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Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress
Open accessAbstract
In both the United States and Europe, concerns have been raised about whether preservice and in-service training succeeds in equipping teachers with the professional knowledge they need to deliver consistently high-quality instruction. This article investigates the significance of teachers’ content knowledge and pedagogical content knowledge for high-quality instruction and student progress in secondary-level mathematics. It reports findings from a 1-year study conducted in Germany with a representative sample of Grade 10 classes and their mathematics teachers. Teachers’ pedagogical content knowledge was theoretically and empirically distinguishable from their content knowledge. Multilevel structural equation models revealed a substantial positive effect of pedagogical content knowledge on students’ learning gains that was mediated by the provision of cognitive activation and individual learning support.
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“Baumert et al. (2010:139) argue that MCK and MPCK are not picked up incidentally but rather developed through university courses, mentoring received during practice teaching and “reflection on classroom experience”.”
From Mentoring and preparing primary school mathematics teachers (2020) · cites this paper as Baumert et al. (2010:139)
In the citing paper
“Teachers' discipline-specific knowledge is dynamic (Baumert et al., 2010)”
From Preservice teachers' mathematical knowledge for teaching: Focus on lesson planning and reflection (2024) · cites this paper as Baumert et al., 2010
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Copur-Gencturk, Y., Choi, H.-J., & Cohen, A. (2022) · Journal of Mathematics Teacher Education · doi:10.1007/s10857-021-09529-w · Cited by 7
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Koyuncu, İ. (2021) · lnternational Electronic Journal of Elementary Education · doi:10.26822/iejee.2022.237 · Cited by 7
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“know how to use their knowledge related to the use of explanations, examples, and representations (Baumert et al., 2010).”
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“(Baumert et al. 2010, 168)”
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“There is evidence in support of (a) an association between these knowledge facets and student achievement (Baumert et al., 2010; Hill, Rowan, & Loewenberg Ball, 2005), and (b) the separability of the constructs content knowledge and pedagogical content knowledge (Baumert et al.”
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“More recent findings show that content knowledge continues to be inert in classrooms unless it is accompanied by a rich repertoire of knowledge and skills related directly to the curriculum, instruction and student learning (Baumert, 2010, Darling-Hammond, 2016)[49, 48].”
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BackgroundResultThe Influence of a Teaching Assistant Orientation on Teaching Assistant Perceptions of Self-Efficacy
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BackgroundGlassow, L. N., Franck, E., & Hansen, K. Y. (2023) · International Journal of Educational Research · doi:10.1016/j.ijer.2023.102170 · Cited by 11
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“Research has begun to advance our understanding of the knowledge considered most important for school mathematics teaching (e.g., Baumert et al. 2010; Hill et al. 2007; Schmidt et al. 2011; Tatto 2008; Tatto et al. 2010).”
BackgroundHigh school mathematics teachers’ use of beliefs and knowledge in high-quality instruction
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BackgroundInfluentialHartmuth, D., Amin, R. M., Schlichting, D., Schött, S., Haudenschild, J., Küchenhoff, H., & Neuhaus, B. J. (2025) · Cogent Education · doi:10.1080/2331186x.2025.2470563 · Cited by 7
Preservice teachers' mathematical knowledge for teaching: Focus on lesson planning and reflection
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“Common Content Knowledge -CCK (Ball et al., 2008; Baumert et al., 2010) Define mathematical terms Unpack mathematics concepts and/or symbols Solve mathematical problems Specialized Content Knowledge-SCK (Ding & Heffernan, 2018; Hill et al., 2005; Morris & Hiebert, 2017) Anticipate alternative…”
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“…consistently highlight the importance of high-quality teaching in fostering both cognitive and affective learning outcomes, interna-✉ tionally (Baumert et al., 2010; Fauth et al., 2014; Kane & Staiger, 2012; Klieme & Nilsen, 2022; Klieme et al., 2009; Praetorius et al., 2018) and within…”
InfluentialAust, L., Linker, J.-C., Eichholz, L., Schiffer, J., Nührenbörger, M., Selter, C., & Souvignier, E. (2025) · Contemporary Educational Psychology · doi:10.1016/j.cedpsych.2025.102376 · Cited by 9
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“Since our study examined instructional quality on the basis of the generic model of TBD (Baumert et al., 2010; Klieme et al., 2001, 2009), further research referring to other instructional quality conceptualizations from a subject-specific perspective could provide a deeper insight into…”
InfluentialNixon, R. S., & Bennion, A. H. (2024) · Science Education · doi:10.1002/sce.21902 · Cited by 6
Jingle-Jangle in der Messung digitaler Kompetenzen von (angehenden) Lehrkräften
Rubach, C. (2024) · MedienPädagogik Zeitschrift für Theorie und Praxis der Medienbildung · doi:10.21240/mpaed/57/2024.03.25.x · Cited by 8
Bayrhuber, H., & Frederking, V. (2024) · The Journal of Curriculum Studies · doi:10.1080/00220272.2024.2318736 · Cited by 6
“…in the Classroom), a supplementary study to the German PISA surveys of 2003/04 with 198 teachers, investigating teachers’ professional knowledge, cognitively activating mathematics instruction and the development of mathematical competence (Baumert & Kunter, 2006, 2011; Baumert et al., 2010).”
BackgroundÖnen, E. (2023) · Teaching and Teacher Education · doi:10.1016/j.tate.2023.104205 · Cited by 10
König, J., Glutsch, N., Weyers, J., Casale, G., Hanke, P., Knips, C., Pohl, T., Waschewski, T., Becker-Mrotzek, M., Schabmann, A., et al. (2023) · Discover Education · doi:10.1007/s44217-023-00058-7 · Cited by 11
“This model is well established in Germany as the country of our study (e.g., [15, 17, 25, 41, 42, 44]).”
BackgroundResultInfluentialAbdillah, M. G., & Fithriani, R. (2023) · REiLA Journal of Research and Innovation in Language · doi:10.31849/reila.v5i1.13228 · Cited by 15
“…subject knowledge, in particular, can aid teachers and student teachers in establishing clarity in high-level degrees, as pedagogical content knowledge often consists of content-specific strategies for creating authentic instructional material for learners (Ball et al., 2008; Baumert et al., 2010).”
Sacré, M., & Lallemand, C. (2023) · Annual Symposium on HCI Education (EduCHI) · doi:10.1145/3587399.3587402 · Cited by 7
Carré, M. C. P., Rodríguez, J. L. C., Aguilar, D., & Blanch, À. (2023) · European Journal of Educational Research · doi:10.12973/eu-jer.12.2.851 · Cited by 10
“The Instruction dimension assesses the way PTs conducted the teaching and supported the learning process (Baumert et al., 2010; Osborne et al., 2015).”
BackgroundSpreitzer, C., & Hafner, S. (2023) · European Journal of Educational Research · doi:10.12973/eu-jer.12.2.991 · Cited by 7
Johansson, S., Gustafsson, J., Hansson, Å., & Alatalo, T. (2023) · Scandinavian Journal of Educational Research · doi:10.1080/00313831.2023.2175252 · Cited by 11
“Mathematics teachers ’ disciplinary competences are positively related to students ’ mathematics learning (Baumert et al., 2010; Callingham et al., 2016; Smith et al., 2012), as is their coursework in mathematics (Harris & Sass, 2011; Garet et al., 2010).”
BackgroundMikeska, J. N., Cisterna, D., Lakhani, H., Bookbinder, A. K., Myers, D., & Vaval, L. (2022) · Science Education · doi:10.1002/sce.21779 · Cited by 6
Marks, G. N. (2022) · School Effectiveness and School Improvement · doi:10.1080/09243453.2022.2102042 · Cited by 8
Gated Recurrent Unit Framework for Ideological and Political Teaching System in Colleges
Mu, Y. (2022) · Scientific Programming · doi:10.1155/2022/9615461 · Cited by 4
Charalambous, C. Y., Agathangelou, S. A., Kasapi, E., & Christofidou, E. (2022) · Journal of Mathematics Teacher Education · doi:10.1007/s10857-022-09532-9 · Cited by 11
“1 3 Research that focuses on either cognitive activation (e.g., Baumert et al., 2010; Le Donné et al., 2016) or differentiation (e.g., Reis et al., 2011) has shown this type of teaching to promote student cognitive and affective learning.”
BackgroundBaideldinova, G., Zhetpisbayeva, B., Ospanova, B., & Tleumbetova, D. (2021) · European Journal of Contemporary Education · doi:10.13187/ejced.2021.4.868 · Cited by 6
“(Baumert et al., 2010).”
Neumann, I., Sorge, S., Hoth, J., Lindmeier, A., Neumann, K., & Heinze, A. (2021) · Studies in Higher Education · doi:10.1080/03075079.2021.1953335 · Cited by 8
“More specifically, content knowledge has been found critical to the development of pedagogical content knowledge (e.g. Baumert et al. 2010; Rollnick 2017) that in turn determines quality teaching (e.g. Kunter et al. 2013; Kulgemeyer and Riese 2018) and thus effective learning (e.g. Keller, Neumann,…”
BackgroundFactors Affecting Efficient Teaching and Learning of Mathematics in Senior High Schools in Wa
Gabina, S., Jagri, B., Mohammed, A. A., Anass, A. A., Abdul-Mumin, A.-H., Agyei, E., & Domonaamwin, C. B. (2021) · Teacher Education and Curriculum Studies · doi:10.11648/j.tecs.20210603.11 · Cited by 6
Copur-Gencturk, Y., Jacobson, E., & Rasiej, R. (2021) · Journal of Mathematics Teacher Education · doi:10.1007/s10857-021-09486-4 · Cited by 6
THE RURAL POLICY OF SLOVAKIA AFTER JOINING THE EU
Dudić, B., Dudić, Z., Pejanović, R., Skataric, G., Saxunová, D., & Peráček, T. (2020) · The Journal "Agriculture and Forestry · doi:10.17707/agricultforest.66.3.04 · Cited by 6
Secondary Mathematics Teachers' Content Knowledge for Teaching the Concept of Function
Hatısaru, V. (2020) · International Journal for Mathematics Teaching and Learning · doi:10.4256/ijmtl.v21i1.264 · Cited by 9
“163), teachers’ knowledge about the function concept is critical, which might impede their instructional practices (Hill, Rowan, & Ball, 2005) and effective student learning (Baumert et al., 2010; Roux, Nieuwoudt & Nieuwoudt, 2015; Watson & Harel, 2013).”
BackgroundInfluentialEffortless or less effort? Effects of tracks on students’ engagement
Dockx, J., den Branden, N. V., & Fraine, B. D. (2019) · British Journal of Educational Psychology · doi:10.1111/bjep.12290 · Cited by 9
Teacher Education in Tanzania: Pre-Service Teachers Preparation for the 21st Century
Ngao, A., & Tian, X.-H. (2020) · Journal of Education and Practice · doi:10.7176/jep/11-11-09 · Cited by 6
“Baumert et al. (2010) Stated that, professional knowledge including Content Knowledge, Pedagogical Content Knowledge and General Pedagogical Knowledge is one of the important cognitive disposition that impacts teaching quality and students learning.”
BackgroundKersting, N., Smith, J. E., Vezino, B., Chen, M.-K., Wood, M., & Stigler, J. (2020) · Zdm · doi:10.1007/s11858-020-01135-z · Cited by 6
“…teaching (Shulman, 1986, 1987), much of the research on teacher knowledge has focused on identifying knowledge domains specific to teaching (Ball 2000, 2003) and on examining their impact on teaching and student learning (Hill, Schilling & Ball, 2004; Baumert, Kunter, Blum, Brunner et al., 2010).”
BackgroundWie fach(un)abhängig ist bildungswissenschaftliches Wissen?
Lohse-Bossenz, H., Holzberger, D., Kunina‐Habenicht, O., Seidel, T., & Kunter, M. (2018) · Zeitschrift für Erziehungswissenschaft · doi:10.1007/s11618-018-0817-z · Cited by 7
Self-citationKabael, T., & Akın, A. (2018) · doi:10.21890/ijres.383126 · Cited by 6
“Baumert et al. (2010) emphasize that sufficient content knowledge of mathematics is essential for enhancing pedagogical content knowledge. For this reason, insufficient mathematical content knowledge is correlated with the lack of pedagogical content knowledge (Van den Kieboom et al., 2014). In other respects, several…”
BackgroundEL CONOCIMIENTO PEDAGÓGICO DEL CONTENIDO EN PROFESORES DE BIOLOGÍA UNA REVISIÓN DOCUMENTAL
Amaya, G. F. (2017) · doi:10.17227/bio-grafia.vol.10.num19-7219 · Cited by 6
“A pesar de las diferentes conceptualizaciones de pck (Abell, 2007; Park et al., 2011; Baumert et al., 2010; Baxter y Lederman 1999; Berry et al., 2008; Blomeke et al., 2008; Hashweh, 2005; Hill et al., 2005; Magnusson et al., 1999), existe un acuerdo con respecto a dos aspectos críticos del pck:…”
BackgroundInfluentialKoopman, M., Thurlings, M. C. G., & Brok, P. J. D. (2017) · Research Papers in Education · doi:10.1080/02671522.2017.1390595 · Cited by 15
Nair, S., & Yassin, S. (2017) · doi:10.18488/journal.1.2017.79.754.763 · Cited by 6
“Similarly studies by Hill et al. (2005); Baumert et al. (2010) and Voss et al. (2011) indicate that teachers’ pedagogical content knowledge have an impact on the quality of instruction and children’s learning outcome.”
BackgroundTeacher Behaviours Explaining Turkish and Dutch Students' Mathematic Achievements.
Yalçın, S. (2017) · International Journal of Evaluation and Research in Education (IJERE) · doi:10.11591/ijere.v6i2.7596 · Cited by 6
“Furthermore, cognitive activation is significantly related to higher mathematics achievement [26],[27].”
BackgroundPre-Service Physics Teachers' Argumentation in a Model Rocketry Physics Experience *
Gürel, C., & Süzük, E. (2016) · doi:10.12738/estp.2017.1.0042 · Cited by 6
“Gürel, Süzük / Pre-Service Physics Teachers’ Argumentation in a Model Rocketry Physics Experience Sadler, T. D., & Zeidler, D. L. (2005a).”
BackgroundInfluentialPrompting Teacher Geometric Reasoning through Coaching in a Dynamic Geometry Software Context
Knapp, A. K., Barrett, J. E., & Moore, C. J. (2016) · School Science and Mathematics · doi:10.1111/ssm.12184 · Cited by 6
Modeling cognitive dispositions of educators for early mathematics education
Lindmeier, A., Hepberger, B., Heinze, A., & Opitz, E. M. (2016) · doi:10.5167/uzh-133541 · Cited by 6
Montemayor, M., Silvey, B. A., Adams, A., & Witt, K. (2016) · doi:10.1177/0022429415612201 · Cited by 6
Hänze, M., Fischer, E., Schreiber, S., Biehler, R., & Hochmuth, R. (2013) · Zeitschrift für Hochschulentwicklung · doi:10.3217/zfhe-8-04/09 · Cited by 6
“Insbesondere für das Fach Mathematik ist aus der Schulforschung die herausragende Rolle des fachlichen und fachdidaktischen Wissens der Lehrkräfte bekannt (Coactiv-Studie: KRAUSS et al., 2008; BAUMERT et al., 2010).”
BackgroundGünhan, B. C., & Cetingoz, D. (2013) · doi:10.5897/err12.168 · Cited by 6
Research on the influencing factors of business teachers' teaching quality: PLS-SEM and ANN approach
Liu, R., Zhang, Y., & Fang, X. (2025) · The International Journal of Management Education · doi:10.1016/j.ijme.2025.101134 · Cited by 6
Ganendra, A., Joyoatmojo, S., Martono, T., & Wardani, E. K. (2025) · Educational Process: International Journal · doi:10.22521/edupij.2025.15.115 · Cited by 6
“Baumert et al. (2010) and König et al. (2011) explained that pedagogical competence consists of several key components, including classroom management, teaching methods, learning assessment, lesson planning, and adaptive teaching.”
Preparing Mathematics Teachers in Singapore: The Issue of Mathematics Content Knowledge
Tay, E.-G., Lim, S., Ho, W., & Toh, T. (2017) · doi:10.1007/978-981-10-3386-5_7 · Cited by 6
Hsieh, F.-J., Chu, C.-T., Hsieh, C.-J., & Lin, P. (2014) · Advances in mathematics education · doi:10.1007/978-94-007-6437-8_6 · Cited by 6
Das Deutsche Zentrum für Lehrerbildung Mathematik (DZLM)
Kramer, J., & Lange, T. (2014) · doi:10.1007/978-3-658-03104-6_35 · Cited by 6
From Diagnostics to Learning Success
Beck, K., & Zlatkin‐Troitschanskaia, O. (2013) · SensePublishers eBooks · doi:10.1007/978-94-6209-191-7 · Cited by 8
Assessing computer science pedagogical content knowledge: a systematic literature review
Weißenrieder, F., Lenzer, S., & Mühling, A. (2025) · Computer Science Education · doi:10.1080/08993408.2025.2586872 · Cited by 5
Charalambous, C. Y., Grob, U., Praetorius, A., Köhler, C., & Miao, Z. (2025) · Learning and Instruction · doi:10.1016/j.learninstruc.2025.102176 · Cited by 6
Kirschning, H., Bernholt, A., Kauper, T., Møller, J., & Zimmermann, F. (2025) · Teaching and Teacher Education · doi:10.1016/j.tate.2025.105217 · Cited by 9
Jaggy, A., Wagner, W., Fütterer, T., Göllner, R., & Trautwein, U. (2025) · International Journal of STEM Education · doi:10.1186/s40594-025-00576-w · Cited by 5
“…deep reasoning, promoting active problem-solving, engaging intensively with the learning material, and connecting the material to students’ prior knowledge and their understanding of essential learning content and concepts (Baumert et al., 2010; Fütterer et al., 2023; Holz-berger & Prestele, 2021).”
Yang, X., Li, X., Chen, X., König, J., & Kaiser, G. (2025) · ZDM · doi:10.1007/s11858-025-01738-4 · Cited by 11
“…competence was employed as the main theoretical construct embracing affective and cognitive dimensions in line with conceptualizations of other large-scale studies on teacher education and teacher professional development (Baumert et al., 2010; Blömeke & Kaiser, 2014; Tatto et al., 2008).”
Pre-service teacher perceptions of an outdoor learning experience within a science methods course
Dean, S., & Landreth, S. (2025) · Interdisciplinary Journal of Environmental and Science Education · doi:10.29333/ijese/16809 · Cited by 5
Aderinoye-Rabiu, R. A., Bello, A., Usman, A. A., Falebita, O. T., & Oloyede, G. O. (2025) · Pedagogical Research · doi:10.29333/pr/16665 · Cited by 5
In-service elementary school science teachers’ self-reported pedagogical content knowledge in Ghana
Siemoh, R. K., Duku, P., & Boye, S. (2025) · Discover Education · doi:10.1007/s44217-025-00459-w · Cited by 5
Herreros-Torres, D., Sanz, M. T., & Gómez-Ferragud, C. B. (2025) · Frontiers in Education · doi:10.3389/feduc.2025.1274102 · Cited by 5
Financial Literacy, Numeracy, and Schooling: Evidence from Developed Countries
Lamboglia, S., & Stacchini, M. (2025) · Italian Economic Journal · doi:10.1007/s40797-025-00314-9 · Cited by 9
“Withregardtomathematics, thevalueofteachingmightlieinitsabilitytoenhancestudents’cognitiveprocessing (Baumertetal.2010).”
Metadata
- Authors
- Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., & Tsai, Y.-M.
- Affiliations
- Max Planck Society (DE)
- University of Kassel (DE)
- Bielefeld University (DE)
- Carl von Ossietzky Universität Oldenburg (DE)
- ORCID
- Venue
- American Educational Research Journal
- Published
- 2010-03
- Volume
- 47
- Issue
- 1
- Pages
- 133-180
- ISSN
- 0002-8312 (ISSN-L)
- 1935-1011
- OpenAlex
- W2141462352
- Cited by
- 2,100
- References
- 127
- Citations by year
- 2026: 115 · 2025: 119 · 2024: 134 · 2023: 156 · 2022: 174 · 2021: 179 · 2020: 170 · 2019: 145 · 2018: 133 · 2017: 163 · 2016: 143 · 2015: 155 · 2014: 89 · 2013: 105 · 2012: 66
- FWCI
- 165.41
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- American Educational Research Journal (publishedVersion)
- University of Regensburg Publication Server (University of Regensburg) (acceptedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Kobra (Universitätsbibliothek Kassel) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- University of Regensburg Publication Server (University of Regensburg)
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Education › Teacher Education and Leadership Studies
- Social Sciences › Education › Mathematics Education and Pedagogy
- Keywords
- pedagogical content knowledge, content knowledge, cognitive activation, learning gains, secondary mathematics instruction, teacher professional knowledge, mathematics teachers, teacher professional development
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