were constructed using mean scores (OTL: M = .86, SD = .19, intensity of OTL use: M = 2.79, SD = 0.47). The extent of each PD group was collected as a level two variable since the PD extent varied for organizational reasons and not all groups could complete all PD units. We also asked participants to rate their overall experience of the program on a scale from 1 - very bad to 6 - very good ( M = 4.89, SD = 0.95). 3.4 PD Program To support teachers in dealing with the identified IME demands—identifying, assessing/diagnosing and supporting/facilitating learning requirements—we developed a PD program with an interdisciplinary team of experts in mathematics education, educational science, and special education. The program’s development was guided by the principles of evidence-based effectiveness, with a particular focus on teacher competence growth (Desimone, 2009 ). The program comprises 18 hours of coursework over a four- to six-month period, ensuring in-depth coverage of the selected topics and long-term engagement. To maintain high quality implementation, we carefully selected PDs’ facilitators, trained them extensively, and provided ongoing support throughout the program. At the content level, the PD program follows central algebra topics with units on equivalence transformations, term equivalence, finding and describing algebraic terms, and comparing aspects of the variable concept (see Fig. 2). In these units, the prerequisites for successful learning as defined by Hasselhorn and Gold ( 2022 ), are addressed successively in addition to the mathematics pedagogical content. Following the demands of IME, for each of these prerequisites, teachers first have the opportunity to identify the respective learning requirements for specific instructional situations and materials in algebra education so that these can then be used as categories for the subsequent PD activities on diagnosis and intervention and, thus, professional knowledge and teacher noticing (König et al., 2019 ). Figure 2 Overview of the PD and its topics Note . The pretest was conducted at the beginning of unit 1, the posttest at the end of unit 6. IME – inclusive (mathematics) education. The program’s participants are first confronted with the widespread differentiation approach of altering cognitive demand (in terms of technical complexity) and recognize why this approach falls short in IME. This motivates them to master the more complex requirements of facilitating learning at different prerequisite levels for all students on the same teaching objects and objectives. To promote the use of different learning goals for individual students and their connection within a common learning object, an adapted version of Siemon’s ( 2021 ) concept of learning trajectories is introduced. Further, teachers and facilitators approach newly developed or adapted teaching materials that allow them to reconstruct the materials’ underlying basic mental models and to build linkages of representations that promote conceptual understanding. On this basis, teachers can then construct learning trajectories for individual students. Given the highly complex nature of this process, we introduce four example students who symbolize four significant levels of prior knowledge for the learning of each new concept and who are used systematically in each unit. The teachers then create learning trajectories for these four students. To further support a change in teachers’ attitudes about the importance of understanding basic principles and mental models while considering different levels of prior knowledge, the algebraic topics were ordered as moving backward through the curriculum from equivalence equation transformation to aspects of variables, allowing the identification of important prior knowledge first followed by how it should be taught and learned. The interdisciplinary learning prerequisites, such as selective memory and attention, are introduced after the first unit (see Fig. 2) and are initially approached in isolation but are thereafter treated in close connection with subject-specific aspects. All contents of the PD program are covered by specific teaching materials and learning and teaching situations presented by video or text vignettes, not only to promote professional knowledge but also to facilitate the development of teacher noticing. The use of various methods aims at a high level of cognitive activation as regards the program’s learning objectives. 3.5 Data analysis 3.5.1 Data scaling We scaled the data from the teacher noticing and knowledge instrument using ConQuest 5.39 software (Adams et al., 1997–2024) and using two-dimensional Rasch models for both teacher noticing and professional knowledge. Weighted likelihood estimates (WLEs) were then used to create ability scores for M_PID-IT, P_PID-IT, MPCK-IT, and GPK-IT. All models reached acceptable to good reliability and showed sufficient variance (Table 2 ). Sub-dimensions showed high correlations (M_PID-IT and P_PID-IT: r = .86, MPCK-IT and GPK-IT: r = .77) but were distinguishable, as shown by model comparison by König et al. (submitted). Table 2 Statistics for the competence measures based on two two-dimensional models Competence measure EAP reliability WLE reliability Variance Weighed mean squares (min – max) Discrimination (mean; min – max) M_PID-IT .71 .59 .34 0.91–1.13 .28; .08 – .46] P_PID-IT .71 .61 .42 MPCK-IT .76 .70 .52 0.86–1.11 .32; .16 – .53 GPK-IT .68 .53 .49 Note . EAP – expected as posteriori. WLE – Weighted likelihood estimates. 3.5.2 Multiple data imputation Given that listwise exclusion of cases with missing values is considered statistically inadequate for analyzing longitudinal data (Asendorpf et al., 2014 ), we used multiple imputation to avoid biases due to systematic panel attrition. The average percentage of missing data was 21.7%, ranging from no missing data for the experience group and gender to 52.7% for MPCK-IT and GPK-IT scores at T2. Following Graham et al. ( 2007 ) recommendations and accounting for the imputation uncertainty, we generated 100 datasets in which all missing data were imputed with plausible values using the statistical software R version 4.4.1 (R Core Team, 2024 ) and its packages mice (van Buuren & Groothuis-Oudshoorn, 2011 ) und mitml (Grund et al., 2023 ). To impute each variable, predictors from a pool of all investigated variables, such as noticing and knowledge scores, and auxiliary variables, such as teaching type and high school diploma grade, were included if they correlated with the respective variable with at least r = .10 (see the ESM). The PD group was used as a cluster variable for the imputation. For each analysis, the 100 imputed datasets were analyzed separately and then pooled with Rubin’s rule to achieve the combined results reported herein. 3.5.3 Analysis methods To address the first research question concerning changes in teachers’ competencies over the course of the program against the control group and experience group-specific differences, we computed descriptive statistics, paired sample t-tests, and the effect size Cohen’s d for within-subjects design for the intervention and control group as well as experience group-specific statistics for the intervention group. The t-test results were corrected for multiple testing using the Bonferroni–Holm method. To further investigate differences between the intervention and control groups, we calculated a linear mixed model with the PD group as a cluster variable and modeled the interaction effect of measurement time and condition (i.e., intervention or control group) for M_PID-IT and P_PID-IT. Teaching type and grade were controlled to account for differences between the conditions. For the second research question, we used multiple regression analysis with the intervention group as a subset to examine the effect of possible predictors on T2 ability scores while controlling for T1 scores and examining the changes in each. The PD group was introduced as a cluster variable, since intraclass correlation revealed a significant proportion of variance on cluster level (M_PID-IT (T2): ICC = .15, P_PID-IT (T2): ICC = .15, MPCK-IT (T2): ICC = .17, GPK-IT (T2): ICC = .12). To examine possible changes in influence when including other predictors, we computed four models for each ability score at T2. First, we considered only the T1 ability score, grade, and teaching type as control variables (M1). We then included the experience group membership as a level two predictor (M2). In two further models, we added PD-related characteristics (M3), such as OTL, and all prior knowledge and skills—that is, all professional knowledge and teacher noticing scores at T1 (M4). 4 Results 4.1 Effects of the PD program on teacher noticing and professional knowledge To address the first research question and its sub-questions, we analyzed the mean ability scores by group and conducted t-tests. Table 3 presents the mean ability scores of the intervention and control group for all investigated competence facets and t-test comparisons of T1 and T2. The knowledge tests’ scores tended to be higher than the teacher noticing scores, suggesting a higher level of knowledge than situation-specific skills in the sample. The intervention group’s T2 results were significantly higher than at T1 for all tests with the greatest effects for P_PID-IT ( d = 0.31) and MPCK-IT ( d = 0.28) with small effect sizes, providing first indicators for the program’s effectiveness. Table 3 Mean scores of professional knowledge and teacher noticing skills at each measurement time Test T1 T2 t ( df ) p Cohen’s d M SD M SD Intervention group ( n = 539) M_PID-IT 45.9 8.1 47.1 8.4 -2.52 (190) .019 0.14 P_PID-IT 48.2 8.2 50.7 8.4 -6.30 (222) < .001 0.31 MPCK-IT 56.6 8.4 58.9 8.3 -5.88 (185) < .001 0.28 GPK-IT 55.0 9.8 56.7 9.0 -3.39 (209) .002 0.18 Control group ( n = 114) M_PID-IT 46.4 7.1 47.2 7.7 -1.02 (83) .312 0.11 P_PID-IT 51.1 7.1 51.7 7.5 -0.80 (86) .312 0.09 Note . To facilitate reading, WLE ability estimates were linearly transformed by multiplying by 10 and adding 50. All p-values were corrected for multiple testing using the Bonferroni–Holm method. The control group only participated in the M_PID-IT and P_PID-IT tests. For the control group, no significant change was found for all investigated competence facets (M_PID-IT and P_PID-IT), substantiating the improvements observed in the intervention group. To further investigate whether the differences between the significant increases in the intervention group and the nonsignificant results in the control group were themselves significant, we examined the interaction effect of measurement time and condition while controlling for grade and teaching type. The regression model (full model results in the ESM) demonstrated a significant small interaction effect for P_PID-IT (β = .23, t (1929) = 2.2, p = .027), while no interaction effect was observed for M_PID-IT (β = .04, t (1282) = 0.3, p = .749). Thus, the increase in P_PID-IT in the intervention group was significant compared to the control group, while the difference between the significant improvement in the intervention group and lack of increases in the control groups in M_PID-IT was not in itself significant. To examine the program’s effectiveness according to experience group, we analyzed the means for each experience group of the intervention group (see Table 4 ). Master students significantly increased all investigated knowledge and teacher noticing facets with small to medium effect sizes and the largest improvement in MPCK-IT ( d = 0.50). By contrast, teachers in preparatory service showed improvement only for P_PID-IT ( d = 0.40) and MPCK-IT ( d = 0.28), and in-service teachers demonstrated significant growth only for P_PID-IT ( d = 0.20) with small effect sizes. This indicates that the PD program particularly affected the master students, while only an increase in teacher noticing from a pedagogical perspective could be achieved for all experience groups. Table 4 Mean scores of professional knowledge and teacher noticing skills for each experience group of the intervention group at each measurement time Test T1 T2 t ( df ) p Cohen’s d M SD M SD Master students ( n = 179) M_PID-IT 46.49 7.11 49.26 7.49 -4.19 (118) < .001 0.38 P_PID-IT 50.37 6.84 53.08 7.42 -4.85 (126) < .001 0.38 MPCK-IT 57.17 7.37 60.81 7.13 -6.29 (110) < .001 0.50 GPK-IT 55.71 9.66 58.16 8.28 -3.03 (114) .012 0.27 Teachers in preparatory service ( n = 162) M_PID-IT 46.94 8.81 47.18 8.78 -0.27 (63) .568 0.03 P_PID-IT 47.96 8.65 51.42 8.51 -4.29 (72) < .001 0.40 MPCK-IT 57.16 8.86 59.64 8.75 -3.08 (62) .012 0.28 GPK-IT 55.57 9.51 56.98 9.44 -1.64 (73) .252 0.15 In-service teachers ( n = 198) M_PID-IT 44.59 8.09 44.96 8.38 -0.57 (118) .568 0.04 P_PID-IT 46.35 8.37 48.00 8.31 -2.59 (140) .031 0.20 MPCK-IT 55.53 8.86 56.61 8.37 -1.66 (93) .252 0.12 GPK-IT 53.93 10.17 55.07 8.93 -1.37 (92) .262 0.12 Note . To facilitate reading, WLE ability estimates were linearly transformed by multiplying by 10 and adding 50. All p-values were corrected for multiple testing using the Bonferroni–Holm method. 4.2 Influences on the changes in professional knowledge and teacher noticing To investigate possible influences on the changes in our PD program and to address the second research question, we calculated four regression models for each ability score at T2 while controlling for the score at T1 to focus on the ability changes (see Table 5 ). Autocorrelations for M_PID-IT ( r = .56), P_PID-IT ( r = .60)., MPCK-IT ( r = .66), and GPK_IT ( r = .57) were moderate, indicating stable overall constructs but also highlighting variations and, thus, possible PD-induced changes (correlations between the competence facets at T1 and T2 and possible predictors can be found in the ESM). Autoregressive paths also showed moderate to large influences of T1 ability scores on the respective ability scores at T2 that were reduced only when all other professional knowledge and teacher noticing scores were included in M4 (see Table 5 ). Overall, a significant proportion of variance could be explained by each regression model as qualified by coefficients of determination values. First, we focused on high school diploma grade (Abitur) and teaching type (M1). Regression analysis demonstrated a significant influence of the grade for both teacher noticing skills but not for professional knowledge that vanished when considering experience group and prior knowledge and skills. Teaching type consistently predicted scores only for MPCK-IT with a small effect size, attesting that teachers from academic-track schools were better able to use the PD to develop their MPCK-IT. In a second model (M2), we added the experience group as a predictor using two dummy variables. In line with the mean comparisons, in-service teachers exhibited significantly less change in M_PID-IT, P_PID-IT, and MPCK-IT than master students did, while teachers in preparatory service did not differ from master students when controlling for grade, teaching type, and ability score at T1. We then introduced OTL, intensity of OTL use, program extent, and program evaluation. However, no significant prediction of these variables was observed for all ability scores. Thus, the PD program’s investigated characteristics could not explain the changes in participants’ professional knowledge and teacher noticing skills. In a final step, we added all ability scores at T1 (M4). This reduced the autoregressive coefficient due to shared variance, although considerable autoregressive prediction remained. For M_PID-IT, all other ability scores significantly predicted the change in M_PID-IT with small regression coefficients. M_PID and MPCK-IT at T1 significantly influenced the changes in P_PID-IT, while GPK-IT did not. In terms of prior knowledge and skills, changes in MPCK-IT were predicted only by itself and M_PID-IT and changes in GPK-IT were predicted only by itself and MPCK-IT. Table 5 Multiple regression models for M_PID-IT, P_PID-IT, MPCK-IT, and GPK-IT at T2 Variable M_PID-IT (T2) P_PID-IT (T2) MPCK-IT (T2) GPK-IT (T2) M1 M2 M3 M4 M1 M2 M3 M4 M1 M2 M3 M4 M1 M2 M3 M4 β β β β β β β β β β β β β β β β Grade (Abitur) − .12* − .11* − .11* − .05 − .13** − .12* − .12* − .05 − .03 − .01 − .01 .02 − .07 − .06 − .06 .01 Teaching type .22* .20 .19 .11 .14 .12 .12 .03 .23* .22* .22* .20* .09 .08 .08 − .02 TPS − .24 − .22 − .17 .00 .00 − .08 − .09 − .08 − .08 − .11 − .08 − .11 IST − .31* − .32* − .25 − .26* − .25* − .28** − .31** − .29** − .24* − .21 − .21 − .19 OTL .04 .03 − .04 − .02 − .06 − .04 .00 .01 OTL-int − .01 .01 .02 .03 .00 .01 .02 .03 Program extent .01 .01 − .01 − .01 .03 .04 .06 .05 Program eva .07 .06 .04 .02 .03 .03 .01 .00 M_PID-IT (T1) .49*** .49*** .49*** .27*** .22*** .19*** .08 P_PID-IT (T1) .23*** .55*** .54*** .54*** .42*** .08 .03 MPCK-IT (T1) .21*** .17** .60*** .61*** .60*** .48*** .27*** GPK-IT (T1) .13* − .03 .06 .53*** .53*** .53*** .40*** R 2 .35 .36 .37 .48 .40 .41 .42 .49 .46 .48 .48 .53 .34 .34 .35 .42 Note . * – p < .05, ** – p < .01, *** – p < .001. TPS – teachers in preparatory service (dummy variable with master students as reference). IST – in-service teachers (dummy variable with master students as reference). OTL – opportunities to learn. OTL-int – intensity in the use of opportunities to learn. Program eva – Program evaluation. 5 Discussion and limitations 5.1 Summary and discussion This study examined the effects of an innovative PD program aimed at promoting teacher noticing skills and professional knowledge for IME of master students, teachers in preparatory service, and in-service teachers in secondary algebra education. The comprehensive 18-hour PD program included newly developed instructional materials and video-based learning activities to introduce participants to teaching that enables all students to learn from the same learning object and that considers both mathematics pedagogical and general pedagogical perspectives on inclusive teaching. We used extensive, mainly video-based instruments to assess teacher competence with reliable scales that also combined subject-specific and pedagogical perspectives and were based on a comprehensive understanding of IME. For the intervention group, teacher noticing and professional knowledge increased significantly in the mathematics pedagogical and general pedagogical domains, while the control group showed no significant changes. Although some of the effect sizes were small, these findings must be emphasized, given that the growth in teacher competence could be achieved in all the focused facets. Participants’ competence changed particularly in P_PID-IT and MPCK-IT—somewhat surprisingly, given that the changes focused neither on one competence domain (knowledge or teacher noticing) nor on one of the included perspectives (mathematics pedagogy or general pedagogy). This may indicate that the pedagogical aspects were more successfully transferred in a situation-specific context in the PD, while the mathematics pedagogical parts were easier to understand independently of specific situations, but it may also imply an insufficient fit between the M_PID-IT and GPK-IT tests and the PD as the instruments may not have been sensitive enough to changes in the program. In any case, these results call for further research to improve the effectiveness of the PD for M_PID-IT and GPK-IT. In the intervention group, master students particularly benefited from the program while in-service teachers mainly improved their teacher noticing skills from a pedagogical perspective. This highlights the difficulty of developing competencies, particularly for in-service teachers (Liu & Phelps, 2020 ; Prediger et al., 2022 ). It may also highlight the challenge of developing PD programs suitable for all phases of teacher education. Based on the results, the program will be further developed and tailored to in-service teachers to enhance its effects and promote all professional knowledge and teacher noticing facets. Growth in teacher competence varied according to experience group, which again highlights the need to adapt the PD program to better suit in-service teachers (Prediger et al., 2022 ), and partly by high school diploma grade and teaching type. Higher levels of professional knowledge for academic-track teachers are already known from empirical research (Kleickmann et al., 2013 )—for example, from the TEDS research program (Blömeke et al., 2014 )—and their greater benefit from the knowledge-related aspects of the PD complements these findings. Changes in ability were particularly predicted by prior knowledge and skills. This may indicate that a solid base of knowledge and skills was required to integrate the PD content into one’s knowledge and skills and may indicate that the PD program is cognitive challenging. The number and intensity of OTL as well as program evaluation and extent exhibited no influence on teacher competence change in this study. Therefore, the observed growth could not be explained by more superficial characteristics, such as the length of PD, nor by more specific variables such as the intensity of OTL use. This raises the issue of averaging the OTL items, which may have led to the disappearance of explanatory power, and calls for more detailed consideration of the program’s OTL. Further research is needed to investigate which features of the PD may cause the change in participants’ competencies and to uncover the effects of specific activities, calling for the development of more advanced methods to assess OTL and PD activities (Bastian et al., 2024 ). 5.2 Study limitations First, the results presented in this study were obtained using a convenience sample, and thus caution is recommended as regards generalization. The intervention and control groups and the experience groups within the intervention group differed in high school diploma grade and teaching type, which, although controlled for in the analyses, may have introduced some bias to the results. Moreover, only changes in M_PID-IT and P_PIT-IT were controlled using a control group. Thus, the effects of the PD on professional knowledge must be considered with particular caution. Further, for M_PID-IT, the difference between significant changes in the intervention group and the absence of significant changes in the control group was not itself not significant, which relativizes the improvements for the intervention group for M_PID-IT. OTL and intensity of OTL use were measured only through self-assessment and by operationalizing it as a list of topics from the PD, which may have not been specific enough. Future studies should develop more precise and comprehensive measures of OTL to yield insight into individual PD activities’ effectiveness. Only teacher competence was investigated as a program outcome, and effects on other levels may thus have been overlooked. Future research will analyze other levels of effectiveness, including PD quality and the instructional quality of the participants’ own teaching throughout the PD. 6 Conclusions Subject-specific approaches to inclusive education have become increasingly important for facilitating all students’ learning, requiring PD for teachers to enable inclusive teaching and to transfer new findings from research into school practice (Fränkel et al., 2023 ; Prediger et al., 2020 ). Thorough empirical monitoring of PD is necessary to promote effective teacher education (König et al., 2023 ). In this study, we demonstrated small to medium effects of a PD program for IME on several facets of teacher competence, particularly teacher noticing, and for three different experience groups using extensive measurement instruments. However, further evaluation studies of PD programs for IME are required to compare effect sizes, and more research is needed to achieve more substantial growth in teacher competence for IME. This PD program integrated both mathematics pedagogical and general pedagogical perspectives on inclusive teaching and focused teaching, which allow students to learn from the same learning object while also considering their individual needs. Furthermore, the program incorporated the joint improvement of teacher noticing and respective professional knowledge to enable comprehensive competence development. Overall, this study yields initial insights into the effectiveness of a PD program aimed at fostering teacher noticing and professional knowledge for IME under a broad conceptualization of inclusive education and demonstrates suitable methods for empirically investigating the effects using standardized testing. Declarations Declaration of conflict of interest The authors declare no conflict of interest. Funding This work was supported by BMBF Germany, grant number 01NV2125A and 01NV2125B. References Adams RJ, Wu M, Macaskill G, Haldane S, Sun XX, Cloney D, Berezner A (1997–2024). ConQuest . In (Version 5.39) Australian Council for Educational Research. Adeniji SM, Baker P (2023) Effects of Worked Example on Students’ Learning Outcomes in Complex Algebraic Problems. Int J Instruction 16(2):229–246. https://doi.org/10.29333/iji.2023.16214a Amador JM, Bragelman J, Superfine AC (2021) Prospective teachers’ noticing: A literature review of methodological approaches to support and analyze noticing. Teach Teacher Educ 99:1–16. https://doi.org/10.1016/j.tate.2020.103256 Asendorpf JB, van de Schoot R, Denissen JJA, Hutteman R (2014) Reducing bias due to systematic attrition in longitudinal studies: The benefits of multiple imputation. 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Teach Teacher Educ 122. https://doi.org/10.1016/j.tate.2022.103970 Yoon KS, Duncan T, Wen-Yu LS, Scarloss B, Shapley KL (2007) Reviewing the evidence on how teacher professional development affects student achievement . https://ies.ed.gov/ncee/edlabs/regions/southwest/pdf/rel_2007033.pdf Footnotes Overall, 654 persons participated in the TEDS-IME study. In this study, we included only participants who achieved a valid score for at least one test for one measurement time of interest. Given the large number of cases (n = 653) and the limited coder resources, a higher percentage of double coding (e.g., 20%) was not feasible for this study. Instead, the coders were initially trained for two days, and each case of the 10% double coding was discussed in detail. For some variables, values for the control group were missing by design, explaining the high percentage of missing data in those variables. Those values were estimated in the imputation but later deleted from the analysis. The ESM details the percentage of missing data per variable. In the intervention group, 13 cases were missing for the PD group. Since the group variable was used as a cluster variable for imputation, they could not be imputed. Therefore, we reassigned these cases to new groups based on their experience group and state. We did the same for the control group to better model the clusters in the data. Typically, variance analysis is employed to investigate the interaction effects and impacts of different conditions. In the absence of any consensus on a procedure for repeated measures variance analysis with imputed data sets, we used linear mixed models instead, as they are statistically equivalent. Additional Declarations The authors declare no competing interests. The study was reviewed for compliance with the required ethical standards by the Data Protection Committee of the University of Hamburg and the Ministry for School Education in cooperation with the Ethics Committee of the University of Hamburg. Supplementary Files ZDMElectronicsupplementarymaterialinclusive.docx Electronic supplementary material for Teacher competence in inclusive mathematics education: Examining the effects of an innovative professional development program on teacher noticing Cite Share Download PDF Status: Published Journal Publication published 27 Aug, 2025 Read the published version in ZDM – Mathematics Education → 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. 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Kaiser","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABO0lEQVRIie2RP0vDQByGf+GgWS7Nei7tV7iSxcHdr3GhQ5amBLp0CHggxEXsWqEfIiA4JwTicopj4ETSvUhdSkQIJqVW5LA4Ct4z3L+Xh/eOA9Bo/iQYgMHxdk6abQ/A4Ajaw136g0L2ivM7BXZKi8ub4aDSP73P1+WU9ABny7SaPnuxPOcoCG/HVN49wmqqKAMxHs6ZIA5YEc2wmPjxU8rRPJcT+jAKjIVQFT5ywI2Iy22gmRExPy7ci3fckW4sMENWpCqzVaPU5Izb5jp9q5lHC5cjXH8qtfoW0rZwwsC6pInFGdsqVtQqZoIsriiUvAyB5WQQYRFkOGeD661yJSdHAkO6yNWWmZ8ZVXjSt7F381qFrN8tvBLhjRx3hbksV6HakuwWHfUDAO/Tby3qXb8wywOhRqPR/B8+APq8cvT4r52pAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-6239-0169","institution":"University of Hamburg","correspondingAuthor":true,"prefix":"","firstName":"Gabriele","middleName":"","lastName":"Kaiser","suffix":""}],"badges":[],"createdAt":"2025-01-02 15:33:53","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5752892/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5752892/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11858-025-01731-x","type":"published","date":"2025-08-28T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":73269186,"identity":"97e9d443-d62d-4fc9-86b0-09904169a07c","added_by":"auto","created_at":"2025-01-08 10:42:08","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":26437,"visible":true,"origin":"","legend":"\u003cp\u003eStudy design\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5752892/v1/b4197b665ebe5162a52c34e7.png"},{"id":73267528,"identity":"25c1a7ea-22e3-486b-a086-5b528a72c0b5","added_by":"auto","created_at":"2025-01-08 10:34:08","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":25892,"visible":true,"origin":"","legend":"\u003cp\u003eOverview of the PD and its topics\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5752892/v1/02bbb4e414b5589d55b53456.png"},{"id":90536565,"identity":"b0fe8845-a651-4fce-9bd0-4c241628173a","added_by":"auto","created_at":"2025-09-03 20:30:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1355147,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5752892/v1/efff481e-b1ed-434e-9001-7839072b1350.pdf"},{"id":73267531,"identity":"738c880c-79fa-4f88-8713-9338e14995d7","added_by":"auto","created_at":"2025-01-08 10:34:08","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":430652,"visible":true,"origin":"","legend":"\u003cp\u003eElectronic supplementary material for Teacher competence in inclusive mathematics education: Examining the effects of an innovative professional development program on teacher noticing\u003c/p\u003e","description":"","filename":"ZDMElectronicsupplementarymaterialinclusive.docx","url":"https://assets-eu.researchsquare.com/files/rs-5752892/v1/cc038af8d5154ca6dba97065.docx"}],"financialInterests":"\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eThe study was reviewed for compliance with the required \u003cem\u003eethical\u003c/em\u003e standards by the Data Protection \u003cem\u003eCommittee\u003c/em\u003e of the University of Hamburg and the Ministry for School Education in cooperation with the \u003cem\u003eEthics Committee\u003c/em\u003e of the University of Hamburg.\u003c/p\u003e","formattedTitle":"\u003cp\u003e\u003cstrong\u003eTeacher competence in inclusive mathematics education: Examining the effects of an innovative professional development program on teacher noticing\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eSince the United Nations General Assembly adopted the convention on the rights of persons with disabilities (United Nations, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), inclusive education and diversity-sensitive teaching have been identified as key challenges and goals for education systems worldwide. Teachers\u0026rsquo; competencies play a crucial role in shaping educational practice and achieving an education that meets all students\u0026rsquo; needs (European Agency for Development in Special Needs Education, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). To teach classes with diverse students who have varying content-specific and interdisciplinary skill levels and individual needs across a wide range of content with multiple representations and approaches, teachers require professional knowledge about subject-specific and general inclusive education and situation-specific skills to apply and translate their knowledge into successful classroom performance (Keppens et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; K\u0026ouml;nig et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe conceptualization, measurement, and\u0026mdash;particularly\u0026mdash;development of teachers\u0026rsquo; competencies for inclusive education is thus a central issue for education researchers and policy makers (Fr\u0026auml;nkel et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; K\u0026ouml;nig et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Teachers require both general pedagogical and subject-specific perspectives on inclusive education to diagnose and support all students according to their individual needs (K\u0026ouml;nig et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Moser Opitz, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and to comprehensively conceptualize, measure, and develop teacher competencies for subject-specific inclusive education. Herein, therefore, we focus on inclusive mathematics education (IME), given the need for subject-specific professional development (PD) programs that prepare teachers for the challenges of inclusive education. However, subject-specific conceptualizations of IME are scarce, as are measurement instruments for teacher noticing and professional knowledge in IME and PD programs for secondary education in this area, despite the urgent need for such programs (Scherer et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Weyers et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Even fewer studies have examined the effectiveness of their PD program for IME to ensure evidence-based professional development measured with standardized assessments. The Teacher Education and Development Study - Inclusive Mathematics Education (TEDS-IME) project from the TEDS research program addresses this research gap on two levels: on a practical level by developing an innovative PD program that aims at the development of teacher noticing for IME and on a theoretical level by conceptualizing and assessing teacher noticing (and professional knowledge as an influencing factor) for IME using the example of secondary algebra instruction for all phases of teacher education in Germany\u0026mdash;higher education at universities, practical teacher training (known as preparatory service or induction phase), and elective PD for in-service teachers. Below, we present the initial results of a pretest\u0026ndash;posttest evaluation of a PD program. In particular, we explore (1) changes in the participants\u0026rsquo; teacher noticing skills and professional knowledge compared to the control group and (2) influences, such as participants\u0026rsquo; and PD characteristics, on these changes.\u003c/p\u003e"},{"header":"2 Literature survey, theoretical framework, and research questions","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Inclusive (mathematics) education\u003c/h2\u003e \u003cp\u003eCurrent discourse conceptualizes inclusive education heterogeneously, based on legal, cultural, and social influences and resulting in different normative understandings of what constitutes inclusion (Grosche, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). G\u0026ouml;ransson and Nilholm (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) identified four different conceptualizations of inclusion: (1) placing students with special needs in regular classrooms, (2) addressing these students\u0026rsquo; social and academic needs, (3) addressing all students\u0026rsquo; social and academic needs, and (4) the creation of specific communities. Piezunka et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) conceptualized a spectrum encompassing the non-discrimination of individuals with special needs, individualized support for all students to pragmatically develop student achievement or facilitate well-being, and inclusion as a utopia of noncategorical thinking. Both systematizations highlight the tension between narrower definitions focused on students with disabilities and broader definitions focusing on all students and their diverse individual backgrounds and the creation of inclusive communities. This tension is reflected in the current mathematics educational discourse, with studies on inclusion ranging from focusing on specific diagnoses or students with disabilities to examining the effects of interventions on students with differing prerequisites (Adeniji \u0026amp; Baker, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Long et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Teacher competence for inclusive (mathematics) education\u003c/h2\u003e \u003cp\u003eOver the last two decades, researchers have reached the consensus that teacher competence may be understood as a multifaceted construct comprising a body of dispositions (professional knowledge and beliefs) and situation-specific skills mediating dispositions and classroom performance (Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Kaiser et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Krauss et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Mathematics education research often defines professional knowledge with reference to Shulman (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1987\u003c/span\u003e), differentiating it into mathematics content knowledge (MCK), mathematics pedagogical content knowledge (MPCK), and general pedagogical knowledge (GPK) or comparable differentiations (Kaiser et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Krauss et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The teacher noticing construct, sometimes termed \u0026ldquo;professional vision,\u0026rdquo; was originally introduced to promote student-centered teaching by attending to and making sense of instructional events (Sherin et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; van Es \u0026amp; Sherin, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) and was later included as a situation-specific dimension in a framework of teacher competence by Bl\u0026ouml;meke et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) with the facets perception, interpretation, and decision-making in instructional settings. Although the specific definitions vary, conceptualizations of teacher noticing often include perceptual and interpretive facets and are increasingly complemented with a decision-oriented facet or even the decision\u0026rsquo;s enactment (Dindyal et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; K\u0026ouml;nig et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Sherin et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Thomas et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eComprehensive competence frameworks specifically addressing inclusive education in general or IME in particular remain scarce, particularly for secondary education. Studies sometimes include a general conceptualization of teacher competence in the context of inclusive education without any adaption for its specific requirements (Pit-ten Cate et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). However, some competence catalogues and practice descriptions have been produced. Prediger and Bur\u0026oacute; (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) identified 133 productive and unproductive practices in IME, structured within a framework of five demands: identifying learning prerequisites and assessing students\u0026rsquo; abilities, differentiating learning goals, compensating for limited abilities, enhancing abilities, and organizing collaborative learning. K\u0026ouml;nig et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) review distinguishes four demands of inclusive education: diagnosis, intervention and support, management and organization, and counseling and communication, of which the first two are most relevant to teaching itself. Diagnosis entails recognizing students\u0026rsquo; skills and possible learning difficulties in addition to (formative) assessment. It may be understood as an aspect of perceiving and interpreting classroom events and thus of teacher noticing (Heinrichs \u0026amp; Kaiser, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; K\u0026ouml;nig et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Intervention and support include all pedagogical and methodological means for individualization and negotiating heterogeneity, their successful use, and the associated challenges for classroom management and lesson structure. Intervention can thus be regarded as part of the interpretation and decision-making facets of teacher noticing (K\u0026ouml;nig et al., submitted). Hence, as diagnostic competencies, such as diagnosis, and individual support can also be considered domains of teacher noticing, its development is particularly relevant to IME (Heinrichs \u0026amp; Kaiser, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; K\u0026ouml;nig et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; K\u0026ouml;nig et al., submitted; Leuders et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). However, no PD programs for IME specifically address teacher noticing.\u003c/p\u003e \u003cp\u003eOverall, teacher noticing has rarely been linked to IME, and even less so using standardized assessment methods, as highlighted in the literature reviews by K\u0026ouml;nig et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and Weyers et al. (\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). An exception is the work by Keppens et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) and colleagues, who conceptualized teacher noticing of teacher-student interactions and differentiated instruction as two aspects of inclusive education and developed two comparative judgment-based test instruments for primary and secondary education. They identified connections between high proficiency in teacher noticing for inclusive education in both investigated aspects and the implementation of inclusive teaching practices (Gheyssens et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Other studies have adopted a more comprehensive conceptualization of inclusive education, focusing on the differences between teacher noticing in inclusive and special needs schools (Smit et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) or on the development of teacher noticing skills in co-teaching (Meadows \u0026amp; Caniglia, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) but without using standardized testing. Research that uses standardized testing to comprehensively examine teacher noticing for inclusive education in general, particularly for IME with the consideration of subject-specific aspects, remains a desideratum.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Professional development for inclusive (mathematics) education\u003c/h2\u003e \u003cp\u003ePD programs are essential interventions for translating research findings into classroom practice and impacting student achievement (Desimone, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Prediger et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, PD for IME and inclusive education in general has hitherto focused on primary education, with few programs targeting secondary education. The project \u003cem\u003eMathilda - Learning to teach mathematics inclusively\u003c/em\u003e, aimed at developing teachers\u0026rsquo; skills to teach a unit on understanding percentages inclusively considering the diverse needs of all students (Prediger et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), is a rare example. The program entailed collaborative coursework and testing of materials in teachers\u0026rsquo; own teaching. Kuhl et al. (2022) demonstrated the PD program\u0026rsquo;s intervention effects at the student level through increased learning gains without considering possible teacher learning gains. To the best of our knowledge, PD programs for other core topics in the secondary mathematics curriculum and evidence-based evaluations of the effects of PD on teacher competence for IME are still lacking and possible influences on these programs\u0026rsquo; effects have not been investigated. Overall, PD programs\u0026rsquo; effects on teacher competence and especially teacher noticing and in-service teachers are seldom examined (Amador et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; K\u0026ouml;nig et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; K\u0026ouml;nig et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Yoon et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Study framework\u003c/h2\u003e \u003cp\u003eShaped by our research interest and the literature review, we define inclusive education with reference to Piezunka et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) as the best possible academic support for all students\u0026mdash;considering their learning needs\u0026mdash;to achieve the best possible individual learning outcome, thus adopting a broad understanding of inclusion with a focus on learning achievement. We focus on diagnosis and intervention as two main demands of IME and conceptualize them as part of teacher noticing (Kaiser et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; K\u0026ouml;nig et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). We analytically conceptualize teacher noticing as having three facets: perceiving instructional events, interpreting the perceived events, and making decisions about the events\u0026mdash;for example, deciding on the lessons\u0026rsquo; progress or proposing alternative instructional strategies (Kaiser et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). We understand teacher noticing for IME as combining a subject-specific perspective (M_PID-IT: teaching under a mathematics pedagogical perspective for inclusive teaching: perception, interpretation, decision-making) and a general pedagogical perspective (P_PID-IT: teaching under a general pedagogical perspective for inclusive teaching: perception, interpretation, decision-making) to facilitate comprehensive measurement and PD of teachers\u0026rsquo; skills. Teacher noticing constitutes one part of teacher competence for IME. We also include professional knowledge as a foundational influencing factor for teacher noticing and thus diagnosis and intervention. Following Shulman (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1987\u003c/span\u003e), we consider MPCK for inclusive teaching (MPCK-IT) and GPK for inclusive teaching (GPK-IT).\u003c/p\u003e \u003cp\u003eFor the PD program, we focus on algebra as a core secondary mathematics topic that poses several comprehension barriers for students. Additionally, possible student errors and difficulties as well as sustainable basic mental models have already been researched through subject-specific analysis (Korntreff \u0026amp; Prediger, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Malle, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1993\u003c/span\u003e). However, despite its relevance for the students\u0026rsquo; learning trajectories, few PD programs address this topic, particularly regarding inclusive teaching. To facilitate teachers\u0026rsquo; learning, two demands of IME\u0026mdash;diagnosis and intervention\u0026mdash;are complemented by the identification of learning needs as a third demand and an important prerequisite for the others (K\u0026ouml;nig et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Prediger \u0026amp; Bur\u0026oacute;, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Four of the five prerequisites for successful learning as identified by Hasselhorn and Gold (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2022\u003c/span\u003e)\u0026mdash;prior knowledge, selective attention and working memory, learning strategies and metacognitive regulation, and motivation and self-concept\u0026mdash;are included as pedagogical categories and linked to algebra to combine subject-specific and interdisciplinary approaches.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Research questions\u003c/h2\u003e \u003cp\u003eBased on the research gaps identified in our literature review and theoretical framework, this study aims to develop measurement instruments for teacher noticing and professional knowledge for IME and to use these instruments to evaluate an innovative PD program for secondary IME in the field of algebra education from the TEDS-IME project. The study is guided by the following research questions:\u003c/p\u003e \u003cp\u003e(1) To what extent do the facets of pre-service and in-service teachers\u0026rsquo; noticing and professional knowledge change over the course of the PD program?\u003c/p\u003e \u003cp\u003ea. Can the changes be validated in comparison to a control group?\u003c/p\u003e \u003cp\u003eb. How do these changes differ between the three experience groups that participated in the PD program?\u003c/p\u003e \u003cp\u003e(2) To what extent do participants\u0026rsquo; characteristics, differential use of opportunities to learn, evaluation of the PD program, and prior knowledge and skills influence the change in skills?\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Methodological approach","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Study design\u003c/h2\u003e \u003cp\u003eIn the TEDS-IME project, we developed an innovative PD program for IME focusing on algebra instruction and administered it to three experience groups corresponding to the teacher education phases\u0026mdash;master students, teachers in preparatory service, and in-service teachers\u0026mdash;in four German federal states. To evaluate the PD program, we tested the participants\u0026rsquo; competencies in a pre\u0026ndash;post-follow-up design using a control group to control for the program\u0026rsquo;s effects. Herein, we focus on the teacher noticing and professional knowledge tests at the pre- and posttest stages (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The intervention group engaged in the program over four to six months and took the pretest survey at the program\u0026rsquo;s beginning and the posttest after the last content unit. Following a similar timeframe, teachers in the control group took a pretest and posttest survey with a reduced competence test consisting only of the teacher noticing tests, since it was necessary to reduce the testing time to convince teachers to participate without the incentive of a PD program.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Sample\u003c/h2\u003e \u003cp\u003eThe sample comprises 653 pre-service and in-service teachers\u003ca class=\"FNLink\" href=\"#Fn1\" id=\"#FNLinkFn1\"\u003e\u003c/a\u003e (master students: \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;241, teachers in preparatory service: \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;169, in-service teachers: \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;243) with 539 participants in the intervention group and 114 participants in the control group. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the descriptive statistics. The intervention and control groups show no differences in gender, age, and teaching experience duration but differ significantly with respect to teaching type, with more academic-track teachers in the control group and high school diploma grade, with a higher grade mean for the control group. Both variables are associated with higher levels of teacher competence (Kleickmann et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), favoring the control group. This must be considered when comparing the groups. For the intervention group, the three experience groups exhibit significant differences in age and teaching experience by design. Moreover, teaching type and high school diploma grade vary significantly, both in favor of the master students (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001 and \u003cem\u003eF\u003c/em\u003e (2, 624)\u0026thinsp;=\u0026thinsp;336.3, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001; full descriptive statistics are provided in the electronic supplemental material (ESM)). This is also considered in the analysis and discussion.\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\u003e\u003cem\u003eDescriptive characteristics of the intervention and control group\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eCondition\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTest of group differences\u003csup\u003ec\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eIntervention group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eControl group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e539\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e114\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender (% female)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e64.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e58.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.565\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeaching type\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(% academic)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e44.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e68.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001\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\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge (in years)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e32.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e11.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003et (154)\u003c/em\u003e = -1.45, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.149\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeaching experience \u003c/p\u003e \u003cp\u003e(in years)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003et (140)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.95, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.342\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGrade (Abitur)\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003et (165)\u003c/em\u003e = -2.02, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.045\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003cem\u003eNote.\u003c/em\u003e \u003csup\u003ea\u003c/sup\u003eThis variable was dichotomously coded in 0 \u0026ndash; non-academic-track school and 1 \u0026ndash; academic-track school (Gymnasium). \u003csup\u003eb\u003c/sup\u003eThe German high school diploma that qualifies for university admission. Grades rage from 1 (best) to 4 (pass). \u003csup\u003ec\u003c/sup\u003eFisher\u0026rsquo;s exact test was conducted for nominal data; t-tests were used for metric data.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Assessment instruments\u003c/h2\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Teacher noticing\u003c/h2\u003e \u003cp\u003eTo measure teacher noticing for IME, we developed an innovative standardized video-based instrument that assesses teachers\u0026rsquo; abilities to perceive, interpret, and make decisions in inclusive secondary algebra education from a mathematics pedagogical perspective (M_PID-IT) and a general pedagogical perspective (P_PID-IT) based on the established TEDS-FU video instrument (Kaiser et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; K\u0026ouml;nig et al., submitted). The instrument comprises four scripted (i.e., staged) video vignettes ranging from 2.45 to 4.00 minutes and covering a wide range of algebraic topics, including variables, algebraic terms, and equations as well as instructional phases, such as group exploration or review of students\u0026rsquo; work. In addition, the classroom situations include students at varying levels of learning prerequisites, including those who lack prerequisites such as the necessary prior knowledge to achieve the lesson\u0026rsquo;s objectives and those who do have sufficient prerequisites. The video vignettes were developed in close collaboration with experienced teachers and experts in IME to simulate authentic typical classroom situations.\u003c/p\u003e \u003cp\u003eEach participant worked on three randomly selected video vignettes administered in a random incomplete test design. For each vignette, participants first received contextual information about the class, such as grade level and school type, the current lesson, such as the lesson\u0026rsquo;s objective and topic, and the task addressed. They were then permitted to watch the vignette once to simulate a corresponding classroom situation. Participants responded to open-response and Likert-type rating scale items that test their skills in perception, interpretation, and decision-making. In total, the test comprised 63 items, divided into M_PID-IT (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;32) and P_PID-IT (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;31) items, and takes 60 minutes to complete. Each item was additionally related to diagnosis (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;27) or intervention (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;36).\u003c/p\u003e \u003cp\u003eExtensive expert ratings were conducted with 47 experts to determine correct responses for each item and to ensure a high-quality instrument. For open-response items, we developed a comprehensive coding manual with sample responses from a pilot study and detailed descriptions of correct responses to ensure reliability and validity. Coders were extensively trained and achieved good overall interrater reliability in double coding of 10% of the answers to open-response items at T1 (κ: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.77).\u003ca class=\"FNLink\" href=\"#Fn2\" id=\"#FNLinkFn2\"\u003e\u003c/a\u003e All rating scale and open-response items were scored dichotomously. The ESM presents example items and an example vignette.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Professional knowledge\u003c/h2\u003e \u003cp\u003eTo assess teachers\u0026rsquo; knowledge of IME as an influencing factor of teacher noticing, we developed a two-dimensional instrument with items focusing on MPCK-IT or GPK-IT. MPCK-IT comprises questions on algebra pedagogy, such as basic mental models of variables and functions, and items on more general topics, including conceptual understanding or language-sensitive mathematics instruction. For GPK-IT, the items cover learning processes, diagnosis, classroom management, structuring, and individualization/differentiation. Overall, the items include selected and partially adapted items from previous studies, including the MPCK instrument from TEDS-M (Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) and the GPK-IT test from K\u0026ouml;nig et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), as well as newly developed items. This resulted in 50 single- or multiple-choice items (MPCK-IT: \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;37, GPK-IT: \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;13) and a test duration of 25 minutes. All items were scored dichotomously. The ESM presents example items.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.3.3 Further instruments\u003c/h2\u003e \u003cp\u003eDemographic data and personal characteristics, such as age, gender, experience duration, and teaching type, were collected at T1. At T2, we used an additional questionnaire with the intervention group to inquire about the number of opportunities to learn (OTL) to account for differences in participation frequency using a dichotomous scale and the intensity of OTL use using a four-point Likert scale (see ESM for examples). Scales were constructed using mean scores (OTL: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.86, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.19, intensity of OTL use: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.79, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.47). The extent of each PD group was collected as a level two variable since the PD extent varied for organizational reasons and not all groups could complete all PD units. We also asked participants to rate their overall experience of the program on a scale from 1 - very bad to 6 - very good (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.89, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.95).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.4 PD Program\u003c/h2\u003e \u003cp\u003eTo support teachers in dealing with the identified IME demands\u0026mdash;identifying, assessing/diagnosing and supporting/facilitating learning requirements\u0026mdash;we developed a PD program with an interdisciplinary team of experts in mathematics education, educational science, and special education. The program\u0026rsquo;s development was guided by the principles of evidence-based effectiveness, with a particular focus on teacher competence growth (Desimone, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). The program comprises 18 hours of coursework over a four- to six-month period, ensuring in-depth coverage of the selected topics and long-term engagement. To maintain high quality implementation, we carefully selected PDs\u0026rsquo; facilitators, trained them extensively, and provided ongoing support throughout the program.\u003c/p\u003e \u003cp\u003eAt the content level, the PD program follows central algebra topics with units on equivalence transformations, term equivalence, finding and describing algebraic terms, and comparing aspects of the variable concept (see Fig.\u0026nbsp;2). In these units, the prerequisites for successful learning as defined by Hasselhorn and Gold (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), are addressed successively in addition to the mathematics pedagogical content. Following the demands of IME, for each of these prerequisites, teachers first have the opportunity to identify the respective learning requirements for specific instructional situations and materials in algebra education so that these can then be used as categories for the subsequent PD activities on diagnosis and intervention and, thus, professional knowledge and teacher noticing (K\u0026ouml;nig et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 2\u003c/b\u003e \u003cem\u003eOverview of the PD and its topics\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003eNote\u003c/em\u003e. The pretest was conducted at the beginning of unit 1, the posttest at the end of unit 6. IME \u0026ndash; inclusive (mathematics) education.\u003c/p\u003e \u003cp\u003eThe program\u0026rsquo;s participants are first confronted with the widespread differentiation approach of altering cognitive demand (in terms of technical complexity) and recognize why this approach falls short in IME. This motivates them to master the more complex requirements of facilitating learning at different prerequisite levels for all students on the same teaching objects and objectives. To promote the use of different learning goals for individual students and their connection within a common learning object, an adapted version of Siemon\u0026rsquo;s (\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) concept of learning trajectories is introduced. Further, teachers and facilitators approach newly developed or adapted teaching materials that allow them to reconstruct the materials\u0026rsquo; underlying basic mental models and to build linkages of representations that promote conceptual understanding. On this basis, teachers can then construct learning trajectories for individual students. Given the highly complex nature of this process, we introduce four example students who symbolize four significant levels of prior knowledge for the learning of each new concept and who are used systematically in each unit. The teachers then create learning trajectories for these four students. To further support a change in teachers\u0026rsquo; attitudes about the importance of understanding basic principles and mental models while considering different levels of prior knowledge, the algebraic topics were ordered as moving backward through the curriculum from equivalence equation transformation to aspects of variables, allowing the identification of important prior knowledge first followed by how it should be taught and learned.\u003c/p\u003e \u003cp\u003eThe interdisciplinary learning prerequisites, such as selective memory and attention, are introduced after the first unit (see Fig.\u0026nbsp;2) and are initially approached in isolation but are thereafter treated in close connection with subject-specific aspects. All contents of the PD program are covered by specific teaching materials and learning and teaching situations presented by video or text vignettes, not only to promote professional knowledge but also to facilitate the development of teacher noticing. The use of various methods aims at a high level of cognitive activation as regards the program\u0026rsquo;s learning objectives.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Data analysis\u003c/h2\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.5.1 Data scaling\u003c/h2\u003e \u003cp\u003eWe scaled the data from the teacher noticing and knowledge instrument using \u003cem\u003eConQuest 5.39\u003c/em\u003e software (Adams et al., 1997\u0026ndash;2024) and using two-dimensional Rasch models for both teacher noticing and professional knowledge. Weighted likelihood estimates (WLEs) were then used to create ability scores for M_PID-IT, P_PID-IT, MPCK-IT, and GPK-IT. All models reached acceptable to good reliability and showed sufficient variance (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Sub-dimensions showed high correlations (M_PID-IT and P_PID-IT: \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.86, MPCK-IT and GPK-IT: \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.77) but were distinguishable, as shown by model comparison by K\u0026ouml;nig et al. (submitted).\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\u003e\u003cem\u003eStatistics for the competence measures based on two two-dimensional models\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCompetence measure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEAP reliability\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWLE reliability\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eVariance\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eWeighed mean squares (min \u0026ndash; max)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDiscrimination \u003c/p\u003e \u003cp\u003e(mean; min \u0026ndash; max)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.91\u0026ndash;1.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e.28; .08 \u0026ndash; .46]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMPCK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.86\u0026ndash;1.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e.32; .16 \u0026ndash; .53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003cem\u003eNote\u003c/em\u003e. EAP \u0026ndash; expected as posteriori. WLE \u0026ndash; Weighted likelihood estimates.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.5.2 Multiple data imputation\u003c/h2\u003e \u003cp\u003eGiven that listwise exclusion of cases with missing values is considered statistically inadequate for analyzing longitudinal data (Asendorpf et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), we used multiple imputation to avoid biases due to systematic panel attrition. The average percentage of missing data was 21.7%, ranging from no missing data for the experience group and gender to 52.7% for MPCK-IT and GPK-IT scores at T2.\u003ca class=\"FNLink\" href=\"#Fn3\" id=\"#FNLinkFn3\"\u003e\u003c/a\u003e Following Graham et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) recommendations and accounting for the imputation uncertainty, we generated 100 datasets in which all missing data were imputed with plausible values using the statistical software \u003cem\u003eR\u003c/em\u003e version 4.4.1 (R Core Team, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) and its packages \u003cem\u003emice\u003c/em\u003e (van Buuren \u0026amp; Groothuis-Oudshoorn, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) und \u003cem\u003emitml\u003c/em\u003e (Grund et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). To impute each variable, predictors from a pool of all investigated variables, such as noticing and knowledge scores, and auxiliary variables, such as teaching type and high school diploma grade, were included if they correlated with the respective variable with at least \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.10 (see the ESM). The PD group was used as a cluster variable for the imputation.\u003ca class=\"FNLink\" href=\"#Fn4\" id=\"#FNLinkFn4\"\u003e\u003c/a\u003e For each analysis, the 100 imputed datasets were analyzed separately and then pooled with Rubin\u0026rsquo;s rule to achieve the combined results reported herein.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e3.5.3 Analysis methods\u003c/h2\u003e \u003cp\u003eTo address the first research question concerning changes in teachers\u0026rsquo; competencies over the course of the program against the control group and experience group-specific differences, we computed descriptive statistics, paired sample t-tests, and the effect size Cohen\u0026rsquo;s d for within-subjects design for the intervention and control group as well as experience group-specific statistics for the intervention group. The t-test results were corrected for multiple testing using the Bonferroni\u0026ndash;Holm method. To further investigate differences between the intervention and control groups, we calculated a linear mixed model with the PD group as a cluster variable and modeled the interaction effect of measurement time and condition (i.e., intervention or control group) for M_PID-IT and P_PID-IT.\u003ca class=\"FNLink\" href=\"#Fn5\" id=\"#FNLinkFn5\"\u003e\u003c/a\u003e Teaching type and grade were controlled to account for differences between the conditions.\u003c/p\u003e \u003cp\u003eFor the second research question, we used multiple regression analysis with the intervention group as a subset to examine the effect of possible predictors on T2 ability scores while controlling for T1 scores and examining the changes in each. The PD group was introduced as a cluster variable, since intraclass correlation revealed a significant proportion of variance on cluster level (M_PID-IT (T2): ICC\u0026thinsp;=\u0026thinsp;.15, P_PID-IT (T2): ICC\u0026thinsp;=\u0026thinsp;.15, MPCK-IT (T2): ICC\u0026thinsp;=\u0026thinsp;.17, GPK-IT (T2): ICC\u0026thinsp;=\u0026thinsp;.12). To examine possible changes in influence when including other predictors, we computed four models for each ability score at T2. First, we considered only the T1 ability score, grade, and teaching type as control variables (M1). We then included the experience group membership as a level two predictor (M2). In two further models, we added PD-related characteristics (M3), such as OTL, and all prior knowledge and skills\u0026mdash;that is, all professional knowledge and teacher noticing scores at T1 (M4).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4 Results","content":"\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Effects of the PD program on teacher noticing and professional knowledge\u003c/h2\u003e \u003cp\u003eTo address the first research question and its sub-questions, we analyzed the mean ability scores by group and conducted t-tests. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the mean ability scores of the intervention and control group for all investigated competence facets and t-test comparisons of T1 and T2. The knowledge tests\u0026rsquo; scores tended to be higher than the teacher noticing scores, suggesting a higher level of knowledge than situation-specific skills in the sample. The intervention group\u0026rsquo;s T2 results were significantly higher than at T1 for all tests with the greatest effects for P_PID-IT (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.31) and MPCK-IT (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.28) with small effect sizes, providing first indicators for the program\u0026rsquo;s effectiveness.\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\u003e\u003cem\u003eMean scores of professional knowledge and teacher noticing skills at each measurement time\u003c/em\u003e\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=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eT1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eT2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003et\u003c/em\u003e (\u003cem\u003edf\u003c/em\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"8\" nameend=\"c8\" namest=\"c1\"\u003e \u003cp\u003eIntervention group (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;539)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e47.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.52 (190)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e48.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-6.30 (222)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMPCK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e56.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e58.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-5.88 (185)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e55.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e56.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.39 (209)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"8\" nameend=\"c8\" namest=\"c1\"\u003e \u003cp\u003eControl group (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;114)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e46.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e47.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.02 (83)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e51.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e51.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.80 (86)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cem\u003eNote\u003c/em\u003e. To facilitate reading, WLE ability estimates were linearly transformed by multiplying by 10 and adding 50. All p-values were corrected for multiple testing using the Bonferroni\u0026ndash;Holm method. The control group only participated in the M_PID-IT and P_PID-IT tests.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor the control group, no significant change was found for all investigated competence facets (M_PID-IT and P_PID-IT), substantiating the improvements observed in the intervention group. To further investigate whether the differences between the significant increases in the intervention group and the nonsignificant results in the control group were themselves significant, we examined the interaction effect of measurement time and condition while controlling for grade and teaching type. The regression model (full model results in the ESM) demonstrated a significant small interaction effect for P_PID-IT (β\u0026thinsp;=\u0026thinsp;.23, \u003cem\u003et\u003c/em\u003e (1929)\u0026thinsp;=\u0026thinsp;2.2, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.027), while no interaction effect was observed for M_PID-IT (β\u0026thinsp;=\u0026thinsp;.04, \u003cem\u003et\u003c/em\u003e (1282)\u0026thinsp;=\u0026thinsp;0.3, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.749). Thus, the increase in P_PID-IT in the intervention group was significant compared to the control group, while the difference between the significant improvement in the intervention group and lack of increases in the control groups in M_PID-IT was not in itself significant.\u003c/p\u003e \u003cp\u003eTo examine the program\u0026rsquo;s effectiveness according to experience group, we analyzed the means for each experience group of the intervention group (see Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Master students significantly increased all investigated knowledge and teacher noticing facets with small to medium effect sizes and the largest improvement in MPCK-IT (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.50). By contrast, teachers in preparatory service showed improvement only for P_PID-IT (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.40) and MPCK-IT (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.28), and in-service teachers demonstrated significant growth only for P_PID-IT (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.20) with small effect sizes. This indicates that the PD program particularly affected the master students, while only an increase in teacher noticing from a pedagogical perspective could be achieved for all experience groups.\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\u003e\u003cem\u003eMean scores of professional knowledge and teacher noticing skills for each experience group of the intervention group at each measurement time\u003c/em\u003e\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=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eT1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eT2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003et\u003c/em\u003e (\u003cem\u003edf\u003c/em\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"8\" nameend=\"c8\" namest=\"c1\"\u003e \u003cp\u003eMaster students (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;179)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e46.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e49.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-4.19 (118)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e50.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e53.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-4.85 (126)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMPCK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e57.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e60.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-6.29 (110)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e55.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e58.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.03 (114)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"8\" nameend=\"c8\" namest=\"c1\"\u003e \u003cp\u003eTeachers in preparatory service (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;162)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e46.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e47.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.27 (63)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.568\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e47.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e51.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-4.29 (72)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMPCK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e57.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e59.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.08 (62)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e55.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e56.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.64 (73)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.252\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"8\" nameend=\"c8\" namest=\"c1\"\u003e \u003cp\u003eIn-service teachers (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;198)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e44.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e44.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.57 (118)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.568\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e46.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e48.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.59 (140)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMPCK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e55.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e56.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.66 (93)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.252\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e53.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e55.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.37 (92)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.262\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cem\u003eNote\u003c/em\u003e. To facilitate reading, WLE ability estimates were linearly transformed by multiplying by 10 and adding 50. All p-values were corrected for multiple testing using the Bonferroni\u0026ndash;Holm method.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Influences on the changes in professional knowledge and teacher noticing\u003c/h2\u003e \u003cp\u003eTo investigate possible influences on the changes in our PD program and to address the second research question, we calculated four regression models for each ability score at T2 while controlling for the score at T1 to focus on the ability changes (see Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Autocorrelations for M_PID-IT (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.56), P_PID-IT (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.60)., MPCK-IT (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.66), and GPK_IT (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.57) were moderate, indicating stable overall constructs but also highlighting variations and, thus, possible PD-induced changes (correlations between the competence facets at T1 and T2 and possible predictors can be found in the ESM). Autoregressive paths also showed moderate to large influences of T1 ability scores on the respective ability scores at T2 that were reduced only when all other professional knowledge and teacher noticing scores were included in M4 (see Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Overall, a significant proportion of variance could be explained by each regression model as qualified by coefficients of determination values.\u003c/p\u003e \u003cp\u003eFirst, we focused on high school diploma grade (Abitur) and teaching type (M1). Regression analysis demonstrated a significant influence of the grade for both teacher noticing skills but not for professional knowledge that vanished when considering experience group and prior knowledge and skills. Teaching type consistently predicted scores only for MPCK-IT with a small effect size, attesting that teachers from academic-track schools were better able to use the PD to develop their MPCK-IT. In a second model (M2), we added the experience group as a predictor using two dummy variables. In line with the mean comparisons, in-service teachers exhibited significantly less change in M_PID-IT, P_PID-IT, and MPCK-IT than master students did, while teachers in preparatory service did not differ from master students when controlling for grade, teaching type, and ability score at T1. We then introduced OTL, intensity of OTL use, program extent, and program evaluation. However, no significant prediction of these variables was observed for all ability scores. Thus, the PD program\u0026rsquo;s investigated characteristics could not explain the changes in participants\u0026rsquo; professional knowledge and teacher noticing skills. In a final step, we added all ability scores at T1 (M4). This reduced the autoregressive coefficient due to shared variance, although considerable autoregressive prediction remained. For M_PID-IT, all other ability scores significantly predicted the change in M_PID-IT with small regression coefficients. M_PID and MPCK-IT at T1 significantly influenced the changes in P_PID-IT, while GPK-IT did not. In terms of prior knowledge and skills, changes in MPCK-IT were predicted only by itself and M_PID-IT and changes in GPK-IT were predicted only by itself and MPCK-IT.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eMultiple regression models for M_PID-IT, P_PID-IT, MPCK-IT, and GPK-IT at T2\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"17\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c17\" colnum=\"17\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eM_PID-IT (T2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c9\" namest=\"c6\"\u003e \u003cp\u003eP_PID-IT (T2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c13\" namest=\"c10\"\u003e \u003cp\u003eMPCK-IT (T2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c17\" namest=\"c14\"\u003e \u003cp\u003eGPK-IT (T2)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eM2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eM3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eM4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eM1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eM2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eM3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eM4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eM1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eM2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003eM3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003eM4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003eM1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003eM2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003eM3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003eM4\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\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003eβ\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGrade (Abitur)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.12*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.11*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.11*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.13**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.12*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.12*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeaching type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.22*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e.23*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e.22*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e.22*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.20*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTPS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIST\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.31*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.32*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.26*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.25*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.28**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.31**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.29**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.24*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOTL\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=\"left\" colname=\"c4\"\u003e \u003cp\u003e.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOTL-int\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=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProgram extent\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=\"left\" colname=\"c4\"\u003e \u003cp\u003e.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProgram eva\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=\"left\" colname=\"c4\"\u003e \u003cp\u003e.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM_PID-IT (T1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.49***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.49***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.49***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.27***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.22***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.19***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eP_PID-IT (T1)\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=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.23***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.55***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.54***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.54***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.42***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMPCK-IT (T1)\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=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.21***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.17**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e.60***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e.61***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e.60***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.48***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.27***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPK-IT (T1)\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=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.13*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e.53***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e.53***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e.53***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.40***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c15\"\u003e \u003cp\u003e.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c16\"\u003e \u003cp\u003e.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"17\"\u003e\u003cem\u003eNote\u003c/em\u003e. * \u0026ndash; \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.05, ** \u0026ndash; \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.01, *** \u0026ndash; \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001. TPS \u0026ndash; teachers in preparatory service (dummy variable with master students as reference). IST \u0026ndash; in-service teachers (dummy variable with master students as reference). OTL \u0026ndash; opportunities to learn. OTL-int \u0026ndash; intensity in the use of opportunities to learn. Program eva \u0026ndash; Program evaluation.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5 Discussion and limitations","content":"\u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Summary and discussion\u003c/h2\u003e \u003cp\u003eThis study examined the effects of an innovative PD program aimed at promoting teacher noticing skills and professional knowledge for IME of master students, teachers in preparatory service, and in-service teachers in secondary algebra education. The comprehensive 18-hour PD program included newly developed instructional materials and video-based learning activities to introduce participants to teaching that enables all students to learn from the same learning object and that considers both mathematics pedagogical and general pedagogical perspectives on inclusive teaching. We used extensive, mainly video-based instruments to assess teacher competence with reliable scales that also combined subject-specific and pedagogical perspectives and were based on a comprehensive understanding of IME. For the intervention group, teacher noticing and professional knowledge increased significantly in the mathematics pedagogical and general pedagogical domains, while the control group showed no significant changes. Although some of the effect sizes were small, these findings must be emphasized, given that the growth in teacher competence could be achieved in all the focused facets.\u003c/p\u003e \u003cp\u003eParticipants\u0026rsquo; competence changed particularly in P_PID-IT and MPCK-IT\u0026mdash;somewhat surprisingly, given that the changes focused neither on one competence domain (knowledge or teacher noticing) nor on one of the included perspectives (mathematics pedagogy or general pedagogy). This may indicate that the pedagogical aspects were more successfully transferred in a situation-specific context in the PD, while the mathematics pedagogical parts were easier to understand independently of specific situations, but it may also imply an insufficient fit between the M_PID-IT and GPK-IT tests and the PD as the instruments may not have been sensitive enough to changes in the program. In any case, these results call for further research to improve the effectiveness of the PD for M_PID-IT and GPK-IT.\u003c/p\u003e \u003cp\u003eIn the intervention group, master students particularly benefited from the program while in-service teachers mainly improved their teacher noticing skills from a pedagogical perspective. This highlights the difficulty of developing competencies, particularly for in-service teachers (Liu \u0026amp; Phelps, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Prediger et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). It may also highlight the challenge of developing PD programs suitable for all phases of teacher education. Based on the results, the program will be further developed and tailored to in-service teachers to enhance its effects and promote all professional knowledge and teacher noticing facets.\u003c/p\u003e \u003cp\u003eGrowth in teacher competence varied according to experience group, which again highlights the need to adapt the PD program to better suit in-service teachers (Prediger et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), and partly by high school diploma grade and teaching type. Higher levels of professional knowledge for academic-track teachers are already known from empirical research (Kleickmann et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2013\u003c/span\u003e)\u0026mdash;for example, from the TEDS research program (Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2014\u003c/span\u003e)\u0026mdash;and their greater benefit from the knowledge-related aspects of the PD complements these findings. Changes in ability were particularly predicted by prior knowledge and skills. This may indicate that a solid base of knowledge and skills was required to integrate the PD content into one\u0026rsquo;s knowledge and skills and may indicate that the PD program is cognitive challenging. The number and intensity of OTL as well as program evaluation and extent exhibited no influence on teacher competence change in this study. Therefore, the observed growth could not be explained by more superficial characteristics, such as the length of PD, nor by more specific variables such as the intensity of OTL use. This raises the issue of averaging the OTL items, which may have led to the disappearance of explanatory power, and calls for more detailed consideration of the program\u0026rsquo;s OTL. Further research is needed to investigate which features of the PD may cause the change in participants\u0026rsquo; competencies and to uncover the effects of specific activities, calling for the development of more advanced methods to assess OTL and PD activities (Bastian et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Study limitations\u003c/h2\u003e \u003cp\u003eFirst, the results presented in this study were obtained using a convenience sample, and thus caution is recommended as regards generalization. The intervention and control groups and the experience groups within the intervention group differed in high school diploma grade and teaching type, which, although controlled for in the analyses, may have introduced some bias to the results. Moreover, only changes in M_PID-IT and P_PIT-IT were controlled using a control group. Thus, the effects of the PD on professional knowledge must be considered with particular caution. Further, for M_PID-IT, the difference between significant changes in the intervention group and the absence of significant changes in the control group was not itself not significant, which relativizes the improvements for the intervention group for M_PID-IT.\u003c/p\u003e \u003cp\u003eOTL and intensity of OTL use were measured only through self-assessment and by operationalizing it as a list of topics from the PD, which may have not been specific enough. Future studies should develop more precise and comprehensive measures of OTL to yield insight into individual PD activities\u0026rsquo; effectiveness.\u003c/p\u003e \u003cp\u003eOnly teacher competence was investigated as a program outcome, and effects on other levels may thus have been overlooked. Future research will analyze other levels of effectiveness, including PD quality and the instructional quality of the participants\u0026rsquo; own teaching throughout the PD.\u003c/p\u003e \u003c/div\u003e"},{"header":"6 Conclusions","content":"\u003cp\u003eSubject-specific approaches to inclusive education have become increasingly important for facilitating all students\u0026rsquo; learning, requiring PD for teachers to enable inclusive teaching and to transfer new findings from research into school practice (Fr\u0026auml;nkel et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Prediger et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Thorough empirical monitoring of PD is necessary to promote effective teacher education (K\u0026ouml;nig et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In this study, we demonstrated small to medium effects of a PD program for IME on several facets of teacher competence, particularly teacher noticing, and for three different experience groups using extensive measurement instruments. However, further evaluation studies of PD programs for IME are required to compare effect sizes, and more research is needed to achieve more substantial growth in teacher competence for IME.\u003c/p\u003e \u003cp\u003eThis PD program integrated both mathematics pedagogical and general pedagogical perspectives on inclusive teaching and focused teaching, which allow students to learn from the same learning object while also considering their individual needs. Furthermore, the program incorporated the joint improvement of teacher noticing and respective professional knowledge to enable comprehensive competence development. Overall, this study yields initial insights into the effectiveness of a PD program aimed at fostering teacher noticing and professional knowledge for IME under a broad conceptualization of inclusive education and demonstrates suitable methods for empirically investigating the effects using standardized testing.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of conflict of interest\u003c/h2\u003e \u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work was supported by BMBF Germany, grant number 01NV2125A and 01NV2125B.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAdams RJ, Wu M, Macaskill G, Haldane S, Sun XX, Cloney D, Berezner A (1997\u0026ndash;2024). \u003cem\u003eConQuest\u003c/em\u003e. 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Teach Teacher Educ 122. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.tate.2022.103970\u003c/span\u003e\u003cspan address=\"10.1016/j.tate.2022.103970\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYoon KS, Duncan T, Wen-Yu LS, Scarloss B, Shapley KL (2007) \u003cem\u003eReviewing the evidence on how teacher professional development affects student achievement\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://ies.ed.gov/ncee/edlabs/regions/southwest/pdf/rel_2007033.pdf\u003c/span\u003e\u003cspan address=\"https://ies.ed.gov/ncee/edlabs/regions/southwest/pdf/rel_2007033.pdf\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Overall, 654 persons participated in the TEDS-IME study. In this study, we included only participants who achieved a valid score for at least one test for one measurement time of interest.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Given the large number of cases (n\u0026thinsp;=\u0026thinsp;653) and the limited coder resources, a higher percentage of double coding (e.g., 20%) was not feasible for this study. Instead, the coders were initially trained for two days, and each case of the 10% double coding was discussed in detail.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e For some variables, values for the control group were missing by design, explaining the high percentage of missing data in those variables. Those values were estimated in the imputation but later deleted from the analysis. The ESM details the percentage of missing data per variable.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In the intervention group, 13 cases were missing for the PD group. Since the group variable was used as a cluster variable for imputation, they could not be imputed. Therefore, we reassigned these cases to new groups based on their experience group and state. We did the same for the control group to better model the clusters in the data.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Typically, variance analysis is employed to investigate the interaction effects and impacts of different conditions. In the absence of any consensus on a procedure for repeated measures variance analysis with imputed data sets, we used linear mixed models instead, as they are statistically equivalent.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"Bundesministerium für Bildung und Forschung","isAcceptedByJournal":true,"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":"Inclusive education, teacher noticing, professional development, teacher competence, professional knowledge, secondary algebra instruction","lastPublishedDoi":"10.21203/rs.3.rs-5752892/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5752892/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigated the effects of an innovative professional development program aimed at enhancing teacher noticing skills and professional knowledge in inclusive (mathematics) education in secondary algebra instruction. A total of 653 participants, comprising master\u0026rsquo;s students, teachers in preparatory service, and in-service teachers from Germany, participated in a pretest\u0026ndash;posttest evaluation design that included a control group. The program comprised 18 hours of coursework that integrated novel teaching materials and video-based learning activities that combined both mathematics pedagogical and general pedagogical perspectives on teacher noticing and associated knowledge.\u003c/p\u003e \u003cp\u003eThe results indicated significant improvements in teachers\u0026rsquo; noticing skills and professional knowledge for the intervention group across all investigated facets, particularly for teacher noticing under a pedagogical perspective and mathematics pedagogical knowledge, compared to a control group that exhibited no significant changes. Effect sizes ranged from small to medium, suggesting that the professional development program effectively improved participants\u0026rsquo; knowledge of inclusive teaching and their abilities to perceive, interpret, and make decisions in inclusive contexts. Notably, master\u0026rsquo;s students exhibited the most substantial gains in all competencies, while in-service teachers primarily improved their teacher noticing from a pedagogical perspective.\u003c/p\u003e \u003cp\u003eThe findings underscore the importance of tailored professional development for fostering teacher noticing in inclusive mathematics education and yield valuable insights into the competencies necessary for inclusive (mathematics) education.\u003c/p\u003e","manuscriptTitle":"Teacher competence in inclusive mathematics education: Examining the effects of an innovative professional development program on teacher noticing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-08 10:34:03","doi":"10.21203/rs.3.rs-5752892/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":"5c145390-bd89-4cb8-a854-90d297b76b72","owner":[],"postedDate":"January 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":42283172,"name":"Educational Psychology"},{"id":42283173,"name":"Special Education"}],"tags":[],"updatedAt":"2025-09-03T20:30:04+00:00","versionOfRecord":{"articleIdentity":"rs-5752892","link":"https://doi.org/10.1007/s11858-025-01731-x","journal":{"identity":"zdm-mathematics-education","isVorOnly":true,"title":"ZDM – Mathematics Education"},"publishedOn":"2025-08-28 00:00:00","publishedOnDateReadable":"August 28th, 2025"},"versionCreatedAt":"2025-01-08 10:34:03","video":"","vorDoi":"10.1007/s11858-025-01731-x","vorDoiUrl":"https://doi.org/10.1007/s11858-025-01731-x","workflowStages":[]},"version":"v1","identity":"rs-5752892","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5752892","identity":"rs-5752892","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}