Teacher noticing in inclusive mathematics education: Analyzing its structure and expert-novice differences using a novel video-based test instrument

Teacher noticing in inclusive mathematics education: Analyzing its structure and expert-novice differences using a novel video-based test instrument | 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 noticing in inclusive mathematics education: Analyzing its structure and expert-novice differences using a novel video-based test instrument Johannes König, Gabriele Kaiser, Anton Bastian, Jonas Weyers, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5738066/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Teachers’ professional noticing—often conceptualized as their situation-specific skills of perception, interpretation and decision-making—constitutes an important component of their professional competence. Noticing has become increasingly significant worldwide in the pursuit of inclusive mathematics education in classroom settings, whereby teachers are required to provide equal opportunities for students across all ability levels. However, current teacher noticing frameworks lack the requisite specificity to support inclusive mathematics education, particularly regarding diagnostic applications and adequate learning support, and thus a revision of existing frameworks is warranted. On the one hand, such frameworks must incorporate selected facets of teacher knowledge, including mathematical pedagogical content knowledge (MPCK) and general pedagogical knowledge (GPK) specified for inclusive teaching; on the other hand, the differentiation into dispositions and situation-specific skills as decisive components of competence viewed as a continuum must be considered, as Sigrid Blömeke et al. suggested in their seminal framework. This paper describes the methodological challenges associated with the development of standardized instruments to measure teachers’ professional knowledge and noticing within inclusive mathematics education, as undertaken by the project Teacher Education and Development Study – Inclusive Mathematics Education (TEDS-IME). Using a large sample of 628 pre-service and in-service teachers, the paper aims to examine the dimensionality of teachers’ competence for inclusive mathematics education and expert–novice differences in the pattern of their competence facets. Our findings indicate that the newly developed video-based instrument for teachers’ noticing in inclusive mathematics education serves as a reliable and multidimensional measurement for both pre-service and in-service teachers. Special Education Educational Psychology School Counseling competence inclusive education teacher professional knowledge mathematical education noticing skills (mathematics) teacher Figures Figure 1 Figure 2 Figure 3 1. Introduction Inclusivity in education and diversity-driven teaching have become crucial issues for many educational systems worldwide and have significant implications for educational reform. Teachers are increasingly required to meet new demands associated with inclusivity and student diversity. Consequently, teacher education systems in many countries are experiencing challenges amid the need for curriculum reform in a way that will prepare new generations of teachers to master the principles of inclusive teaching (Florian & Camedda, 2020 ). The last decade has witnessed increased scholarly interest in demonstrating the effectiveness of teacher education targeting the professionalization of pre-service and in-service teachers with an emphasis on competence in inclusive teaching. This is attested by several literature reviews related to interventions in initial teacher education and teacher professional development in general (e.g., Dignath et al., 2022 ; Khamzina et al., 2024 ) and for mathematics education, in particular (Allsopp & Haley, 2015 ). However, as a recent overall synthesis and meta-analysis of such literature reviews shows (König et al., under review), certain research gaps persist, one of which relates to the rigorous measurement of relevant competence facets that professional teachers require today as a prerequisite for coping with the novel demands of inclusive mathematics teaching. One such competence facet is teacher knowledge, defined as “a body of professional knowledge that encompasses both knowledge of general pedagogical principles and skills and knowledge of the subject matter to be taught” (Grossman & Richert, 1988 , p. 54). This facet has become a major focus of research on (mathematics) teaching and teacher education (Cochran-Smith, 2001 ; Gitomer & Zisk, 2015 ; Kaiser & König, 2019 ; van Driel et al., 2014 ). While scholars broadly agree that mathematics teachers require professional knowledge for effective teaching (Baumert et al., 2010 ; Blömeke et al., 2022 ), recent developments in the mathematics teacher cognition agenda-driven research have prompted a shift toward the inclusion of facets that are more of situation-specific in nature (Blömeke et al., 2016 ; Kersting et al., 2012 ). Blömeke et al.’s ( 2015 ) pioneering work suggested framing teacher competence “as a continuum.” To date, their influential model (Fig. 1 ) has enriched numerous scholars’ scientific understanding that not only teacher knowledge but also situation-specific skills—comprising the perception and interpretation of classroom events as well as the ability to make adequate decisions in such situations—are all relevant in predicting teacher performance and instructional quality (Blömeke et al., 2022 ). These situation-specific skills have been further theoretically framed as the so-called PID-model (PID – perceive, interpret, decide; Kaiser et al., 2015 , 2017 ) and can more broadly be embedded within the “teacher noticing” research field (König et al., 2022 ). However, as the research on teacher noticing demonstrates, inclusive mathematics teaching remains largely overlooked in the conceptualization and measurement of relevant teacher competence facets (Roose et al., 2018 ). Against this background, the paper presents a novel video-based test instrument for measuring teachers’ professional noticing focusing inclusive mathematics education. The underlying conceptualization distinguishes, on the one hand, between challenges specific to inclusive mathematics instruction and those related to inclusive instruction in general, both of which require specific knowledge and skills. On the other hand, it distinguishes theoretically between the professional knowledge acquired during training and its situation-specific application—that is, situation-specific skills. The first question aims to assess the extent to which the newly developed instrument can capture this assumed multidimensionality. The paper further examines possible expert–novice differences in the competence facets’ pattern, since competence should be acquired during initial teacher education and in-service teaching. This second question focuses on three target groups with different levels of teaching experience (master’s students, teacher candidates in the second phase of German teacher education, in-service teachers). We analyze potential differences in knowledge and skills that relate to the assumptions that are prevalent in teacher expertise research (Stigler & Miller, 2018 )—in particular, the evolution from novice to experienced. In presenting a novel approach that connects teacher noticing with inclusive mathematics education and the research on teacher knowledge, we discuss the implications for teacher education design. 2. Literature review 2.1 Teacher professional competence Researchers broadly agree that mathematics teachers’ professional competence comprises relevant knowledge and cognitive skills (Blömeke & Delaney, 2012 ; Blömeke et al., 2016 ; Krauss et al., 2020 ). In recent decades, empirical research on teacher knowledge and skills has progressed considerably, in particular, the measurement of pre-service and in-service teachers’ professional knowledge and its psychometric quality has advanced significantly, with frequent recourse to Shulman’s ( 1987 ) influential classification and differentiating the professional knowledge base into content knowledge (CK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK). Among the most prominent approaches is the international-comparative large-scale assessment TEDS-M 2008 (Teacher Education and Development Study: Learning to Teach Mathematics), led by the International Association for the Evaluation of Educational Achievement (IEA) with the participation of 17 countries worldwide (Tatto & Senk 2011 ). Mathematics teachers’ professional knowledge was directly assessed using representative country samples with future teachers selected shortly prior to attaining full professional certification. In Germany, as the country that participated in TEDS-M 2008 under Sigrid Blömeke’s leadership (Blömeke, 2021 ), numerous other mathematics teacher education and development studies followed (for a recent overview of the so-called TEDS research program, see Kaiser, 2024 ). TEDS-M, along with other studies on mathematics teacher knowledge (Ball et al., 2008 ; Baumert et al., 2010 ; Kersting et al., 2012 ) achieved pioneering work in the large-scale conceptualization, operationalization, and assessment of mathematics teacher knowledge (Blömeke & Delaney, 2012 ; Blömeke, 2021 ). However, the continuing discourse on the adequate measurement and modeling of teacher competence highlighted the need for more action-oriented concepts and operationalizations. Knowledge constitutes a highly relevant basis for teachers’ professionalism (van Driel et al., 2014 ; Gitomer & Zisk, 2015 ; Magnusson et al., 1999). Meanwhile, it is reasonable to assume—not least based on findings from teacher expertise research (Bromme, 2001 ; Stigler & Miller, 2018 )—that successful teachers draw on specific skills in their teaching and during interactions with students according to situations that arise in the classroom. The importance of distinguishing between knowledge and skills is clearly illustrated in the Refined Consensus Model of PCK (e.g., Mientus et al., 2022 ). This model delineates several key aspects, notably the differentiation between an individual teacher’s available knowledge base (personal PCK) and the specific knowledge elements employed while planning, implementing, and reflecting on teaching during pedagogical reasoning (enacted PCK). Blömeke et al. ( 2015 ) suggested adding situation-specific skills to conventional teacher competence models (Fig. 1 ). Their model (Blömeke et al., 2015 ) inspired scholars to expand previously focused cognitive or affective–motivational dispositions to include situation-specific skills to proximally predict observable performance. The proposed model considers individual constructs not in isolation but on a continuum, bridging knowledge and performance and bringing together previously entrenched positions in competence measurement (Kaiser et al., 2015 ; 2017 ). Until today, this theoretical approach has had a lasting impact on the discourse on modeling and assessment of competencies, as exemplified by the measurement of competencies of pre-service and in-service teachers and has prompted significant further developments. Particularly noteworthy is Krauss et al.’s ( 2020 ) “Cascade Model”, which considers teachers’ situation-specific skills as a predictor of instructional quality and the orchestration of learning opportunities. Instructional quality and learning opportunities, mediated by student participation and engagement, in turn, are assumed to influence student learning outcomes on both the affective–motivational (e.g., enjoyment of learning) and cognitive (e.g., mathematics performance) levels. 2.2 Teacher noticing as part of teacher professional competence Blömeke et al.’s ( 2015 ) model also overlaps somewhat with teacher noticing research. Teacher noticing refers to the abilities and cognitive skills that teachers need, such as the ability to pay attention to relevant classroom processes and events of social interaction, to select important information, to draw appropriate conclusions, and to quickly decide how to proceed with the course of instruction. In their comprehensive literature review, König et al. ( 2022 ) demonstrated the existence of various approaches to conceptualizing teacher noticing, impeding any precise definition of teacher noticing as a scientific term. The heterogeneity of teacher noticing research may be attributed to the various perspectives that have shaped empirical approaches, including cognitive–psychological, socio-cultural, or expertise-related perspectives. Moreover, teacher noticing researchers have developed various conceptualizations, distinguishing several noticing facets such as attention, perception, interpretation, and decision-making, which are applied in different ways. However, advances in modeling teacher professional competence not only integrate conceptualizations of teacher noticing but also link noticing to professional knowledge, as teacher knowledge research has described and classified (Shulman, 1987 ) and teacher expertise research has referenced (Bromme, 2001 ; Stigler & Miller, 2018 ). A good example is the TEDS-M Follow-Up study conducted in Germany (TEDS-FU). TEDS-FU focused on early career teachers who were originally assessed in TEDS-M in Germany at the end of the second teacher education phase. They were surveyed again after their successful transition from teacher education into professional teaching. For this purpose, Kaiser et al. ( 2015 ) developed a novel video-based test instrument to measure teacher noticing in mathematics classrooms. The knowledge tests from TEDS-M and PID-skills measured using this instrument were further used to comprehensively and multidimensionally measure mathematics teacher competence in the classroom (Blömeke, 2021 ). 2.3 Teacher competence and teacher expertise Teacher competence and teacher expertise researchers agree that teacher knowledge and skills are malleable, not fixed (Kaiser et al., 2017 ; Kaiser et al., in this issue). Teacher knowledge and skills are considered as outcomes of education programs and professional development (Cochran-Smith, 2001 ; Kaiser & König, 2019 ). Formal and non-formal learning opportunities support pre-service teachers, teacher candidates, and in-service teachers to acquire professional knowledge but also to update, consolidate, or transform their professional knowledge base—for example, through deliberate practice (Berliner, 2004 ; Ericsson et al., 1993 ). Novice teachers (e.g., student teachers, pre-service teachers with little teaching experience), who are at an early stage in their teaching careers, differ in their level and quality of professional knowledge and teacher noticing in contrast with experienced in-service teachers (Carter et al., 1988 ). This finding was related to the competence continuum (Blömeke et al. 2015 ) model developed by Bastian et al. ( 2022 ), who reported that master’s students showed a considerable increase in noticing skills relative to those of in-service teachers, confirming certain assumptions regarding the development of teacher professional competence. 3. Theoretical framework: A video-based instrument for the professional noticing of teachers focusing inclusive mathematics education Inclusive education is a central concern in education policy, and its implementation has sparked vigorous debates (UNESCO, 2018; UN, 2006), altering expectations regarding teacher education and professional development (Florian & Camedda, 2020 ). Teacher professionalization research asks what prerequisites teachers must meet to satisfy the demands of inclusive education and become adequately qualified (e.g., Allsop & Haley, 2015; Khamzina et al., 2024 ). Research suggests that knowledge and skills should be considered prerequisites for teachers to satisfy the demands of inclusive teaching (König et al., 2019 ). In the course of the TEDS research program (Kaiser, 2024 ), the Teacher Education and Development Study – Inclusive Mathematics Education (TEDS-IME) was carried out in Germany between 2022 and 2024. One of its major goals was to develop a video-based test instrument to measure teachers’ professional noticing in inclusive mathematics education. The project’s interdisciplinary approach synthesized mathematical and pedagogical perspectives (Blömeke, 2021 ). Moreover, to facilitate analyses of knowledge and skills, specific knowledge tests referring to inclusive education were also developed. With reference to the discussion on competence (Blömeke et al., 2015 ), teacher competence for inclusive education was defined not only as mathematical pedagogical content knowledge (MPCK) and GPK for inclusive teaching (MPCK-IT and GPK-IT), but also as situation-specific skills, with the following competence facets distinguished (Kaiser et al., 2015 ): the perception of central events in the lesson (perception – P), the interpretation of these events (interpretation – I), and the development of decisions for action in the classroom and the planning of alternative lesson plans (decision-making – D). These conceptualizations, which have already been implemented in similar measurement instruments (e.g., Kaiser et al., 2015 ), are concretized in TEDS-IME for the first time for inclusive teaching from a mathematics didactic (M_PID-IT) and pedagogical (P_PID-IT) perspective. The perception facet is conceptualized as perception of the need for wide support, the interpretation facet as the interpretation of the learning status or development problem underlying the need for support, and the decision-making facet as determining the most appropriate support measure. The TEDS-IME project focuses on two areas identified in relevant competence catalogs for inclusive education—competence in diagnosis and intervention and support (König et al., 2019 )—which are primarily located at the classroom level: Diagnosis includes the identification of learning difficulties in the classroom, which requires an analysis of the teaching situation in terms of professional teaching perception as part of teacher noticing (Sherin et al., 2011 ; Ricken, 2017 ). This task of diagnosis from a mathematics didactics perspective was specified as the teachers’ perception of students’ individual misconceptions and errors, comprehension difficulties, and learning strategies. Regarding the competence model that Blömeke et al. ( 2015 ) viewed as a continuum, diagnostic competence is understood as a facet of professional teaching perception and interpretation (Heinrichs & Kaiser, 2018 ), which is particularly important in inclusive teaching. To date, however, few studies have systematically related the concept of professional teacher noticing in classrooms to the specific challenges of inclusive teaching (König et al., 2022 ). Intervention and support includes didactic and methodological measures for individualization and dealing with student heterogeneity in inclusive settings. Conventional approaches to differentiation are important for mathematics lessons from an inclusive perspective (Leuders & Prediger, 2017 ); task variation is crucial, as due to the variation of the task’s internal structure, this generates opportunities to respond to learners of different performance levels—from mathematically gifted learners to learners with partial mathematical weaknesses. In addition to forms of internal differentiation, elementary school approaches are used, such as forms of natural differentiation (e.g., Korff, 2018 ). Misconceptions and errors play a particularly important role in mathematics lessons, and it thus seems particularly important in the context of promoting diagnostic and support skills to familiarize (pre-service) teachers with systematically occurring error patterns based on misconceptions of central mathematical content (Heinrichs & Kaiser, 2018 ; Larrain & Kaiser, 2020 ). These considerations were incorporated into the novel video-based test instrument’s development in the TEDS-IME project and implemented into a survey design with three groups of secondary mathematics teachers with different experience levels (master’s students, teacher candidates in the second teacher education phase, experienced in-service teachers of secondary mathematics). 3. Research questions and hypotheses RQ 1 Is the theoretically postulated structure of teachers’ competence for inclusive mathematics education empirically verifiable? Shulman’s ( 1987 ) classification of PCK and GPK (e.g., Blömeke & Delaney, 2012 ) and Blömeke et al.’s ( 2015 ) differentiation into knowledge and situation-specific skills create a matrix to be filled with specific test instruments that all relate to inclusive teaching in the mathematics classroom (Fig. 2). We hypothesize that a four-dimensional model accounting for the theoretically assumed differentiations fits mathematics teacher competence test data better than accounting only for two-dimensional differentiations—mathematics vs. pedagogy or knowledge vs. skills (H1a). Moreover, we hypothesize that two-dimensional models are superior to a holistic model (general factor model) without any differentiation (H1b). RQ2 How do abilities differ between different pre- and in-service teacher groups with varying teaching experience regarding (a) the competence structure and (b) their ability levels? Although we do not claim that expert teachers are necessarily part of our study sample design (for further detail, see the Methods section), nevertheless, the three pre- and in-service groups with varying degrees of teaching experience (understood as a possible indicator of teacher expertise, Stigler & Miller, 2018 ) lead us to assume that contrasting groups may be interpreted as expert–novice differences. Master’s students participating in our study had already undergone their long-term (five-month) practicum but had not worked professionally, unlike teacher candidates in the second phase of teacher education or in-service teachers. Therefore, we designate master’s students “novice teachers” (Berliner, 2001). Teacher candidates participating in our study had been exposed to small-scale professional teaching during the second phase of teacher education but were not yet certified and thus had only limited teaching duties and responsibilities (e.g., high-stakes assessment of their students) and were designated “advanced beginners” (Berliner, 2001). Meanwhile, the “competent” status (Berliner, 2001) is fulfilled by in-service teachers who have several years of professional experience and full responsibility. For all three groups, we hypothesize that the dimensionality assumptions (RQ1) will be confirmed in subgroup analysis (H2a), which would support generalization assumptions. On the basis of the assumption regarding the development of expertise among novice, advanced beginner, and competent teachers (Berliner, 2001), we hypothesize that teacher candidates should outperform master’s students, while in-service teachers should exhibit better test results than those of teacher candidates (H2b). 4. Methods 4.1 Study context The present study is part of the larger TEDS-IME project, which aims to conceptualize, measure, and promote secondary school mathematics teachers’ competence for inclusive mathematics education. To evaluate the effectiveness of a targeted professional development program, the team developed new instruments to measure specific competence facets relating to inclusive mathematics education. This study focuses on the development and use of a novel video-based instrument to capture teacher noticing skills for inclusive mathematics education from a mathematics pedagogical perspective (i.e., M_PID-IT) and a general pedagogical perspective (i.e., P_PID-IT). The relationship between this video-based measurement and a knowledge assessment focusing on PCK for inclusive mathematics education (i.e., MPCK-IT) and general pedagogical knowledge for inclusive teaching (i.e., GPK-IT) is also analyzed. A theoretically grounded development and thorough validation of the measurement instruments are key to evaluating the program’s effectiveness and are crucial for ensuring the findings’ quality. 4.2 Sample We use data from the TEDS-IME project that stem from the evaluation of the pre- and in-service teachers at the project’s first time point. They were assigned to intervention and control groups, since, after that first assessment, study participants of the intervention group were educated in a topic-specific professional development program. The present analysis includes only data from the project’s first time point, thus providing insights into the non-manipulated state of teacher competence structure without focusing on potential changes to that competence in the course of the TEDS-IME project’s professional development program. As Table 1 shows, 628 pre-service and in-service mathematics teachers participated in the first measurement (intervention group: 515; control group: 113). This included 233 master’s students, 163 teacher candidates in the second phase of teacher education, and 232 in-service teachers. The survey covered 11 German federal states, focusing on Hamburg (35.5%) and North Rhine-Westphalia (47.0%). The intervention groups completed the survey online in the first session of the professional development program, while the control groups completed the survey onlinein their own time. Table 1 Key demographic characteristics of the sample Master’s students Teacher candidates (Preparatory service) In-service teachers Total N 233 (37%) 163 (26%) 232 (37%) 628 Gender Female 146 (63%) 98 (60%) 159 (69%) 403 (64%) Male 87 (37%) 61 (37%) 70 (30%) 218 (35%) Diverse / Not indicated 0 (0%) 4 (3%) 3 (1%) 7 (1%) Age (M (SD)) 24.5 (3.2) 29.7 (5.5) 41.7 (10.2) 32.2 (10.3) Final secondary school GPA (M (SD)) 1.91 (0.61) 2.06 (0.63) 2.25 (0.64) 2.07 (0.64) Master’s grade (M (SD)) - 1.81 (0.51) 1.93 (0.51) 1.88 (0.51) Finale Grade in teacher training / induction (M (SD)) - - 2.00 (0.72) 2.00 (0.71) Study semester (M (SD)) 8.0 (2.5) - - - Teaching experience (M (SD), in years) 0.3 (0.7) 1.7 (1.7) 12.8 (9.1) 5.3 (8.0) Teacher education program Lower Secondary Education 63 (27%) 50 (30.7%) 119 (51.3%) 232 (36.9%) Upper Secondary Education 148 (63.5%) 75 (46%) 81 (34.9%) 304 (48.4%) Special Needs Education 18 (7.7%) 6 (3.7%) 14 (6%) 38 (6.1%) Alternative and Lateral Entry into Teaching 0 30 (18.4%) 14 (6%) 44 (7.0%) Other 1 4 (1.7%) 2 (1.2%) 4 (1.7%) 10 (1.6%) School Type of Employment Lower secondary school - 15 (9.2%) 42 (18.1%) 57 (14.4%) Lower and upper secondary school - 144 (88.3%) 188 (81.0%) 332 (84.1%) Special needs school - 3 (1.8%) 0 3 (0.8%) Other 2 - 1 (0.6%) 2 (0.9%) 3 (0.8%) Note. 1 = Programs for primary school, vocational school and other programs; 2 = vocational schools and other schools; GPA = Grade Point Average; All grades are based on a scale from 1.0 (very good) to 4.0 (satisfactory) 4.3 Measures of teacher professional competence To capture teacher noticing in inclusive mathematics education, the TEDS-IME project team developed a novel video-based instrument to capture perception, interpretation, and decision-making in inclusive mathematics education from both mathematical pedagogical and general pedagogical perspectives (see further the outline in the Electronic Supplement Material, ESM). Four video vignettes (see ESM Table 1 ) depicting inclusive algebra instruction situations in secondary education are used, providing overview information (e.g., grade level, topic of the lesson unit) and lesson materials (e.g., tasks). Test items relate to the videos and are designed to measure cognitive processes of perception, interpretation, and decision-making (for further details on such processes as well as sample items, see ESM Figs. 1 –3). Interrater reliability is good for participants’ responses to open response items (see the outline of the video-based test instrument in the ESM). Both mathematical PCK for inclusive teaching (MPCK-IT) and general pedagogical knowledge for inclusive teaching (GPK-IT) were measured using online standardized knowledge tests. The ESM provides an outline of the tests, including sample items (ESM Figs. 4–5). 4.4 Data analysis Item response theory models were estimated to analyze the structure of teachers’ competence (RQ1), starting with (1) a one-dimensional model—that is, competence as one holistic construct; (2) a two-dimensional model contrasting subject-specific and general pedagogical aspects; (3) a two-dimensional model contrasting professional knowledge (i.e., cognitive dispositions) and noticing (i.e., situation-specific skills); and (4) a four-dimensional model, including M_PID-IT, P_PID-IT, MPCK-IT, and GPK-IT (see Fig. 2). Models were compared as to relative fit indices (especially model deviance), reliability, and dimensional intercorrelations. For nested models, χ² tests determined whether the model fit change was statistically significant. Comparing the experience groups (RQ2), we investigated to what extent these dimensional analyses hold for the three respective experience groups. Therefore, the competence structure was re-examined separately for each teaching experience group based on the model comparisons (RQ2a). Possible differences between the competence levels of the three groups (RQ2b) were examined using one-way analysis of variance (ANOVA). Exploratory group-wise comparisons were conducted using post-hoc tests (Scheffé post-hoc test for equal variances; if equal variances were not given: Games-Howell post-hoc test). Data preparation and mean comparisons were performed in SPSS (version 29). Item response theory analyses were conducted using ConQuest (version 5.34.2). 5. Results 5.1 Structure of teachers’ competence for inclusive mathematics education RQ1 investigated the structure of teachers’ competence for inclusive mathematics education and asked whether it is empirically verifiable. As Table 2 shows, the model fit of the four different scaling models varied significantly. As we had hypothesized (H1a), the four-dimensional model (4D) accounting for the theoretically assumed differentiations (as Fig. 2 illustrates) fits the data better than accounting only for two-dimensional differentiations into mathematics vs. pedagogy (2D-MP) or knowledge vs. skills (2D-KS). Moreover—again, as hypothesized (H1b)—the four-dimensional model (4D) and the two-dimensional models (2D-MP and 2D-KS) are superior to the holistic model (general factor model, 1D) without any differentiation. Table 3 provides further details on the scaling models’ psychometric quality. First, all scaled dimensions are reliable. While the sparse models with few dimensions indicate good reliability (EAP > .75; WLE > .70 with the exception of Pedagogy .68), the four-dimensional model’s scale reliability is still within acceptable range (EAP > .70 with the exception of P_PID-IT .69; WLE > .55), considering that the number of items measuring a scale is much smaller. Second, intercorrelations of subscales indicate teacher competence for inclusive teaching is of multidimensional nature. Whereas the intercorrelation between mathematics and general pedagogy in the two-dimensional model is relatively high (.80), that between knowledge and situation-specific skills is lower (.68). The four-dimensional model demonstrates that teachers’ competence may reasonably be differentiated into mathematics pedagogy and general pedagogy as well as knowledge and situation-specific skills, as the intercorrelations are relatively low. In particular, knowledge and skills in general pedagogy (P_PID-IT and GPK-IT) are moderately intercorrelated (.50), whereas knowledge and skills in mathematics pedagogy (M_PID-IT and MPCK-IT) are more closely intercorrelated (.77). Here, we use scaling results from the four-dimensional model, whose scale reliability Table 4 illustrates. Table 2 Model comparison Model Deviance BIC AICc Model comparison using χ 2 -tests against the less complex model 1) 2) 3) χ 2 ( df ) p χ 2 ( df ) p χ 2 ( df ) p 1) 1D 46681.6 47355.1 46972.4 2) 2D-MP 46838.7 47300.4 46912.5 157.02 (2) < .001 3) 2D-KS 46531.7 47218.4 46829.5 149.99 (2) < .001 4) 4D 46446.7 47175.3 46769.7 234.92 (9) < .001 391.94 (7) < .001 84.93 (7) < .001 Note . BIC - Bayesian information criterion. AICc - Sample-size corrected Akaike information criterion. 1D - one-dimensional holistic model of competence. 2D-MP - two-dimensional model of mathematics pedagogy and general pedagogy. 2D-KS - two-dimensional model of knowledge and situation-specific skills. 4D - four-dimensional model of two-dimensional knowledge (MPCK-IT and GPK-IT) and two-dimensional situation-specific skills (M_PID-IT and P_PID-IT). Table 3 Reliabilities and Intercorrelations Dimension Variance EAP WLE Latent intercorrelations M1 Holistic 0.30 .84 .84 M2 Mathematics 0.37 .81 .78 Pedagogy 0.29 .77 .68 .80 M3 Skills 0.31 .78 .73 Knowledge 0.43 .80 .77 .68 M_PID-IT P_PID-IT MPCK-IT GPK-IT M4 M_PID-IT 0.39 .76 .60 1 P_PID-IT 0.34 .69 .59 .77 1 MPCK-IT 0.49 .77 .70 .72 .43 1 GPK-IT 0.53 .71 .56 .65 .50 .73 1 Note. EAP - Expected a posteriori estimator. WLE - weighted likelihood estimator. M_PID-IT - mathematics instruction for inclusive teaching: perception, interpretation, decision-making. P_PID-IT - pedagogy for inclusive teaching: perception, interpretation, decision-making. MPCK-IT - mathematics pedagogical content knowledge for inclusive teaching. GPK-IT - general pedagogical knowledge for inclusive teaching. Table 4 Reliability for the individual competence measures and correlations of item difficulties between experience groups based on two two-factor models (PID: mathematics vs. pedagogy; Knowledge: mathematics vs. pedagogy) Variable Reliability Variance WMNSQ Discrimination Correlation MP Correlations between item difficulties EAP WLE MS / TPS MS / IST TPS / IST M_PID-IT 0.671 0.576 0.35 M = 1.00, [.92, 1.11] M = .27, [.10, .45] 0.77 0.93 0.94 0.95 P_PID-IT 0.666 0.590 0.36 0.95 0.94 0.95 MPCK-IT 0.750 0.696 0.50 M = 1.00, [.86, 1.11] M = .31, [.16, .55] 0.73 0.92 0.87 0.86 GPK-IT 0.682 0.564 0.56 0.92 0.85 0.90 Note . EAP - Expected a posteriori estimator. WLE - weighted likelihood estimator. WMNSQ - Weighed mean squares. M_PID-IT - mathematics instruction for inclusive teaching: perception, interpretation, decision-making. P_PID-IT - pedagogy for inclusive teaching: perception, interpretation, decision-making. MPCK-IT - mathematics pedagogical content knowledge for inclusive teaching. GPK-IT - general pedagogical knowledge for inclusive teaching. Correlation MP: Latent correlation between mathematics and pedagogy. MS - Master students, TPS - Teachers in preparatory service, IST - In-service teachers. 5.2 Expert–novice differences in teachers’ competence for inclusive mathematics education RQ2 concerned how pre- and in-service teachers would differ in the four competence facets related to inclusive mathematics education. The dimensionality was again examined for the three subgroups as it had been for the entire sample. The findings indicate that the more differentiated the scaling model is, the better the model fits the data (see Electronic Supplementary Material, ESM, Tables 2 and 3 ), confirming H2a. Dimensionality assumptions may thus be shown for the subgroups—a relevant prerequisite for comparing the subgroups’ mean scores Based on our assumptions regarding the development of teacher competence and expertise (see, Kaiser et al., in this issue), we hypothesized that in-service teachers would outperform teacher candidates in the second phase of teacher education and that the candidates, in turn, would exhibit better test results than master’s students. Figure 3 presents the percentage solution frequency mean scores according to experience group (for statistical details, see ESM Table 4 ). Against our H2b, the mean scores do not correspond with the expected ranking. First, group mean score differences are statistically significant for situation-specific skills but not for knowledge (ESM Table 4 ), and with only small practical relevance (.015 ≤ η 2 ≤ .058). In both cases, in-service teachers are slightly outperformed by pre-service teachers (see, for details, post-hoc test results in ESM Table 4 and red lines in Fig. 3): Whereas teacher candidates significantly outperform in-service teachers in M_PID-IT (but not master’s students), master’s students score significantly higher than teacher candidates and in-service teachers in P_PID-IT. 6. Discussion Considering new school requirements in the area of inclusive teaching and education (e.g., Piezunka et al., 2017 ; Ricken, 2017 ), teachers—secondary school mathematics teachers among them—require professional knowledge and situation-specific skills that clearly go beyond existing conceptualizations of teachers’ professional knowledge (e.g., Allsopp & Haley, 2015 ; Shulman, 1987 ; Tatto & Senk, 2011 ). While pedagogical demand has long determined expectations that teachers will be able to deal with their students’ heterogeneity and diversity, pressure to act and societal expectations have increased significantly with the UN Conventions on the Rights of Persons with Disabilities (UN, 2006) and its implementation in guidelines and standards in the education system (UNESCO, 2018). Mathematics education research is required to discover how these competencies should be defined and structured. Embedded in the TEDS research program that Sigrid Blömeke initiated and successfully promoted over several years (Kaiser, 2024 ), the TEDS-IME research project has made significant progress in developing novel test instruments to measure knowledge and situation-specific skills of secondary mathematics teachers for inclusive mathematics education. Therefore, we used Shulman’s ( 1987 ) influential classification of teacher knowledge, comprising facets such as MPCK and GPK and specified for inclusive teaching, yielding the MPCK-IT and GPK-IT constructs. Moreover, Blömeke et al.’s ( 2015 ; see Fig. 1 ) model of competence viewed as a continuum influenced the TEDS-IME project to go beyond mere knowledge tests and develop a novel video-based assessment that accounts for situation-specific skills of perception, interpretation, and decision-making (PID-model; Kaiser et al., 2015 , 2017 ), combining perspectives from mathematics pedagogy and general pedagogy. The development of such a comprehensive test instrument inventory with four theoretically specified constructs differentiating knowledge and skills and mathematics pedagogy and general pedagogy (see Fig. 2) prompted extensive research during the TEDS-IME project. This paper’s objective was to present four new instruments for comprehensively measuring mathematics teachers’ professional competence facets, guided by the following questions: What dimensionality could be provided in applying such an approach? Do expert-novice differences exist in the pattern of competence facets among master’s students, teacher candidates in their second phase of teacher education, and in-service teachers? Data were available from the TEDS-IME project’s large-scale assessment in Germany with more than 600 study participants of varying teaching experience thus allowing comparisons following expert–novice interpretations. Although study participants were asked after the first assessment to undergo training via a novel teacher professional program, the data from the first measurement were wholly unmanipulated and provided an appropriate dataset for testing our hypotheses. 6.1 Structure of teachers’ competence for inclusive mathematics education RQ1 targeted the structure of teachers’ competence for inclusive mathematics education. As hypothesized (H1a), the four-dimensional model showed the best fit to our data, confirming that, on the one hand, knowledge and situation-specific skills should be differentiated, as Blömeke et al. ( 2015 ) suggested, and, on the other hand, that mathematics instruction and general pedagogy serve as two distinct resources, as Shulman ( 1987 ) specified. Moreover, sparse models with two dimensions each (knowledge vs. situation-specific skills, mathematics instruction vs. general pedagogy) also showed a better fit than that of a one-dimensional model that corresponded to the assumption a holistic understanding of teachers’ competence for inclusive mathematics education (H1b). In summary, our findings confirm Blömeke’s ( 2021 ) assertion that teacher competence is multidimensional in nature and that its measurement is a complex undertaking. This paper provides evidence for this issue with regards to the complex professional demands in the inclusive mathematics classroom. Meanwhile, in line with current research discourse on teacher professional competence, it confirms conceptually sound differentiations into knowledge and skills as well as mathematics pedagogy and general pedagogy for application in the inclusive mathematics educational context. 6.2 Expert-novice differences in teachers’ competence for inclusive mathematics education The structure of competence in the above subscales for examining RQ1 was again demonstrated for the three different groups of pre-service and in-service teachers. As anticipated with our hypothesis (H2a), the differentiation into a four-dimensional scaling model with inferential statistical testing clearly proved to be the model that best fitted the data for all three groups. Thus, the assumed structure, which had been proven in the overall sample, could be generalized to the two teacher education phases in Germany—study at university with heavy emphasis on theoretical knowledge foundations and second phase of teacher education with initial responsibility for school teaching—as well as the target group of the more experienced in-service teachers. Overall, this result represents an excellent basis for addressing all three target groups equally with the further training measure envisaged in the TEDS-IME project (this was not part of the paper; for findings on the effectiveness of the training future, see publications by the TEDS-IME project team). The three groups’ test scores were also examined, accompanied by an expectation derived from expert-novice comparisons—namely, that in-service teachers should outperform teacher candidates, who, in turn, should achieve better test results than master’s students (H2b). This assumption, relying on teacher expertise development models (Berliner, 2004 ), was reasonable for situation-specific skills in particular, as practicing and reflecting on processes of classroom perception, interpreting events, and making decisions for the further course of action should be intertwined with the amount of teaching experience—a criterion most suitable for distinguishing the three groups according to expertise. Unexpectedly, mean differences had little practical relevance for situation-specific skills and were non-significant for knowledge. Against our hypothesis, the group ranking was virtually the opposite of what we had hypothesized (see Fig. 3): in-service teachers were outperformed by either master’s students (P_PID-IT) or teacher candidates (M_PID-IT), teacher candidates were outperformed by master’s students (P_PID-IT), and master’s students were not outperformed by teacher candidates (M_PID-IT). Although this paper offers no further data analysis, several possible approaches to the findings may be highlighted. First, one might assume that inclusive mathematics education is a bridge too far in terms of the current reality of teaching practice (e.g., Steinmetz et al., 2021 ). Whereas new content, such as inclusive education and teaching for diversity, may have been incorporated into the initial teacher education curriculum in Germany as the country of our study (e.g., KMK, 2022), not least pushed by a half-billion-euro quality initiative (the so-called “Qualitätsoffensive Lehrerbildung”) aimed at expanding topics such as inclusion in teacher education (BMBF, 2024, p. 9), the question arises as to what extent such topics acquired by teachers during initial teacher education continue to be implemented years later and become established as routines in everyday teaching—intertwined with the growth of teacher expertise for inclusive mathematics education. The latter is more likely to be decisive for the acquisition of knowledge and situation-specific skills among in-service teachers. As the in-service teachers in our sample are the least likely to have been exposed to learning opportunities in inclusive education and teaching during their initial teacher education several years ago, we may ask what alternative learning opportunities they might have had to update their teacher competence with regards to mathematics inclusive education in recent years. It is doubtful that they enjoyed abundant opportunities to do so (e.g., Steinmetz et al., 2021 ), but our data are clearly limited, thus leaving open a relevant question for future research on inclusive mathematics teacher education and professional development. Second, inclusive education in Germany is a prominent topic in general pedagogy, not only with a particular focus on inclusive teaching but also considering the broader context of societal and cultural issues as well as topics in educational science and educational psychology. The broader context issues of inclusive education are prioritized in the first phase of teacher education in Germany (e.g., Lohmann et al., 2011 ), whereas the second phase focuses on subject-specific instruction in highly practical situations—with the aim of qualifying teachers to deliver good instruction in the existing school system. This might explain why differences between master’s students and the other two groups are larger in P_PID-IT than in M_PID-IT, the latter, with teacher candidates—that is, pre-service teachers during their second phase—outperforming the other groups (at least on the numerical level). Third, measurement instruments developed in the TEDS-IME project may exhibit a higher level of constructive alignment (Biggs, 2014 ) with initial teacher education than among in-service teachers’ professional development. Future research is required to validate the novel instruments presented for the first time in the present article. 7. Conclusion Given that the development of teachers’ competence for inclusive mathematics education requires support, the rigorous measurement instruments developed as part of the project TEDS-IME are highly valuable from a scientific perspective. Meanwhile, TEDS-IME continued the comprehensive and pioneering work on mathematics teacher competence modeling and measuring that Sigrid Blömeke, an internationally renowned and excellent scholar, had exceptionally achieved over many years. Blömeke invariably and enthusiastically endorsed interdisciplinary research approaches, particularly those that connect mathematics education, general pedagogy, cognitive psychology, and educational measurement, and her work has influenced the present study’s conceptualization of competence measurement. The acknowledgment that teachers require not only pedagogy or mathematics knowledge but a complex and multidimensional profile of competence that goes beyond knowledge to consider the situation-specific skills of perception, interpretation, and decision-making, is an element of Blömeke’s scientific legacy with which we have attempted to comply in the present study and data analysis. The research questions that remain unresolved, such as why in-service teachers were outperformed by pre-service teachers in teacher noticing, should form the starting point for further research wishing to build on outstanding research achievements of our esteemed colleague Sigrid Blömeke. Declarations Disclosure statement: No potential conflict of interest was reported by the author(s). Funding: This work was supported by BMBF Germany, grant number 01NV2125A and 01NV2125B. References Allsopp, D. H., & Haley, K. C. (2015). A Synthesis of Research on Teacher Education, Mathematics, and Students with Learning Disabilities. Learning Disabilities: A Contemporary Journal , 13 (2), 177–206. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education , 59 (5), 389–407. https://doi.org/10.1177/0022487108324554 Bastian, A., Kaiser, G., Meyer, D., Schwarz, B., & König, J. (2022). Teachers‘ noticing and its growth toward expertise: an expert-novice comparison with (pre-service) secondary mathematics teachers. Educational Studies in Mathematics , 110 , 205–232. https://doi.org/10.1007/s10649-021-10128-y Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., & Tsai, Y.‑M. (2010). Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress. American Educational Research Journal , 47 (1), 133–180. https://doi.org/10.3102/0002831209345157 Berliner, D. C. (2004). Describing the behavior and documenting the accomplishments of expert teachers. Bulletin of Science, Technology & Society , 24 (3), 200–212. https://doi.org/10.1177/0270467604265535 Biggs, J. (2014). Constructive alignment in university teaching. HERDSA Review of Higher Education , 1 (1), 5–22. Blömeke, S. (2021). IEA’s Teacher Education and Development Study in Mathematics (TEDS-M). In T. Nilsen, A. Stancel-Piątak, & J.-E. Gustafsson (Eds.), Springer International Handbooks of Education. International Handbook of Comparative Large-Scale Studies in Education (pp. 1–53). Springer International Publishing. https://doi.org/10.1007/978-3-030-38298-8_16-1 Blömeke, S., Busse, A., Kaiser, G., König, J., & Suhl, U. (2016). The relation between content-specific and general teacher knowledge and skills. Teaching and Teacher Education , 56 , 35–46. https://doi.org/10.1016/j.tate.2016.02.003 Blömeke, S., & Delaney, S. (2012). Assessment of teacher knowledge across countries: a review of the state of research. ZDM – Mathematics Education , 44 (3), 223–247. https://doi.org/10.1007/s11858-012-0429-7 Blömeke, S., Gustafsson, J.‑E., & Shavelson, R. J. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift Für Psychologie , 223 (1), 3–13. https://doi.org/10.1027/2151-2604/a000194 Blömeke, S., Jentsch, A., Ross, N., Kaiser, G., & König, J. (2022). Opening up the black box: Teacher competence, instructional quality, and students’ learning progress. Learning and Instruction , 79 , Article 101600. https://doi.org/10.1016/j.learninstruc.2022.101600 Bromme, R. (2001). Teacher expertise. In N. J. Smelser & P. B. Baltes (Eds.), International encyclopedia of the social & behavioral sciences (pp. 15459–15465). Elsevier. https://doi.org/10.1016/B0-08-043076-7/02447-5 BMBF [Bundesministerium für Bildung und Forschung]. (2024). ‘Qualitätsoffensive Lehrerbildung’: A look back, a look ahead . https://www.qualitaetsoffensive-lehrerbildung.de/lehrerbildung/shareddocs/downloads/files/abschlussbroschuere2024_en.pdf?__blob=publicationFile&v=2 Carter, K., Cushing, K., Sabers, D., Stein, P., & Berliner, D. (1988). Expert-novice differences in perceiving and processing visual classroom information. Journal of Teacher Education , 39 (3), 25–31. https://doi.org/10.1177/002248718803900306 Cochran-Smith, M. (2001). Constructing outcomes in teacher education. Education Policy Analysis Archives , 9 (11). https://doi.org/10.14507/epaa.v9n11.2001 Dignath, C., Rimm-Kaufman, S., van Ewijk, R., & Kunter, M. (2022). Teachers’ Beliefs About Inclusive Education and Insights on What Contributes to Those Beliefs: a Meta-analytical Study. Educational Psychology Review , 34 (4), 2609–2660. https://doi.org/10.1007/s10648-022-09695-0 Ericsson, K. A., Krampe, R. T., & Tesch-Römer, C. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review , 100 (3), 363–406. https://doi.org/10.1037/0033-295X.100.3.363 Florian, L., & Camedda, D. (2020). Enhancing teacher education for inclusion. European Journal of Teacher Education , 43 (1), 4–8. https://doi.org/10.1080/02619768.2020.1707579 Gitomer, D. H., & Zisk, R. C. (2015). Knowing What Teachers Know. Review of Research in Education , 39 (1), 1–53. https://doi.org/10.3102/0091732X14557001 Göransson, K., & Nilholm, C. (2014). Conceptual diversities and empirical shortcomings – a critical analysis of research on inclusive education. European Journal of Special Needs Education , 29 (3), 265–280. https://doi.org/10.1080/08856257.2014.933545 Grossman, P. L., & Richert, A. E. (1988). Unacknowledged knowledge growth: A re-examination of the effects of teacher education. Teaching and Teacher Education , 4 (1), 53–62. https://doi.org/10.1016/0742-051X(88)90024-8 Hasselhorn, M., & Gold, A. (2022). Pädagogische Psychologie: Erfolgreiches Lernen und Lehren . W. Kohlhammer GmbH. https://doi.org/10.17433/978-3-17-039783-5 Heinrichs, H., & Kaiser, G. (2018). Diagnostic Competence for Dealing with Students’ Errors: Fostering Diagnostic Competence in Error Situations. In T. Leuders, K. Philipp, & J. Leuders (Eds.), Diagnostic Competence of Mathematics Teachers (pp. 79–94). Springer International Publishing. https://doi.org/10.1007/978-3-319-66327-2_4 Kaiser, G. (2024). The TEDS research program. Its origin and development (in memoriam Sigrid Blömeke). In J. König, C. Hanisch, P. Hanke, T. Hennemann, K. Kaspar, M. Martens, & S. Strauß (Eds.), Auf die Lehrperson und ihren Unterricht kommt es an. Zehn Jahre empirische Professions- und Unterrichtsforschung im IZeF der Universität zu Köln (pp. 261–287). Waxmann Verlag GmbH. Kaiser, G. (2025). Research on Teacher Expertise and Teacher Competence – Are they complementary or contradictory paradigmatic approaches? ZDM – Mathematics Education . in this issue Kaiser, G., Blömeke, S., König, J., Busse, A., Döhrmann, M., & Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers—cognitive versus situated approaches. Educational Studies in Mathematics , 94 (2), 161–182. https://doi.org/10.1007/s10649-016-9713-8 Kaiser, G., Busse, A., Hoth, J., König, J., & Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education , 13 (2), 369–387. https://doi.org/10.1007/s10763-015-9616-7 Kaiser, G., & König, J. (2019). Competence measurement in (mathematics) teacher education and beyond: Implications for policy. Higher Education Policy , 32 (4), 597–615. https://doi.org/10.1057/s41307-019-00139-z Kersting, N. B., Givvin, K. B., Thompson, B. J., Santagata, R., & Stigler, J. W. (2012). Measuring usable knowledge: Teachers’ analyses of mathematics classroom videos predict teaching quality and student learning. American Educational Research Journal , 49 (3), 568–589. https://doi.org/10.3102/0002831212437853 Khamzina, K., Stanczak, A., Brasselet, C., Desombre, C., Legrain, C., Rossi, S., Guirimand, N., & Cilia, F. (2024). Designing Effective Pre-service Teacher Training in Inclusive Education: a Narrative Review of the Effects of Duration and Content Delivery Mode on Teachers’ Attitudes Toward Inclusive Education. Educational Psychology Review , 36 (1). https://doi.org/10.1007/s10648-024-09851-8 König, J., Gerhard, K., Kaspar, K., & Melzer, C. (2019). Professionelles Wissen von Lehrkräften zur Inklusion: Überlegungen zur Modellierung und Erfassung mithilfe standardisierter Testinstrumente. Pädagogische Rundschau , 73, (1), 43–64. https://doi.org/10.3726/PR012019.0004 König, J., Gerhard, K., Melzer, C., Rühl, A.‑M., Zenner, J., & Kaspar, K. (2017). Erfassung von pädagogischem Wissen für inklusiven Unterricht bei angehenden Lehrkräften: Testkonstruktion und Validierung. Unterrichtswissenschaft , 45 , 223–242. König, J., Heine, S., Weyers, J., Arntz, C.‑G., Kramer, C., Strauß, S., Gerhard, K., Mühle, J., Engartner, T., Großschedl, J., Hanisch, C., Hanke, P., Hennemann, T., Jost, J., Kaspar, K., & Rott, B. (under review). 1 Effectiveness of interventions in teacher education: Synthesis of reviews (2010–2024). Zeitschrift Für Erziehungswissenschaft . König, J., Santagata, R., Scheiner, T., Adleff, A.‑K., Yang, X., & Kaiser, G. (2022). Teacher noticing: A systematic literature review of conceptualizations, research designs, and findings on learning to notice. Educational Research Review , 36 , Article 100453. https://doi.org/10.1016/j.edurev.2022.100453 Korff, N. (2018). Inklusiver Mathematikunterricht in der Primarstufe: Erfahrungen, Perspektiven und Herausforderungen (3. unveränderte Auflage). Schneider Verlag Hohengehren. Krauss, S., Bruckmaier, G., Lindl, A., Hilbert, S., Binder, K., Steib, N., & Blum, W. (2020). Competence as a continuum in the COACTIV study: the “cascade model”. ZDM – Mathematics Education , 52 (2), 311–327. https://doi.org/10.1007/s11858-020-01151-z KMK [Kultusministerkonferenz]. (2004/2022). Standards für die Lehrerbildung: Bildungswissenschaften [Beschluss der Kultusministerkonferenz vom 16.12.2004 i. d. F. 16.05.2022]. Larrain, M., & Kaiser, G. (2020). Analysis of students’ mathematical errors as a means to promote future primary school teachers’ diagnostic competence. UNIPLURIVERSIDAD , 19 (2), 17–39. https://doi.org/10.17533/udea.unipluri.19.2.02 Leuders, T., & Prediger, S. (2017). Flexibel differenzieren erfordert fachdidaktische Kategorien. In J. Leuders, T. Leuders, S. Prediger, & S. Ruwisch (Eds.), Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik. Mit Heterogenität im Mathematikunterricht umgehen lernen (pp. 3–16). Springer. https://doi.org/10.1007/978-3-658-16903-9_1 Lohmann, V., Seidel, V., & Terhart, E. (2011). Bildungswissenschaften in der universitären Lehrerbildung: Curriculare Strukturen und Verbindlichkeiten. Eine Analyse aktueller Studienordnungen an nordrhein-westfälischen Universitäten. Lehrerbildung auf dem Prüfstand , 4 (2), 271–302. https://doi.org/10.25656/01:14724 Magnusson, S., Krajcik, J., & Borko, H. (2002). Nature, Sources, and Development of Pedagogical Content Knowledge for Science Teaching. In J. Gess-Newsome & N. G. Lederman (Eds.), Science & Technology Education Library. Examining Pedagogical Content Knowledge (Vol. 6, pp. 95–132). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47217-1_4 Mientus, L., Hume, A., Wulff, P., Meiners, A., & Borowski, A. (2022). Modelling STEM Teachers’ Pedagogical Content Knowledge in the Framework of the Refined Consensus Model: A Systematic Literature Review. Education Sciences , 12 (6), 385. https://doi.org/10.3390/educsci12060385 Piezunka, A., Schaffus, T., & Grosche, M. (2017). Vier Definitionen von schulischer Inklusion und ihr konsensueller Kern: Ergebnisse von Experteninterviews mit Inklusionsforschenden. Unterrichtswissenschaft , 45 (4), 207–222. https://doi.org/10.3262/UW1704207 Ricken, G. (2017). Kompetent sein für Inklusive Schulen heißt auch Diagnostizieren lernen. In M. Gercke, S. Opalinski, & T. Thonagel (Eds.), Inklusive Bildung und gesellschaftliche Exklusion (pp. 187–199). Springer. https://doi.org/10.1007/978-3-658-17084-4_12 Roose, I., Goossens, M., Vanderlinde, R., Vantieghem, W., & van Avermaet, P. (2018). Measuring professional vision of inclusive classrooms in secondary education through video-based comparative judgement: An expert study. Studies in Educational Evaluation , 56 , 71–84. https://doi.org/10.1016/j.stueduc.2017.11.007 Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes . Routledge. Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review , 57 (1), 1–22. https://doi.org/10.17763/haer.57.1.j463w79r56455411 Steinmetz, S., Wrase, M., Helbig, M., & Döttinger, I. (2021). Die Umsetzung schulischer Inklusion nach der UN-Behindertenrechtskonvention in den deutschen Bundesländern . Nomos Verlagsgesellschaft mbH & Co. KG. https://doi.org/10.5771/9783748924401 Stigler, J. W., & Miller, K. F. (2018). Expertise and Expert Performance in Teaching. In K. A. Ericsson, R. R. Hoffman, A. Kozbelt, & A. M. Williams (Eds.), The Cambridge Handbook of Expertise and Expert Performance (pp. 431–452). Cambridge University Press. https://doi.org/10.1017/9781316480748.024 Tatto, M. T., & Senk, S. (2011). The Mathematics Education of Future Primary and Secondary Teachers: Methods and Findings from the Teacher Education and Development Study in Mathematics. Journal of Teacher Education , 62 (2), 121–137. https://doi.org/10.1177/0022487110391807 UN [United Nations]. (2006). Convention on the Rights of Persons with Disabilities . https://social.desa.un.org/issues/disability/crpd/convention-on-the-rights-of-persons-with-disabilities-articles UNESCO [United Nations Educational, Scientific and Cultural Organisation]. (2018). Global Education Meeting 2018: Brussels Declaration [Document ED-2018/GEM/1]. https://unesdoc.unesco.org/ark:/48223/pf0000366394 van Driel, J. H., Berry, A., & Meirink, J. (2014). Research on science teacher knowledge. In N. G. Lederman & S. K. Abell (Eds.), Handbook of Research on Science Education (pp. 848–870). Routledge. https://doi.org/10.4324/9780203097267 Additional Declarations The authors declare no competing interests. Supplementary Files KoenigKaiseretalelectronicsupplementarymaterial.docx Supplementary material to Koenig et al. on teacher noticing in inclusive math education Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5738066","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":395987238,"identity":"9f1b75df-7df8-46f4-b630-b64b9b1c6111","order_by":0,"name":"Johannes König","email":"","orcid":"https://orcid.org/0000-0003-3374-9408","institution":"University of Cologne","correspondingAuthor":false,"prefix":"","firstName":"Johannes","middleName":"","lastName":"König","suffix":""},{"id":395987239,"identity":"d47467ca-90e4-4007-80a6-ec1643c8c8f2","order_by":1,"name":"Gabriele Kaiser","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-6239-0169","institution":"University of Hamburg","correspondingAuthor":true,"prefix":"","firstName":"Gabriele","middleName":"","lastName":"Kaiser","suffix":""},{"id":395987240,"identity":"b7ea7693-02f2-4062-ab5a-d2d7cf789d30","order_by":2,"name":"Anton Bastian","email":"","orcid":"https://orcid.org/0000-0002-1177-6336","institution":"University of Hamburg","correspondingAuthor":false,"prefix":"","firstName":"Anton","middleName":"","lastName":"Bastian","suffix":""},{"id":395987241,"identity":"934cfe99-e0e2-4e81-829f-2c29d8d5c51b","order_by":3,"name":"Jonas Weyers","email":"","orcid":"https://orcid.org/0000-0003-1804-4434","institution":"University of Cologne","correspondingAuthor":false,"prefix":"","firstName":"Jonas","middleName":"","lastName":"Weyers","suffix":""},{"id":395987242,"identity":"95948c87-9119-4e6b-b4b3-a8fef4401ce3","order_by":4,"name":"Nils Buchholtz","email":"","orcid":"https://orcid.org/0000-0003-4254-7525","institution":"University of Hamburg","correspondingAuthor":false,"prefix":"","firstName":"Nils","middleName":"","lastName":"Buchholtz","suffix":""},{"id":395987243,"identity":"1a2c3699-d5aa-4ced-8ae9-f8a34e9c68b6","order_by":5,"name":"Natalie Ross","email":"","orcid":"https://orcid.org/0000-0002-4529-9478","institution":"University of Hamburg","correspondingAuthor":false,"prefix":"","firstName":"Natalie","middleName":"","lastName":"Ross","suffix":""}],"badges":[],"createdAt":"2024-12-30 23:03:08","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-5738066/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5738066/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":72730592,"identity":"5b3687be-02b6-420e-b43b-33ce3202e330","added_by":"auto","created_at":"2025-01-01 06:20:01","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":107068,"visible":true,"origin":"","legend":"\u003cp\u003eModeling teacher competence as a continuum (Blömeke et al., 2015, p. 7)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5738066/v1/ccc17431d5f968936f07c23d.png"},{"id":72730595,"identity":"f3fbb433-c862-492c-8673-7bfccc941b34","added_by":"auto","created_at":"2025-01-01 06:20:01","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":19557,"visible":true,"origin":"","legend":"\u003cp\u003eMatrix for measuring teachers’ competence for inclusive mathematics education\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote.\u003c/em\u003e M_PID-IT - mathematics instruction for inclusive teaching: perception, interpretation, decision-making. P_PID-IT - pedagogy for inclusive teaching: perception, interpretation, decision-making. MPCK-IT - mathematics pedagogical content knowledge for inclusive teaching. GPK-IT - general pedagogical knowledge for inclusive teaching.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5738066/v1/7b0305b35280234171f7e163.png"},{"id":72730590,"identity":"884d4040-81eb-4b9b-8dd0-13e1f029e1d5","added_by":"auto","created_at":"2025-01-01 06:20:01","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":14680,"visible":true,"origin":"","legend":"\u003cp\u003ePercentage solution frequency mean scores by experience group and significant mean differences indicated by post-hoc tests\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote\u003c/em\u003e. M_PID-IT - mathematics instruction for inclusive teaching: perception, interpretation, decision-making. P_PID-IT - pedagogy for inclusive teaching: perception, interpretation, decision-making. MPCK-IT - mathematics pedagogical content knowledge for inclusive teaching. GPK-IT - general pedagogical knowledge for inclusive teaching. MS – Master’s students, TPS - Teachers in preparatory service, IST - In-service teachers.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5738066/v1/72eac8da01e6e9a7fa683652.png"},{"id":72731180,"identity":"72ffad83-54db-4af0-8a0e-a92cc2fccdd6","added_by":"auto","created_at":"2025-01-01 06:28:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1100144,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5738066/v1/100603fa-3776-40f7-adad-c01976083211.pdf"},{"id":72730586,"identity":"43bcf092-1634-4931-95e3-46aa13df88c1","added_by":"auto","created_at":"2025-01-01 06:20:01","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":214366,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary material to Koenig et al. on teacher noticing in inclusive math education\u003c/p\u003e","description":"","filename":"KoenigKaiseretalelectronicsupplementarymaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-5738066/v1/de830fdc78f7ac24581f586d.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eTeacher noticing in inclusive mathematics education: Analyzing its structure and expert-novice differences using a novel video-based test instrument\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eInclusivity in education and diversity-driven teaching have become crucial issues for many educational systems worldwide and have significant implications for educational reform. Teachers are increasingly required to meet new demands associated with inclusivity and student diversity. Consequently, teacher education systems in many countries are experiencing challenges amid the need for curriculum reform in a way that will prepare new generations of teachers to master the principles of inclusive teaching (Florian \u0026amp; Camedda, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe last decade has witnessed increased scholarly interest in demonstrating the effectiveness of teacher education targeting the professionalization of pre-service and in-service teachers with an emphasis on competence in inclusive teaching. This is attested by several literature reviews related to interventions in initial teacher education and teacher professional development in general (e.g., Dignath et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Khamzina et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) and for mathematics education, in particular (Allsopp \u0026amp; Haley, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). However, as a recent overall synthesis and meta-analysis of such literature reviews shows (K\u0026ouml;nig et al., under review), certain research gaps persist, one of which relates to the rigorous measurement of relevant competence facets that professional teachers require today as a prerequisite for coping with the novel demands of inclusive mathematics teaching.\u003c/p\u003e \u003cp\u003eOne such competence facet is teacher knowledge, defined as \u0026ldquo;a body of professional knowledge that encompasses both knowledge of general pedagogical principles and skills and knowledge of the subject matter to be taught\u0026rdquo; (Grossman \u0026amp; Richert, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1988\u003c/span\u003e, p. 54). This facet has become a major focus of research on (mathematics) teaching and teacher education (Cochran-Smith, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Gitomer \u0026amp; Zisk, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Kaiser \u0026amp; K\u0026ouml;nig, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; van Driel et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). While scholars broadly agree that mathematics teachers require professional knowledge for effective teaching (Baumert et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), recent developments in the mathematics teacher cognition agenda-driven research have prompted a shift toward the inclusion of facets that are more of situation-specific in nature (Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Kersting et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBl\u0026ouml;meke et al.\u0026rsquo;s (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) pioneering work suggested framing teacher competence \u0026ldquo;as a continuum.\u0026rdquo; To date, their influential model (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) has enriched numerous scholars\u0026rsquo; scientific understanding that not only teacher knowledge but also situation-specific skills\u0026mdash;comprising the perception and interpretation of classroom events as well as the ability to make adequate decisions in such situations\u0026mdash;are all relevant in predicting teacher performance and instructional quality (Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). These situation-specific skills have been further theoretically framed as the so-called PID-model (PID \u0026ndash; perceive, interpret, decide; Kaiser et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2015\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and can more broadly be embedded within the \u0026ldquo;teacher noticing\u0026rdquo; research field (K\u0026ouml;nig et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, as the research on teacher noticing demonstrates, inclusive mathematics teaching remains largely overlooked in the conceptualization and measurement of relevant teacher competence facets (Roose et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAgainst this background, the paper presents a novel video-based test instrument for measuring teachers\u0026rsquo; professional noticing focusing inclusive mathematics education. The underlying conceptualization distinguishes, on the one hand, between challenges specific to inclusive mathematics instruction and those related to inclusive instruction in general, both of which require specific knowledge and skills. On the other hand, it distinguishes theoretically between the professional knowledge acquired during training and its situation-specific application\u0026mdash;that is, situation-specific skills. The first question aims to assess the extent to which the newly developed instrument can capture this assumed multidimensionality. The paper further examines possible expert\u0026ndash;novice differences in the competence facets\u0026rsquo; pattern, since competence should be acquired during initial teacher education and in-service teaching. This second question focuses on three target groups with different levels of teaching experience (master\u0026rsquo;s students, teacher candidates in the second phase of German teacher education, in-service teachers). We analyze potential differences in knowledge and skills that relate to the assumptions that are prevalent in teacher expertise research (Stigler \u0026amp; Miller, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u0026mdash;in particular, the evolution from novice to experienced. In presenting a novel approach that connects teacher noticing with inclusive mathematics education and the research on teacher knowledge, we discuss the implications for teacher education design.\u003c/p\u003e"},{"header":"2. Literature review","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Teacher professional competence\u003c/h2\u003e \u003cp\u003eResearchers broadly agree that mathematics teachers\u0026rsquo; professional competence comprises relevant knowledge and cognitive skills (Bl\u0026ouml;meke \u0026amp; Delaney, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Krauss et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). In recent decades, empirical research on teacher knowledge and skills has progressed considerably, in particular, the measurement of pre-service and in-service teachers\u0026rsquo; professional knowledge and its psychometric quality has advanced significantly, with frequent recourse to Shulman\u0026rsquo;s (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1987\u003c/span\u003e) influential classification and differentiating the professional knowledge base into content knowledge (CK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK).\u003c/p\u003e \u003cp\u003eAmong the most prominent approaches is the international-comparative large-scale assessment TEDS-M 2008 (Teacher Education and Development Study: Learning to Teach Mathematics), led by the International Association for the Evaluation of Educational Achievement (IEA) with the participation of 17 countries worldwide (Tatto \u0026amp; Senk \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Mathematics teachers\u0026rsquo; professional knowledge was directly assessed using representative country samples with future teachers selected shortly prior to attaining full professional certification. In Germany, as the country that participated in TEDS-M 2008 under Sigrid Bl\u0026ouml;meke\u0026rsquo;s leadership (Bl\u0026ouml;meke, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), numerous other mathematics teacher education and development studies followed (for a recent overview of the so-called TEDS research program, see Kaiser, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTEDS-M, along with other studies on mathematics teacher knowledge (Ball et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Baumert et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Kersting et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) achieved pioneering work in the large-scale conceptualization, operationalization, and assessment of mathematics teacher knowledge (Bl\u0026ouml;meke \u0026amp; Delaney, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Bl\u0026ouml;meke, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, the continuing discourse on the adequate measurement and modeling of teacher competence highlighted the need for more action-oriented concepts and operationalizations. Knowledge constitutes a highly relevant basis for teachers\u0026rsquo; professionalism (van Driel et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Gitomer \u0026amp; Zisk, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Magnusson et al., 1999). Meanwhile, it is reasonable to assume\u0026mdash;not least based on findings from teacher expertise research (Bromme, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Stigler \u0026amp; Miller, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e)\u0026mdash;that successful teachers draw on specific skills in their teaching and during interactions with students according to situations that arise in the classroom. The importance of distinguishing between knowledge and skills is clearly illustrated in the Refined Consensus Model of PCK (e.g., Mientus et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This model delineates several key aspects, notably the differentiation between an individual teacher\u0026rsquo;s available knowledge base (personal PCK) and the specific knowledge elements employed while planning, implementing, and reflecting on teaching during pedagogical reasoning (enacted PCK).\u003c/p\u003e \u003cp\u003eBl\u0026ouml;meke et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) suggested adding situation-specific skills to conventional teacher competence models (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Their model (Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) inspired scholars to expand previously focused cognitive or affective\u0026ndash;motivational dispositions to include situation-specific skills to proximally predict observable performance. The proposed model considers individual constructs not in isolation but on a continuum, bridging knowledge and performance and bringing together previously entrenched positions in competence measurement (Kaiser et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Until today, this theoretical approach has had a lasting impact on the discourse on modeling and assessment of competencies, as exemplified by the measurement of competencies of pre-service and in-service teachers and has prompted significant further developments. Particularly noteworthy is Krauss et al.\u0026rsquo;s (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) \u0026ldquo;Cascade Model\u0026rdquo;, which considers teachers\u0026rsquo; situation-specific skills as a predictor of instructional quality and the orchestration of learning opportunities. Instructional quality and learning opportunities, mediated by student participation and engagement, in turn, are assumed to influence student learning outcomes on both the affective\u0026ndash;motivational (e.g., enjoyment of learning) and cognitive (e.g., mathematics performance) levels.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Teacher noticing as part of teacher professional competence\u003c/h2\u003e \u003cp\u003eBl\u0026ouml;meke et al.\u0026rsquo;s (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) model also overlaps somewhat with teacher noticing research. Teacher noticing refers to the abilities and cognitive skills that teachers need, such as the ability to pay attention to relevant classroom processes and events of social interaction, to select important information, to draw appropriate conclusions, and to quickly decide how to proceed with the course of instruction. In their comprehensive literature review, K\u0026ouml;nig et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) demonstrated the existence of various approaches to conceptualizing teacher noticing, impeding any precise definition of teacher noticing as a scientific term. The heterogeneity of teacher noticing research may be attributed to the various perspectives that have shaped empirical approaches, including cognitive\u0026ndash;psychological, socio-cultural, or expertise-related perspectives. Moreover, teacher noticing researchers have developed various conceptualizations, distinguishing several noticing facets such as attention, perception, interpretation, and decision-making, which are applied in different ways.\u003c/p\u003e \u003cp\u003eHowever, advances in modeling teacher professional competence not only integrate conceptualizations of teacher noticing but also link noticing to professional knowledge, as teacher knowledge research has described and classified (Shulman, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1987\u003c/span\u003e) and teacher expertise research has referenced (Bromme, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Stigler \u0026amp; Miller, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). A good example is the TEDS-M Follow-Up study conducted in Germany (TEDS-FU). TEDS-FU focused on early career teachers who were originally assessed in TEDS-M in Germany at the end of the second teacher education phase. They were surveyed again after their successful transition from teacher education into professional teaching. For this purpose, Kaiser et al. (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) developed a novel video-based test instrument to measure teacher noticing in mathematics classrooms. The knowledge tests from TEDS-M and PID-skills measured using this instrument were further used to comprehensively and multidimensionally measure mathematics teacher competence in the classroom (Bl\u0026ouml;meke, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Teacher competence and teacher expertise\u003c/h2\u003e \u003cp\u003eTeacher competence and teacher expertise researchers agree that teacher knowledge and skills are malleable, not fixed (Kaiser et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Kaiser et al., in this issue). Teacher knowledge and skills are considered as outcomes of education programs and professional development (Cochran-Smith, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Kaiser \u0026amp; K\u0026ouml;nig, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Formal and non-formal learning opportunities support pre-service teachers, teacher candidates, and in-service teachers to acquire professional knowledge but also to update, consolidate, or transform their professional knowledge base\u0026mdash;for example, through deliberate practice (Berliner, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Ericsson et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1993\u003c/span\u003e). Novice teachers (e.g., student teachers, pre-service teachers with little teaching experience), who are at an early stage in their teaching careers, differ in their level and quality of professional knowledge and teacher noticing in contrast with experienced in-service teachers (Carter et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1988\u003c/span\u003e). This finding was related to the competence continuum (Bl\u0026ouml;meke et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) model developed by Bastian et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), who reported that master\u0026rsquo;s students showed a considerable increase in noticing skills relative to those of in-service teachers, confirming certain assumptions regarding the development of teacher professional competence.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Theoretical framework: A video-based instrument for the professional noticing of teachers focusing inclusive mathematics education","content":"\u003cp\u003eInclusive education is a central concern in education policy, and its implementation has sparked vigorous debates (UNESCO, 2018; UN, 2006), altering expectations regarding teacher education and professional development (Florian \u0026amp; Camedda, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Teacher professionalization research asks what prerequisites teachers must meet to satisfy the demands of inclusive education and become adequately qualified (e.g., Allsop \u0026amp; Haley, 2015; Khamzina et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eResearch suggests that knowledge and skills should be considered prerequisites for teachers to satisfy the demands of inclusive teaching (K\u0026ouml;nig et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In the course of the TEDS research program (Kaiser, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), the Teacher Education and Development Study \u0026ndash; Inclusive Mathematics Education (TEDS-IME) was carried out in Germany between 2022 and 2024. One of its major goals was to develop a video-based test instrument to measure teachers\u0026rsquo; professional noticing in inclusive mathematics education. The project\u0026rsquo;s interdisciplinary approach synthesized mathematical and pedagogical perspectives (Bl\u0026ouml;meke, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Moreover, to facilitate analyses of knowledge and skills, specific knowledge tests referring to inclusive education were also developed.\u003c/p\u003e \u003cp\u003eWith reference to the discussion on competence (Bl\u0026ouml;meke et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), teacher competence for inclusive education was defined not only as mathematical pedagogical content knowledge (MPCK) and GPK for inclusive teaching (MPCK-IT and GPK-IT), but also as situation-specific skills, with the following competence facets distinguished (Kaiser et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2015\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003ethe perception of central events in the lesson (perception \u0026ndash; P),\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ethe interpretation of these events (interpretation \u0026ndash; I), and\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ethe development of decisions for action in the classroom and the planning of alternative lesson plans (decision-making \u0026ndash; D).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThese conceptualizations, which have already been implemented in similar measurement instruments (e.g., Kaiser et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), are concretized in TEDS-IME for the first time for inclusive teaching from a mathematics didactic (M_PID-IT) and pedagogical (P_PID-IT) perspective. The perception facet is conceptualized as perception of the need for wide support, the interpretation facet as the interpretation of the learning status or development problem underlying the need for support, and the decision-making facet as determining the most appropriate support measure.\u003c/p\u003e \u003cp\u003eThe TEDS-IME project focuses on two areas identified in relevant competence catalogs for inclusive education\u0026mdash;competence in \u003cem\u003ediagnosis\u003c/em\u003e and \u003cem\u003eintervention and support\u003c/em\u003e (K\u0026ouml;nig et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2019\u003c/span\u003e)\u0026mdash;which are primarily located at the classroom level:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cem\u003eDiagnosis\u003c/em\u003e includes the identification of learning difficulties in the classroom, which requires an analysis of the teaching situation in terms of professional teaching perception as part of teacher noticing (Sherin et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Ricken, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). This task of diagnosis from a mathematics didactics perspective was specified as the teachers\u0026rsquo; perception of students\u0026rsquo; individual misconceptions and errors, comprehension difficulties, and learning strategies. Regarding the competence model that Bl\u0026ouml;meke et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) viewed as a continuum, diagnostic competence is understood as a facet of professional teaching perception and interpretation (Heinrichs \u0026amp; Kaiser, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), which is particularly important in inclusive teaching. To date, however, few studies have systematically related the concept of professional teacher noticing in classrooms to the specific challenges of inclusive teaching (K\u0026ouml;nig et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cem\u003eIntervention and support\u003c/em\u003e includes didactic and methodological measures for individualization and dealing with student heterogeneity in inclusive settings. Conventional approaches to differentiation are important for mathematics lessons from an inclusive perspective (Leuders \u0026amp; Prediger, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2017\u003c/span\u003e); task variation is crucial, as due to the variation of the task\u0026rsquo;s internal structure, this generates opportunities to respond to learners of different performance levels\u0026mdash;from mathematically gifted learners to learners with partial mathematical weaknesses. In addition to forms of internal differentiation, elementary school approaches are used, such as forms of natural differentiation (e.g., Korff, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Misconceptions and errors play a particularly important role in mathematics lessons, and it thus seems particularly important in the context of promoting diagnostic and support skills to familiarize (pre-service) teachers with systematically occurring error patterns based on misconceptions of central mathematical content (Heinrichs \u0026amp; Kaiser, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Larrain \u0026amp; Kaiser, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThese considerations were incorporated into the novel video-based test instrument\u0026rsquo;s development in the TEDS-IME project and implemented into a survey design with three groups of secondary mathematics teachers with different experience levels (master\u0026rsquo;s students, teacher candidates in the second teacher education phase, experienced in-service teachers of secondary mathematics).\u003c/p\u003e"},{"header":"3. Research questions and hypotheses","content":"\u003cp\u003e \u003cstrong\u003eRQ 1\u003c/strong\u003e\u003c/p\u003e \u003cp\u003eIs the theoretically postulated structure of teachers\u0026rsquo; competence for inclusive mathematics education empirically verifiable?\u003c/p\u003e\u003cp\u003eShulman\u0026rsquo;s (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1987\u003c/span\u003e) classification of PCK and GPK (e.g., Bl\u0026ouml;meke \u0026amp; Delaney, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and Bl\u0026ouml;meke et al.\u0026rsquo;s (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) differentiation into knowledge and situation-specific skills create a matrix to be filled with specific test instruments that all relate to inclusive teaching in the mathematics classroom (Fig.\u0026nbsp;2). We hypothesize that a four-dimensional model accounting for the theoretically assumed differentiations fits mathematics teacher competence test data better than accounting only for two-dimensional differentiations\u0026mdash;mathematics vs. pedagogy or knowledge vs. skills (H1a). Moreover, we hypothesize that two-dimensional models are superior to a holistic model (general factor model) without any differentiation (H1b).\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eRQ2\u003c/strong\u003e \u003cp\u003eHow do abilities differ between different pre- and in-service teacher groups with varying teaching experience regarding (a) the competence structure and (b) their ability levels?\u003c/p\u003e \u003c/p\u003e \u003cp\u003eAlthough we do not claim that expert teachers are necessarily part of our study sample design (for further detail, see the Methods section), nevertheless, the three pre- and in-service groups with varying degrees of teaching experience (understood as a possible indicator of teacher expertise, Stigler \u0026amp; Miller, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) lead us to assume that contrasting groups may be interpreted as expert\u0026ndash;novice differences. Master\u0026rsquo;s students participating in our study had already undergone their long-term (five-month) practicum but had not worked professionally, unlike teacher candidates in the second phase of teacher education or in-service teachers. Therefore, we designate master\u0026rsquo;s students \u0026ldquo;novice teachers\u0026rdquo; (Berliner, 2001). Teacher candidates participating in our study had been exposed to small-scale professional teaching during the second phase of teacher education but were not yet certified and thus had only limited teaching duties and responsibilities (e.g., high-stakes assessment of their students) and were designated \u0026ldquo;advanced beginners\u0026rdquo; (Berliner, 2001). Meanwhile, the \u0026ldquo;competent\u0026rdquo; status (Berliner, 2001) is fulfilled by in-service teachers who have several years of professional experience and full responsibility.\u003c/p\u003e \u003cp\u003eFor all three groups, we hypothesize that the dimensionality assumptions (RQ1) will be confirmed in subgroup analysis (H2a), which would support generalization assumptions. On the basis of the assumption regarding the development of expertise among novice, advanced beginner, and competent teachers (Berliner, 2001), we hypothesize that teacher candidates should outperform master\u0026rsquo;s students, while in-service teachers should exhibit better test results than those of teacher candidates (H2b).\u003c/p\u003e"},{"header":"4. Methods","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Study context\u003c/h2\u003e \u003cp\u003eThe present study is part of the larger TEDS-IME project, which aims to conceptualize, measure, and promote secondary school mathematics teachers\u0026rsquo; competence for inclusive mathematics education. To evaluate the effectiveness of a targeted professional development program, the team developed new instruments to measure specific competence facets relating to inclusive mathematics education. This study focuses on the development and use of a novel video-based instrument to capture teacher noticing skills for inclusive mathematics education from a mathematics pedagogical perspective (i.e., M_PID-IT) and a general pedagogical perspective (i.e., P_PID-IT). The relationship between this video-based measurement and a knowledge assessment focusing on PCK for inclusive mathematics education (i.e., MPCK-IT) and general pedagogical knowledge for inclusive teaching (i.e., GPK-IT) is also analyzed. A theoretically grounded development and thorough validation of the measurement instruments are key to evaluating the program\u0026rsquo;s effectiveness and are crucial for ensuring the findings\u0026rsquo; quality.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Sample\u003c/h2\u003e \u003cp\u003eWe use data from the TEDS-IME project that stem from the evaluation of the pre- and in-service teachers at the project\u0026rsquo;s first time point. They were assigned to intervention and control groups, since, after that first assessment, study participants of the intervention group were educated in a topic-specific professional development program. The present analysis includes only data from the project\u0026rsquo;s first time point, thus providing insights into the non-manipulated state of teacher competence structure without focusing on potential changes to that competence in the course of the TEDS-IME project\u0026rsquo;s professional development program.\u003c/p\u003e \u003cp\u003eAs Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows, 628 pre-service and in-service mathematics teachers participated in the first measurement (intervention group: 515; control group: 113). This included 233 master\u0026rsquo;s students, 163 teacher candidates in the second phase of teacher education, and 232 in-service teachers. The survey covered 11 German federal states, focusing on Hamburg (35.5%) and North Rhine-Westphalia (47.0%). The intervention groups completed the survey online in the first session of the professional development program, while the control groups completed the survey onlinein their own time.\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\u003eKey demographic characteristics of the sample\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaster\u0026rsquo;s students\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTeacher candidates (Preparatory service)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIn-service teachers\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e233 (37%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e163 (26%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e232 (37%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e628\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender\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\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e146 (63%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e98 (60%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e159 (69%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e403 (64%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e87 (37%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e61 (37%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70 (30%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e218 (35%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiverse / Not indicated\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0 (0%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4 (3%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3 (1%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7 (1%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge (M (SD))\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e24.5 (3.2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.7 (5.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e41.7 (10.2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e32.2 (10.3)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFinal secondary school GPA \u003c/p\u003e \u003cp\u003e(M (SD))\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.91 (0.61)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.06 (0.63)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.25 (0.64)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.07 (0.64)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaster\u0026rsquo;s grade (M (SD))\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.81 (0.51)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.93 (0.51)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.88 (0.51)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFinale Grade in teacher training / induction (M (SD))\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.00 (0.72)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.00 (0.71)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStudy semester (M (SD))\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.0 (2.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeaching experience (M (SD), in years)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3 (0.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.7 (1.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e12.8 (9.1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.3 (8.0)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeacher education program\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\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLower Secondary Education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e63 (27%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50 (30.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e119 (51.3%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e232 (36.9%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUpper Secondary Education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e148 (63.5%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e75 (46%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e81 (34.9%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e304 (48.4%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecial Needs Education\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18 (7.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6 (3.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14 (6%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e38 (6.1%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlternative and Lateral Entry into Teaching\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30 (18.4%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14 (6%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e44 (7.0%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOther\u003csup\u003e1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4 (1.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2 (1.2%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4 (1.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10 (1.6%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSchool Type of Employment\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\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLower secondary school\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15 (9.2%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e42 (18.1%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e57 (14.4%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLower and upper secondary school\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e144 (88.3%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e188 (81.0%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e332 (84.1%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecial needs school\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3 (1.8%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3 (0.8%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOther\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1 (0.6%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2 (0.9%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3 (0.8%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003e\u003cem\u003eNote.\u003c/em\u003e \u003csup\u003e1\u003c/sup\u003e = Programs for primary school, vocational school and other programs; \u003csup\u003e2\u003c/sup\u003e = vocational schools and other schools; GPA\u0026thinsp;=\u0026thinsp;Grade Point Average; All grades are based on a scale from 1.0 (very good) to 4.0 (satisfactory)\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\u003e4.3 Measures of teacher professional competence\u003c/h2\u003e \u003cp\u003eTo capture teacher noticing in inclusive mathematics education, the TEDS-IME project team developed a novel video-based instrument to capture perception, interpretation, and decision-making in inclusive mathematics education from both mathematical pedagogical and general pedagogical perspectives (see further the outline in the Electronic Supplement Material, ESM). Four video vignettes (see ESM Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) depicting inclusive algebra instruction situations in secondary education are used, providing overview information (e.g., grade level, topic of the lesson unit) and lesson materials (e.g., tasks). Test items relate to the videos and are designed to measure cognitive processes of perception, interpretation, and decision-making (for further details on such processes as well as sample items, see ESM Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;3). Interrater reliability is good for participants\u0026rsquo; responses to open response items (see the outline of the video-based test instrument in the ESM). Both mathematical PCK for inclusive teaching (MPCK-IT) and general pedagogical knowledge for inclusive teaching (GPK-IT) were measured using online standardized knowledge tests. The ESM provides an outline of the tests, including sample items (ESM Figs.\u0026nbsp;4\u0026ndash;5).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Data analysis\u003c/h2\u003e \u003cp\u003eItem response theory models were estimated to analyze the structure of teachers\u0026rsquo; competence (RQ1), starting with (1) a one-dimensional model\u0026mdash;that is, competence as one holistic construct; (2) a two-dimensional model contrasting subject-specific and general pedagogical aspects; (3) a two-dimensional model contrasting professional knowledge (i.e., cognitive dispositions) and noticing (i.e., situation-specific skills); and (4) a four-dimensional model, including M_PID-IT, P_PID-IT, MPCK-IT, and GPK-IT (see Fig.\u0026nbsp;2). Models were compared as to relative fit indices (especially model deviance), reliability, and dimensional intercorrelations. For nested models, χ\u0026sup2; tests determined whether the model fit change was statistically significant.\u003c/p\u003e \u003cp\u003eComparing the experience groups (RQ2), we investigated to what extent these dimensional analyses hold for the three respective experience groups. Therefore, the competence structure was re-examined separately for each teaching experience group based on the model comparisons (RQ2a). Possible differences between the competence levels of the three groups (RQ2b) were examined using one-way analysis of variance (ANOVA). Exploratory group-wise comparisons were conducted using post-hoc tests (Scheff\u0026eacute; post-hoc test for equal variances; if equal variances were not given: Games-Howell post-hoc test). Data preparation and mean comparisons were performed in SPSS (version 29). Item response theory analyses were conducted using ConQuest (version 5.34.2).\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Results","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Structure of teachers\u0026rsquo; competence for inclusive mathematics education\u003c/h2\u003e \u003cp\u003eRQ1 investigated the structure of teachers\u0026rsquo; competence for inclusive mathematics education and asked whether it is empirically verifiable. As Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows, the model fit of the four different scaling models varied significantly. As we had hypothesized (H1a), the four-dimensional model (4D) accounting for the theoretically assumed differentiations (as Fig.\u0026nbsp;2 illustrates) fits the data better than accounting only for two-dimensional differentiations into mathematics vs. pedagogy (2D-MP) or knowledge vs. skills (2D-KS). Moreover\u0026mdash;again, as hypothesized (H1b)\u0026mdash;the four-dimensional model (4D) and the two-dimensional models (2D-MP and 2D-KS) are superior to the holistic model (general factor model, 1D) without any differentiation.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e provides further details on the scaling models\u0026rsquo; psychometric quality. First, all scaled dimensions are reliable. While the sparse models with few dimensions indicate good reliability (EAP\u0026thinsp;\u0026gt;\u0026thinsp;.75; WLE\u0026thinsp;\u0026gt;\u0026thinsp;.70 with the exception of Pedagogy .68), the four-dimensional model\u0026rsquo;s scale reliability is still within acceptable range (EAP\u0026thinsp;\u0026gt;\u0026thinsp;.70 with the exception of P_PID-IT .69; WLE\u0026thinsp;\u0026gt;\u0026thinsp;.55), considering that the number of items measuring a scale is much smaller.\u003c/p\u003e \u003cp\u003eSecond, intercorrelations of subscales indicate teacher competence for inclusive teaching is of multidimensional nature. Whereas the intercorrelation between mathematics and general pedagogy in the two-dimensional model is relatively high (.80), that between knowledge and situation-specific skills is lower (.68). The four-dimensional model demonstrates that teachers\u0026rsquo; competence may reasonably be differentiated into mathematics pedagogy and general pedagogy as well as knowledge and situation-specific skills, as the intercorrelations are relatively low. In particular, knowledge and skills in general pedagogy (P_PID-IT and GPK-IT) are moderately intercorrelated (.50), whereas knowledge and skills in mathematics pedagogy (M_PID-IT and MPCK-IT) are more closely intercorrelated (.77). Here, we use scaling results from the four-dimensional model, whose scale reliability Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates.\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\u003eModel comparison\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDeviance\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAICc\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"6\" nameend=\"c11\" namest=\"c6\"\u003e \u003cp\u003eModel comparison using χ\u003csup\u003e2\u003c/sup\u003e-tests against the less complex model\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e3)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eχ\u003csup\u003e2\u003c/sup\u003e (\u003cem\u003edf\u003c/em\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eχ\u003csup\u003e2\u003c/sup\u003e (\u003cem\u003edf\u003c/em\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eχ\u003csup\u003e2\u003c/sup\u003e (\u003cem\u003edf\u003c/em\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e46681.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47355.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e46972.4\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2D-MP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e46838.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47300.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e46912.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e157.02 (2)\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2D-KS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e46531.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47218.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e46829.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e149.99 (2)\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e46446.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47175.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e46769.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e234.92 (9)\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\u003e391.94 (7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e84.93 (7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"11\"\u003e\u003cem\u003eNote\u003c/em\u003e. BIC - Bayesian information criterion. AICc - Sample-size corrected Akaike information criterion. 1D - one-dimensional holistic model of competence. 2D-MP - two-dimensional model of mathematics pedagogy and general pedagogy. 2D-KS - two-dimensional model of knowledge and situation-specific skills. 4D - four-dimensional model of two-dimensional knowledge (MPCK-IT and GPK-IT) and two-dimensional situation-specific skills (M_PID-IT and P_PID-IT).\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eReliabilities and Intercorrelations\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDimension\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVariance\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEAP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eWLE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e \u003cp\u003eLatent intercorrelations\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHolistic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.84\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMathematics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.78\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePedagogy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSkills\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.73\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKnowledge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\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\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eM_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eP_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMPCK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eGPK-IT\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP_PID-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMPCK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGPK-IT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u003cem\u003eNote.\u003c/em\u003e EAP - Expected a posteriori estimator. WLE - weighted likelihood estimator. M_PID-IT - mathematics instruction for inclusive teaching: perception, interpretation, decision-making. P_PID-IT - pedagogy for inclusive teaching: perception, interpretation, decision-making. MPCK-IT - mathematics pedagogical content knowledge for inclusive teaching. GPK-IT - general pedagogical knowledge for inclusive teaching.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eReliability for the individual competence measures and correlations of item difficulties between experience groups based on two two-factor models (PID: mathematics vs. pedagogy; Knowledge: mathematics vs. pedagogy)\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\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=\"char\" char=\".\" 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=\"char\" char=\".\" 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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eReliability\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\u003eWMNSQ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDiscrimination\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eCorrelation MP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003eCorrelations between item difficulties\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\u003eEAP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWLE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMS / TPS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMS / IST\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eTPS / IST\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\u003e0.671\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.576\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eM\u0026thinsp;=\u0026thinsp;1.00,\u003c/p\u003e \u003cp\u003e[.92, 1.11]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eM\u0026thinsp;=\u0026thinsp;.27, \u003c/p\u003e \u003cp\u003e[.10, .45]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.95\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\u003e0.666\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.590\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.95\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\u003e0.750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.696\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eM\u0026thinsp;=\u0026thinsp;1.00, [.86, 1.11]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eM\u0026thinsp;=\u0026thinsp;.31, \u003c/p\u003e \u003cp\u003e[.16, .55]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.86\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\u003e0.682\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.564\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u003cem\u003eNote\u003c/em\u003e. EAP - Expected a posteriori estimator. WLE - weighted likelihood estimator. WMNSQ - Weighed mean squares. M_PID-IT - mathematics instruction for inclusive teaching: perception, interpretation, decision-making. P_PID-IT - pedagogy for inclusive teaching: perception, interpretation, decision-making. MPCK-IT - mathematics pedagogical content knowledge for inclusive teaching. GPK-IT - general pedagogical knowledge for inclusive teaching. Correlation MP: Latent correlation between mathematics and pedagogy. MS - Master students, TPS - Teachers in preparatory service, IST - In-service teachers.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Expert\u0026ndash;novice differences in teachers\u0026rsquo; competence for inclusive mathematics education\u003c/h2\u003e \u003cp\u003eRQ2 concerned how pre- and in-service teachers would differ in the four competence facets related to inclusive mathematics education. The dimensionality was again examined for the three subgroups as it had been for the entire sample. The findings indicate that the more differentiated the scaling model is, the better the model fits the data (see Electronic Supplementary Material, ESM, Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), confirming H2a. Dimensionality assumptions may thus be shown for the subgroups\u0026mdash;a relevant prerequisite for comparing the subgroups\u0026rsquo; mean scores\u003c/p\u003e \u003cp\u003eBased on our assumptions regarding the development of teacher competence and expertise (see, Kaiser et al., in this issue), we hypothesized that in-service teachers would outperform teacher candidates in the second phase of teacher education and that the candidates, in turn, would exhibit better test results than master\u0026rsquo;s students. Figure\u0026nbsp;3 presents the percentage solution frequency mean scores according to experience group (for statistical details, see ESM Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Against our H2b, the mean scores do not correspond with the expected ranking. First, group mean score differences are statistically significant for situation-specific skills but not for knowledge (ESM Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), and with only small practical relevance (.015\u0026thinsp;\u0026le;\u0026thinsp;η\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;\u0026le;\u0026thinsp;.058). In both cases, in-service teachers are slightly outperformed by pre-service teachers (see, for details, post-hoc test results in ESM Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and red lines in Fig.\u0026nbsp;3): Whereas teacher candidates significantly outperform in-service teachers in M_PID-IT (but not master\u0026rsquo;s students), master\u0026rsquo;s students score significantly higher than teacher candidates and in-service teachers in P_PID-IT.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Discussion","content":"\u003cp\u003eConsidering new school requirements in the area of inclusive teaching and education (e.g., Piezunka et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Ricken, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), teachers\u0026mdash;secondary school mathematics teachers among them\u0026mdash;require professional knowledge and situation-specific skills that clearly go beyond existing conceptualizations of teachers\u0026rsquo; professional knowledge (e.g., Allsopp \u0026amp; Haley, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Shulman, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Tatto \u0026amp; Senk, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). While pedagogical demand has long determined expectations that teachers will be able to deal with their students\u0026rsquo; heterogeneity and diversity, pressure to act and societal expectations have increased significantly with the UN Conventions on the Rights of Persons with Disabilities (UN, 2006) and its implementation in guidelines and standards in the education system (UNESCO, 2018). Mathematics education research is required to discover how these competencies should be defined and structured.\u003c/p\u003e \u003cp\u003eEmbedded in the TEDS research program that Sigrid Bl\u0026ouml;meke initiated and successfully promoted over several years (Kaiser, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), the TEDS-IME research project has made significant progress in developing novel test instruments to measure knowledge and situation-specific skills of secondary mathematics teachers for inclusive mathematics education. Therefore, we used Shulman\u0026rsquo;s (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1987\u003c/span\u003e) influential classification of teacher knowledge, comprising facets such as MPCK and GPK and specified for inclusive teaching, yielding the MPCK-IT and GPK-IT constructs. Moreover, Bl\u0026ouml;meke et al.\u0026rsquo;s (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) model of competence viewed as a continuum influenced the TEDS-IME project to go beyond mere knowledge tests and develop a novel video-based assessment that accounts for situation-specific skills of perception, interpretation, and decision-making (PID-model; Kaiser et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2015\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), combining perspectives from mathematics pedagogy and general pedagogy.\u003c/p\u003e \u003cp\u003eThe development of such a comprehensive test instrument inventory with four theoretically specified constructs differentiating knowledge and skills and mathematics pedagogy and general pedagogy (see Fig.\u0026nbsp;2) prompted extensive research during the TEDS-IME project. This paper\u0026rsquo;s objective was to present four new instruments for comprehensively measuring mathematics teachers\u0026rsquo; professional competence facets, guided by the following questions: What dimensionality could be provided in applying such an approach? Do expert-novice differences exist in the pattern of competence facets among master\u0026rsquo;s students, teacher candidates in their second phase of teacher education, and in-service teachers? Data were available from the TEDS-IME project\u0026rsquo;s large-scale assessment in Germany with more than 600 study participants of varying teaching experience thus allowing comparisons following expert\u0026ndash;novice interpretations. Although study participants were asked after the first assessment to undergo training via a novel teacher professional program, the data from the first measurement were wholly unmanipulated and provided an appropriate dataset for testing our hypotheses.\u003c/p\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e6.1 Structure of teachers\u0026rsquo; competence for inclusive mathematics education\u003c/h2\u003e \u003cp\u003eRQ1 targeted the structure of teachers\u0026rsquo; competence for inclusive mathematics education. As hypothesized (H1a), the four-dimensional model showed the best fit to our data, confirming that, on the one hand, knowledge and situation-specific skills should be differentiated, as Bl\u0026ouml;meke et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) suggested, and, on the other hand, that mathematics instruction and general pedagogy serve as two distinct resources, as Shulman (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1987\u003c/span\u003e) specified. Moreover, sparse models with two dimensions each (knowledge vs. situation-specific skills, mathematics instruction vs. general pedagogy) also showed a better fit than that of a one-dimensional model that corresponded to the assumption a holistic understanding of teachers\u0026rsquo; competence for inclusive mathematics education (H1b). In summary, our findings confirm Bl\u0026ouml;meke\u0026rsquo;s (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) assertion that teacher competence is multidimensional in nature and that its measurement is a complex undertaking. This paper provides evidence for this issue with regards to the complex professional demands in the inclusive mathematics classroom. Meanwhile, in line with current research discourse on teacher professional competence, it confirms conceptually sound differentiations into knowledge and skills as well as mathematics pedagogy and general pedagogy for application in the inclusive mathematics educational context.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e6.2 Expert-novice differences in teachers\u0026rsquo; competence for inclusive mathematics education\u003c/h2\u003e \u003cp\u003eThe structure of competence in the above subscales for examining RQ1 was again demonstrated for the three different groups of pre-service and in-service teachers. As anticipated with our hypothesis (H2a), the differentiation into a four-dimensional scaling model with inferential statistical testing clearly proved to be the model that best fitted the data for all three groups. Thus, the assumed structure, which had been proven in the overall sample, could be generalized to the two teacher education phases in Germany\u0026mdash;study at university with heavy emphasis on theoretical knowledge foundations and second phase of teacher education with initial responsibility for school teaching\u0026mdash;as well as the target group of the more experienced in-service teachers. Overall, this result represents an excellent basis for addressing all three target groups equally with the further training measure envisaged in the TEDS-IME project (this was not part of the paper; for findings on the effectiveness of the training future, see publications by the TEDS-IME project team).\u003c/p\u003e \u003cp\u003eThe three groups\u0026rsquo; test scores were also examined, accompanied by an expectation derived from expert-novice comparisons\u0026mdash;namely, that in-service teachers should outperform teacher candidates, who, in turn, should achieve better test results than master\u0026rsquo;s students (H2b). This assumption, relying on teacher expertise development models (Berliner, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), was reasonable for situation-specific skills in particular, as practicing and reflecting on processes of classroom perception, interpreting events, and making decisions for the further course of action should be intertwined with the amount of teaching experience\u0026mdash;a criterion most suitable for distinguishing the three groups according to expertise. Unexpectedly, mean differences had little practical relevance for situation-specific skills and were non-significant for knowledge. Against our hypothesis, the group ranking was virtually the opposite of what we had hypothesized (see Fig.\u0026nbsp;3): in-service teachers were outperformed by either master\u0026rsquo;s students (P_PID-IT) or teacher candidates (M_PID-IT), teacher candidates were outperformed by master\u0026rsquo;s students (P_PID-IT), and master\u0026rsquo;s students were not outperformed by teacher candidates (M_PID-IT). Although this paper offers no further data analysis, several possible approaches to the findings may be highlighted.\u003c/p\u003e \u003cp\u003eFirst, one might assume that inclusive mathematics education is \u003cem\u003ea bridge too far\u003c/em\u003e in terms of the current reality of teaching practice (e.g., Steinmetz et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Whereas new content, such as inclusive education and teaching for diversity, may have been incorporated into the initial teacher education curriculum in Germany as the country of our study (e.g., KMK, 2022), not least pushed by a half-billion-euro quality initiative (the so-called \u0026ldquo;Qualit\u0026auml;tsoffensive Lehrerbildung\u0026rdquo;) aimed at expanding topics such as inclusion in teacher education (BMBF, 2024, p. 9), the question arises as to what extent such topics acquired by teachers during initial teacher education continue to be implemented years later and become established as routines in everyday teaching\u0026mdash;intertwined with the growth of teacher expertise for inclusive mathematics education. The latter is more likely to be decisive for the acquisition of knowledge and situation-specific skills among in-service teachers. As the in-service teachers in our sample are the least likely to have been exposed to learning opportunities in inclusive education and teaching during their initial teacher education several years ago, we may ask what alternative learning opportunities they might have had to update their teacher competence with regards to mathematics inclusive education in recent years. It is doubtful that they enjoyed abundant opportunities to do so (e.g., Steinmetz et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), but our data are clearly limited, thus leaving open a relevant question for future research on inclusive mathematics teacher education and professional development.\u003c/p\u003e \u003cp\u003eSecond, inclusive education in Germany is a prominent topic in general pedagogy, not only with a particular focus on inclusive teaching but also considering the broader context of societal and cultural issues as well as topics in educational science and educational psychology. The broader context issues of inclusive education are prioritized in the first phase of teacher education in Germany (e.g., Lohmann et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), whereas the second phase focuses on subject-specific instruction in highly practical situations\u0026mdash;with the aim of qualifying teachers to deliver good instruction in the existing school system. This might explain why differences between master\u0026rsquo;s students and the other two groups are larger in P_PID-IT than in M_PID-IT, the latter, with teacher candidates\u0026mdash;that is, pre-service teachers during their second phase\u0026mdash;outperforming the other groups (at least on the numerical level).\u003c/p\u003e \u003cp\u003eThird, measurement instruments developed in the TEDS-IME project may exhibit a higher level of constructive alignment (Biggs, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) with initial teacher education than among in-service teachers\u0026rsquo; professional development. Future research is required to validate the novel instruments presented for the first time in the present article.\u003c/p\u003e \u003c/div\u003e"},{"header":"7. Conclusion","content":"\u003cp\u003eGiven that the development of teachers\u0026rsquo; competence for inclusive mathematics education requires support, the rigorous measurement instruments developed as part of the project TEDS-IME are highly valuable from a scientific perspective. Meanwhile, TEDS-IME continued the comprehensive and pioneering work on mathematics teacher competence modeling and measuring that Sigrid Bl\u0026ouml;meke, an internationally renowned and excellent scholar, had exceptionally achieved over many years. Bl\u0026ouml;meke invariably and enthusiastically endorsed interdisciplinary research approaches, particularly those that connect mathematics education, general pedagogy, cognitive psychology, and educational measurement, and her work has influenced the present study\u0026rsquo;s conceptualization of competence measurement. The acknowledgment that teachers require not only pedagogy or mathematics knowledge but a complex and multidimensional profile of competence that goes beyond knowledge to consider the situation-specific skills of perception, interpretation, and decision-making, is an element of Bl\u0026ouml;meke\u0026rsquo;s scientific legacy with which we have attempted to comply in the present study and data analysis. The research questions that remain unresolved, such as why in-service teachers were outperformed by pre-service teachers in teacher noticing, should form the starting point for further research wishing to build on outstanding research achievements of our esteemed colleague Sigrid Bl\u0026ouml;meke.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDisclosure statement:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo potential conflict of interest was reported by the author(s).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by BMBF Germany, grant number 01NV2125A and 01NV2125B.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAllsopp, D. H., \u0026amp; Haley, K. C. (2015). A Synthesis of Research on Teacher Education, Mathematics, and Students with Learning Disabilities. \u003cem\u003eLearning Disabilities: A Contemporary Journal\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(2), 177\u0026ndash;206.\u003c/li\u003e\n\u003cli\u003eBall, D. L., Thames, M. H., \u0026amp; Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? \u003cem\u003eJournal of Teacher Education\u003c/em\u003e, \u003cem\u003e59\u003c/em\u003e(5), 389\u0026ndash;407. https://doi.org/10.1177/0022487108324554\u003c/li\u003e\n\u003cli\u003eBastian, A., Kaiser, G., Meyer, D., Schwarz, B., \u0026amp; K\u0026ouml;nig, J. (2022). Teachers\u0026lsquo; noticing and its growth toward expertise: an expert-novice comparison with (pre-service) secondary mathematics teachers. \u003cem\u003eEducational Studies in Mathematics\u003c/em\u003e, \u003cem\u003e110\u003c/em\u003e, 205\u0026ndash;232. https://doi.org/10.1007/s10649-021-10128-y \u003c/li\u003e\n\u003cli\u003eBaumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., \u0026amp; Tsai, Y.‑M. (2010). Teachers\u0026rsquo; Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress. \u003cem\u003eAmerican Educational Research Journal\u003c/em\u003e, \u003cem\u003e47\u003c/em\u003e(1), 133\u0026ndash;180. https://doi.org/10.3102/0002831209345157\u003c/li\u003e\n\u003cli\u003eBerliner, D. C. (2004). Describing the behavior and documenting the accomplishments of expert teachers. \u003cem\u003eBulletin of Science, Technology \u0026amp; Society\u003c/em\u003e, \u003cem\u003e24\u003c/em\u003e(3), 200\u0026ndash;212. https://doi.org/10.1177/0270467604265535\u003c/li\u003e\n\u003cli\u003eBiggs, J. (2014). Constructive alignment in university teaching. \u003cem\u003eHERDSA Review of Higher Education\u003c/em\u003e, \u003cem\u003e1\u003c/em\u003e(1), 5\u0026ndash;22.\u003c/li\u003e\n\u003cli\u003eBl\u0026ouml;meke, S. (2021). IEA\u0026rsquo;s Teacher Education and Development Study in Mathematics (TEDS-M). In T. Nilsen, A. Stancel-Piątak, \u0026amp; J.-E. Gustafsson (Eds.), \u003cem\u003eSpringer International Handbooks of Education. International Handbook of Comparative Large-Scale Studies in Education \u003c/em\u003e(pp. 1\u0026ndash;53). Springer International Publishing. https://doi.org/10.1007/978-3-030-38298-8_16-1\u003c/li\u003e\n\u003cli\u003eBl\u0026ouml;meke, S., Busse, A., Kaiser, G., K\u0026ouml;nig, J., \u0026amp; Suhl, U. (2016). The relation between content-specific and general teacher knowledge and skills. \u003cem\u003eTeaching and Teacher Education\u003c/em\u003e, \u003cem\u003e56\u003c/em\u003e, 35\u0026ndash;46. https://doi.org/10.1016/j.tate.2016.02.003\u003c/li\u003e\n\u003cli\u003eBl\u0026ouml;meke, S., \u0026amp; Delaney, S. (2012). Assessment of teacher knowledge across countries: a review of the state of research. \u003cem\u003eZDM \u0026ndash; Mathematics Education\u003c/em\u003e, \u003cem\u003e44\u003c/em\u003e(3), 223\u0026ndash;247. https://doi.org/10.1007/s11858-012-0429-7\u003c/li\u003e\n\u003cli\u003eBl\u0026ouml;meke, S., Gustafsson, J.‑E., \u0026amp; Shavelson, R. J. (2015). Beyond dichotomies: Competence viewed as a continuum. \u003cem\u003eZeitschrift F\u0026uuml;r Psychologie\u003c/em\u003e, \u003cem\u003e223\u003c/em\u003e(1), 3\u0026ndash;13. https://doi.org/10.1027/2151-2604/a000194\u003c/li\u003e\n\u003cli\u003eBl\u0026ouml;meke, S., Jentsch, A., Ross, N., Kaiser, G., \u0026amp; K\u0026ouml;nig, J. (2022). Opening up the black box: Teacher competence, instructional quality, and students\u0026rsquo; learning progress. \u003cem\u003eLearning and Instruction\u003c/em\u003e, \u003cem\u003e79\u003c/em\u003e, Article 101600. https://doi.org/10.1016/j.learninstruc.2022.101600\u003c/li\u003e\n\u003cli\u003eBromme, R. (2001). Teacher expertise. In N. J. Smelser \u0026amp; P. B. Baltes (Eds.), \u003cem\u003eInternational encyclopedia of the social \u0026amp; behavioral sciences \u003c/em\u003e(pp. 15459\u0026ndash;15465). Elsevier. https://doi.org/10.1016/B0-08-043076-7/02447-5\u003c/li\u003e\n\u003cli\u003eBMBF [Bundesministerium f\u0026uuml;r Bildung und Forschung]. (2024). \u003cem\u003e\u0026lsquo;Qualit\u0026auml;tsoffensive Lehrerbildung\u0026rsquo;: A look back, a look ahead\u003c/em\u003e. https://www.qualitaetsoffensive-lehrerbildung.de/lehrerbildung/shareddocs/downloads/files/abschlussbroschuere2024_en.pdf?__blob=publicationFile\u0026amp;v=2\u003c/li\u003e\n\u003cli\u003eCarter, K., Cushing, K., Sabers, D., Stein, P., \u0026amp; Berliner, D. (1988). Expert-novice differences in perceiving and processing visual classroom information. \u003cem\u003eJournal of Teacher Education\u003c/em\u003e, \u003cem\u003e39\u003c/em\u003e(3), 25\u0026ndash;31. https://doi.org/10.1177/002248718803900306\u003c/li\u003e\n\u003cli\u003eCochran-Smith, M. (2001). Constructing outcomes in teacher education. \u003cem\u003eEducation Policy Analysis Archives\u003c/em\u003e, \u003cem\u003e9\u003c/em\u003e(11). https://doi.org/10.14507/epaa.v9n11.2001\u003c/li\u003e\n\u003cli\u003eDignath, C., Rimm-Kaufman, S., van Ewijk, R., \u0026amp; Kunter, M. (2022). Teachers\u0026rsquo; Beliefs About Inclusive Education and Insights on What Contributes to Those Beliefs: a Meta-analytical Study. \u003cem\u003eEducational Psychology Review\u003c/em\u003e, \u003cem\u003e34\u003c/em\u003e(4), 2609\u0026ndash;2660. https://doi.org/10.1007/s10648-022-09695-0\u003c/li\u003e\n\u003cli\u003eEricsson, K. A., Krampe, R. T., \u0026amp; Tesch-R\u0026ouml;mer, C. (1993). The role of deliberate practice in the acquisition of expert performance. \u003cem\u003ePsychological Review\u003c/em\u003e, \u003cem\u003e100\u003c/em\u003e(3), 363\u0026ndash;406. https://doi.org/10.1037/0033-295X.100.3.363\u003c/li\u003e\n\u003cli\u003eFlorian, L., \u0026amp; Camedda, D. (2020). Enhancing teacher education for inclusion. \u003cem\u003eEuropean Journal of Teacher Education\u003c/em\u003e, \u003cem\u003e43\u003c/em\u003e(1), 4\u0026ndash;8. https://doi.org/10.1080/02619768.2020.1707579\u003c/li\u003e\n\u003cli\u003eGitomer, D. H., \u0026amp; Zisk, R. C. (2015). Knowing What Teachers Know. \u003cem\u003eReview of Research in Education\u003c/em\u003e, \u003cem\u003e39\u003c/em\u003e(1), 1\u0026ndash;53. https://doi.org/10.3102/0091732X14557001\u003c/li\u003e\n\u003cli\u003eG\u0026ouml;ransson, K., \u0026amp; Nilholm, C. (2014). Conceptual diversities and empirical shortcomings \u0026ndash; a critical analysis of research on inclusive education. \u003cem\u003eEuropean Journal of Special Needs Education\u003c/em\u003e, \u003cem\u003e29\u003c/em\u003e(3), 265\u0026ndash;280. https://doi.org/10.1080/08856257.2014.933545\u003c/li\u003e\n\u003cli\u003eGrossman, P. L., \u0026amp; Richert, A. E. (1988). Unacknowledged knowledge growth: A re-examination of the effects of teacher education. \u003cem\u003eTeaching and Teacher Education\u003c/em\u003e, \u003cem\u003e4\u003c/em\u003e(1), 53\u0026ndash;62. https://doi.org/10.1016/0742-051X(88)90024-8\u003c/li\u003e\n\u003cli\u003eHasselhorn, M., \u0026amp; Gold, A. (2022). \u003cem\u003eP\u0026auml;dagogische Psychologie: Erfolgreiches Lernen und Lehren\u003c/em\u003e. W. Kohlhammer GmbH. https://doi.org/10.17433/978-3-17-039783-5\u003c/li\u003e\n\u003cli\u003eHeinrichs, H., \u0026amp; Kaiser, G. (2018). Diagnostic Competence for Dealing with Students\u0026rsquo; Errors: Fostering Diagnostic Competence in Error Situations. In T. Leuders, K. Philipp, \u0026amp; J. Leuders (Eds.), \u003cem\u003eDiagnostic Competence of Mathematics Teachers \u003c/em\u003e(pp. 79\u0026ndash;94). Springer International Publishing. https://doi.org/10.1007/978-3-319-66327-2_4\u003c/li\u003e\n\u003cli\u003eKaiser, G. (2024). The TEDS research program. Its origin and development (in memoriam Sigrid Bl\u0026ouml;meke). In J. K\u0026ouml;nig, C. Hanisch, P. Hanke, T. Hennemann, K. Kaspar, M. Martens, \u0026amp; S. Strau\u0026szlig; (Eds.), \u003cem\u003eAuf die Lehrperson und ihren Unterricht kommt es an. Zehn Jahre empirische Professions- und Unterrichtsforschung im IZeF der Universit\u0026auml;t zu K\u0026ouml;ln \u003c/em\u003e(pp. 261\u0026ndash;287). Waxmann Verlag GmbH.\u003c/li\u003e\n\u003cli\u003eKaiser, G. (2025). Research on Teacher Expertise and Teacher Competence \u0026ndash; Are they complementary or contradictory paradigmatic approaches? \u003cem\u003eZDM \u0026ndash; Mathematics Education\u003c/em\u003e. in this issue\u003c/li\u003e\n\u003cli\u003eKaiser, G., Bl\u0026ouml;meke, S., K\u0026ouml;nig, J., Busse, A., D\u0026ouml;hrmann, M., \u0026amp; Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers\u0026mdash;cognitive versus situated approaches. \u003cem\u003eEducational Studies in Mathematics\u003c/em\u003e, \u003cem\u003e94\u003c/em\u003e(2), 161\u0026ndash;182. https://doi.org/10.1007/s10649-016-9713-8\u003c/li\u003e\n\u003cli\u003eKaiser, G., Busse, A., Hoth, J., K\u0026ouml;nig, J., \u0026amp; Bl\u0026ouml;meke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers\u0026rsquo; competence. \u003cem\u003eInternational Journal of Science and Mathematics Education\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(2), 369\u0026ndash;387. https://doi.org/10.1007/s10763-015-9616-7\u003c/li\u003e\n\u003cli\u003eKaiser, G., \u0026amp; K\u0026ouml;nig, J. (2019). Competence measurement in (mathematics) teacher education and beyond: Implications for policy. \u003cem\u003eHigher Education Policy\u003c/em\u003e, \u003cem\u003e32\u003c/em\u003e(4), 597\u0026ndash;615. https://doi.org/10.1057/s41307-019-00139-z\u003c/li\u003e\n\u003cli\u003eKersting, N. B., Givvin, K. B., Thompson, B. J., Santagata, R., \u0026amp; Stigler, J. W. (2012). Measuring usable knowledge: Teachers\u0026rsquo; analyses of mathematics classroom videos predict teaching quality and student learning. \u003cem\u003eAmerican Educational Research Journal\u003c/em\u003e, \u003cem\u003e49\u003c/em\u003e(3), 568\u0026ndash;589. https://doi.org/10.3102/0002831212437853\u003c/li\u003e\n\u003cli\u003eKhamzina, K., Stanczak, A., Brasselet, C., Desombre, C., Legrain, C., Rossi, S., Guirimand, N., \u0026amp; Cilia, F. (2024). Designing Effective Pre-service Teacher Training in Inclusive Education: a Narrative Review of the Effects of Duration and Content Delivery Mode on Teachers\u0026rsquo; Attitudes Toward Inclusive Education. \u003cem\u003eEducational Psychology Review\u003c/em\u003e, \u003cem\u003e36\u003c/em\u003e(1). https://doi.org/10.1007/s10648-024-09851-8\u003c/li\u003e\n\u003cli\u003eK\u0026ouml;nig, J., Gerhard, K., Kaspar, K., \u0026amp; Melzer, C. (2019). Professionelles Wissen von Lehrkr\u0026auml;ften zur Inklusion: \u0026Uuml;berlegungen zur Modellierung und Erfassung mithilfe standardisierter Testinstrumente. \u003cem\u003eP\u0026auml;dagogische Rundschau\u003c/em\u003e, \u003cem\u003e73,\u003c/em\u003e(1), 43\u0026ndash;64. https://doi.org/10.3726/PR012019.0004\u003c/li\u003e\n\u003cli\u003eK\u0026ouml;nig, J., Gerhard, K., Melzer, C., R\u0026uuml;hl, A.‑M., Zenner, J., \u0026amp; Kaspar, K. (2017). Erfassung von p\u0026auml;dagogischem Wissen f\u0026uuml;r inklusiven Unterricht bei angehenden Lehrkr\u0026auml;ften: Testkonstruktion und Validierung. \u003cem\u003eUnterrichtswissenschaft\u003c/em\u003e, \u003cem\u003e45\u003c/em\u003e, 223\u0026ndash;242.\u003c/li\u003e\n\u003cli\u003eK\u0026ouml;nig, J., Heine, S., Weyers, J., Arntz, C.‑G., Kramer, C., Strau\u0026szlig;, S., Gerhard, K., M\u0026uuml;hle, J., Engartner, T., Gro\u0026szlig;schedl, J., Hanisch, C., Hanke, P., Hennemann, T., Jost, J., Kaspar, K., \u0026amp; Rott, B. (under review). 1 Effectiveness of interventions in teacher education: Synthesis of reviews (2010\u0026ndash;2024). \u003cem\u003eZeitschrift F\u0026uuml;r Erziehungswissenschaft\u003c/em\u003e.\u003c/li\u003e\n\u003cli\u003eK\u0026ouml;nig, J., Santagata, R., Scheiner, T., Adleff, A.‑K., Yang, X., \u0026amp; Kaiser, G. (2022). Teacher noticing: A systematic literature review of conceptualizations, research designs, and findings on learning to notice. \u003cem\u003eEducational Research Review\u003c/em\u003e, \u003cem\u003e36\u003c/em\u003e, Article 100453. https://doi.org/10.1016/j.edurev.2022.100453\u003c/li\u003e\n\u003cli\u003eKorff, N. (2018). \u003cem\u003eInklusiver Mathematikunterricht in der Primarstufe: Erfahrungen, Perspektiven und Herausforderungen \u003c/em\u003e(3. unver\u0026auml;nderte Auflage). Schneider Verlag Hohengehren. \u003c/li\u003e\n\u003cli\u003eKrauss, S., Bruckmaier, G., Lindl, A., Hilbert, S., Binder, K., Steib, N., \u0026amp; Blum, W. (2020). Competence as a continuum in the COACTIV study: the \u0026ldquo;cascade model\u0026rdquo;. \u003cem\u003eZDM \u0026ndash; Mathematics Education\u003c/em\u003e, \u003cem\u003e52\u003c/em\u003e(2), 311\u0026ndash;327. https://doi.org/10.1007/s11858-020-01151-z\u003c/li\u003e\n\u003cli\u003eKMK [Kultusministerkonferenz]. (2004/2022). \u003cem\u003eStandards f\u0026uuml;r die Lehrerbildung: Bildungswissenschaften\u003c/em\u003e [Beschluss der Kultusministerkonferenz vom 16.12.2004 i. d. F. 16.05.2022]. \u003c/li\u003e\n\u003cli\u003eLarrain, M., \u0026amp; Kaiser, G. (2020). Analysis of students\u0026rsquo; mathematical errors as a means to promote future primary school teachers\u0026rsquo; diagnostic competence. \u003cem\u003eUNIPLURIVERSIDAD\u003c/em\u003e, \u003cem\u003e19\u003c/em\u003e(2), 17\u0026ndash;39. https://doi.org/10.17533/udea.unipluri.19.2.02\u003c/li\u003e\n\u003cli\u003eLeuders, T., \u0026amp; Prediger, S. (2017). Flexibel differenzieren erfordert fachdidaktische Kategorien. In J. Leuders, T. Leuders, S. Prediger, \u0026amp; S. Ruwisch (Eds.), \u003cem\u003eKonzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik. Mit Heterogenit\u0026auml;t im Mathematikunterricht umgehen lernen \u003c/em\u003e(pp. 3\u0026ndash;16). Springer. https://doi.org/10.1007/978-3-658-16903-9_1\u003c/li\u003e\n\u003cli\u003eLohmann, V., Seidel, V., \u0026amp; Terhart, E. (2011). Bildungswissenschaften in der universit\u0026auml;ren Lehrerbildung: Curriculare Strukturen und Verbindlichkeiten. Eine Analyse aktueller Studienordnungen an nordrhein-westf\u0026auml;lischen Universit\u0026auml;ten. \u003cem\u003eLehrerbildung auf dem Pr\u0026uuml;fstand\u003c/em\u003e, \u003cem\u003e4\u003c/em\u003e(2), 271\u0026ndash;302. https://doi.org/10.25656/01:14724\u003c/li\u003e\n\u003cli\u003eMagnusson, S., Krajcik, J., \u0026amp; Borko, H. (2002). Nature, Sources, and Development of Pedagogical Content Knowledge for Science Teaching. In J. Gess-Newsome \u0026amp; N. G. Lederman (Eds.), \u003cem\u003eScience \u0026amp; Technology Education Library. Examining Pedagogical Content Knowledge \u003c/em\u003e(Vol. 6, pp. 95\u0026ndash;132). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47217-1_4\u003c/li\u003e\n\u003cli\u003eMientus, L., Hume, A., Wulff, P., Meiners, A., \u0026amp; Borowski, A. (2022). Modelling STEM Teachers\u0026rsquo; Pedagogical Content Knowledge in the Framework of the Refined Consensus Model: A Systematic Literature Review. \u003cem\u003eEducation Sciences\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e(6), 385. https://doi.org/10.3390/educsci12060385\u003c/li\u003e\n\u003cli\u003ePiezunka, A., Schaffus, T., \u0026amp; Grosche, M. (2017). Vier Definitionen von schulischer Inklusion und ihr konsensueller Kern: Ergebnisse von Experteninterviews mit Inklusionsforschenden. \u003cem\u003eUnterrichtswissenschaft\u003c/em\u003e, \u003cem\u003e45\u003c/em\u003e(4), 207\u0026ndash;222. https://doi.org/10.3262/UW1704207\u003c/li\u003e\n\u003cli\u003eRicken, G. (2017). Kompetent sein f\u0026uuml;r Inklusive Schulen hei\u0026szlig;t auch Diagnostizieren lernen. In M. Gercke, S. Opalinski, \u0026amp; T. Thonagel (Eds.), \u003cem\u003eInklusive Bildung und gesellschaftliche Exklusion \u003c/em\u003e(pp. 187\u0026ndash;199). Springer. https://doi.org/10.1007/978-3-658-17084-4_12\u003c/li\u003e\n\u003cli\u003eRoose, I., Goossens, M., Vanderlinde, R., Vantieghem, W., \u0026amp; van Avermaet, P. (2018). Measuring professional vision of inclusive classrooms in secondary education through video-based comparative judgement: An expert study. \u003cem\u003eStudies in Educational Evaluation\u003c/em\u003e, \u003cem\u003e56\u003c/em\u003e, 71\u0026ndash;84. https://doi.org/10.1016/j.stueduc.2017.11.007\u003c/li\u003e\n\u003cli\u003eSherin, M. G., Jacobs, V. R., \u0026amp; Philipp, R. A. (Eds.). (2011). \u003cem\u003eMathematics teacher noticing: Seeing through teachers\u0026rsquo; eyes\u003c/em\u003e. Routledge. \u003c/li\u003e\n\u003cli\u003eShulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. \u003cem\u003eHarvard Educational Review\u003c/em\u003e, \u003cem\u003e57\u003c/em\u003e(1), 1\u0026ndash;22. https://doi.org/10.17763/haer.57.1.j463w79r56455411\u003c/li\u003e\n\u003cli\u003eSteinmetz, S., Wrase, M., Helbig, M., \u0026amp; D\u0026ouml;ttinger, I. (2021). \u003cem\u003eDie Umsetzung schulischer Inklusion nach der UN-Behindertenrechtskonvention in den deutschen Bundesl\u0026auml;ndern\u003c/em\u003e. Nomos Verlagsgesellschaft mbH \u0026amp; Co. KG. https://doi.org/10.5771/9783748924401\u003c/li\u003e\n\u003cli\u003eStigler, J. W., \u0026amp; Miller, K. F. (2018). Expertise and Expert Performance in Teaching. In K. A. Ericsson, R. R. Hoffman, A. Kozbelt, \u0026amp; A. M. Williams (Eds.), \u003cem\u003eThe Cambridge Handbook of Expertise and Expert Performance \u003c/em\u003e(pp. 431\u0026ndash;452). Cambridge University Press. https://doi.org/10.1017/9781316480748.024\u003c/li\u003e\n\u003cli\u003eTatto, M. T., \u0026amp; Senk, S. (2011). The Mathematics Education of Future Primary and Secondary Teachers: Methods and Findings from the Teacher Education and Development Study in Mathematics. \u003cem\u003eJournal of Teacher Education\u003c/em\u003e, \u003cem\u003e62\u003c/em\u003e(2), 121\u0026ndash;137. https://doi.org/10.1177/0022487110391807\u003c/li\u003e\n\u003cli\u003eUN [United Nations]. (2006). \u003cem\u003eConvention on the Rights of Persons with Disabilities\u003c/em\u003e. https://social.desa.un.org/issues/disability/crpd/convention-on-the-rights-of-persons-with-disabilities-articles\u003c/li\u003e\n\u003cli\u003eUNESCO [United Nations Educational, Scientific and Cultural Organisation]. (2018). \u003cem\u003eGlobal Education Meeting 2018: Brussels Declaration\u003c/em\u003e [Document ED-2018/GEM/1]. https://unesdoc.unesco.org/ark:/48223/pf0000366394\u003c/li\u003e\n\u003cli\u003evan Driel, J. H., Berry, A., \u0026amp; Meirink, J. (2014). Research on science teacher knowledge. In N. G. Lederman \u0026amp; S. K. Abell (Eds.), \u003cem\u003eHandbook of Research on Science Education \u003c/em\u003e(pp. 848\u0026ndash;870). Routledge. https://doi.org/10.4324/9780203097267\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Federal Ministry of Education and Research","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"competence, inclusive education, teacher professional knowledge, mathematical education, noticing skills, (mathematics) teacher","lastPublishedDoi":"10.21203/rs.3.rs-5738066/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5738066/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTeachers\u0026rsquo; professional noticing\u0026mdash;often conceptualized as their situation-specific skills of perception, interpretation and decision-making\u0026mdash;constitutes an important component of their professional competence. Noticing has become increasingly significant worldwide in the pursuit of inclusive mathematics education in classroom settings, whereby teachers are required to provide equal opportunities for students across all ability levels. However, current teacher noticing frameworks lack the requisite specificity to support inclusive mathematics education, particularly regarding diagnostic applications and adequate learning support, and thus a revision of existing frameworks is warranted. On the one hand, such frameworks must incorporate selected facets of teacher knowledge, including mathematical pedagogical content knowledge (MPCK) and general pedagogical knowledge (GPK) specified for inclusive teaching; on the other hand, the differentiation into dispositions and situation-specific skills as decisive components of competence viewed as a continuum must be considered, as Sigrid Bl\u0026ouml;meke et al. suggested in their seminal framework. This paper describes the methodological challenges associated with the development of standardized instruments to measure teachers\u0026rsquo; professional knowledge and noticing within inclusive mathematics education, as undertaken by the project Teacher Education and Development Study \u0026ndash; Inclusive Mathematics Education (TEDS-IME). Using a large sample of 628 pre-service and in-service teachers, the paper aims to examine the dimensionality of teachers\u0026rsquo; competence for inclusive mathematics education and expert\u0026ndash;novice differences in the pattern of their competence facets. Our findings indicate that the newly developed video-based instrument for teachers\u0026rsquo; noticing in inclusive mathematics education serves as a reliable and multidimensional measurement for both pre-service and in-service teachers.\u003c/p\u003e","manuscriptTitle":"Teacher noticing in inclusive mathematics education: Analyzing its structure and expert-novice differences using a novel video-based test instrument","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-01 06:19:55","doi":"10.21203/rs.3.rs-5738066/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 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":42205129,"name":"Special Education"},{"id":42205130,"name":"Educational Psychology"},{"id":42205131,"name":"School Counseling"}],"tags":[],"updatedAt":"2025-01-01T06:19:55+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-01 06:19:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5738066","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5738066","identity":"rs-5738066","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}