The conceptualization of mathematics teachers’ professional competence in project-based learning contexts

Sha Li; Chunxia Qi; Ruisi Li

doi:10.29333/ejmste/16562

Full Text (PDF)

Sha Li ¹ , Chunxia Qi ¹ ^* , Ruisi Li ¹

More Detail

¹ Faculty of Education, Beijing Normal University, Beijing, CHINA^* Corresponding Author

Abstract

The impact of teacher competence on teaching practice has been increasingly prominent, especially in mathematics education, but little research focuses on teacher competence in project-based learning (PjBL) contexts. Drawing on existing models and frameworks, mathematics teachers’ professional competence in PjBL contexts was conceptualized as a multi-dimensional construct with cognitive facets (mathematics pedagogical content knowledge related to PjBL, namely P-MPCK) and affective-motivational facets (teacher beliefs and teacher self-efficacy). The conceptual model was empirically validated through an assessment instrument combining cognitive tests (e.g., situated text-vignette tasks) and affective scales. Results suggest that teacher beliefs and self-efficacy were loaded on three factors respectively and the four-dimension model of P-MPCK had strong goodness of fit, which were consistent with the conceptual model. This study provides valuable insights for preparing mathematics teachers to teach PjBL and supporting their professional development.

Keywords

teacher competence
project-based learning
assessment instrument
mathematics teacher education

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 21, Issue 7, July 2025, Article No: em2660

https://doi.org/10.29333/ejmste/16562

Publication date: 04 Jul 2025

Article Views: 351

Article Downloads: 216

Open Access References How to cite this article

References

Adams, R. J. (2005). Reliability as a measurement design effect. Studies in Educational Evaluation, 31(2-3), 162-172. https://doi.org/10.1016/j.stueduc.2005.05.008
Adams, R. J., Wilson, M., & Wang, W. C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21(1), 1-23. https://doi.org/10.1177/0146621697211001
Aldabbus, S. (2018). Project-based learning: Implementation & challenges. International Journal of Education, Learning and Development, 6(3), 71-79.
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
Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17, 39-68. https://doi.org/10.1007/BF03217415
Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational Studies in Mathematics, 79, 127-147. https://doi.org/10.1007/s10649-011-9333-2
Blömeke, S., & Delaney, S. (2012). Assessment of teacher knowledge across countries. ZDM–The International Journal on Mathematics Education, 44(3), 223-247. https://doi.org/10.1007/s11858-012-0429-7
Blömeke, S., Gustafsson, J. E., & Shavelson, R. (2015). Beyond dichotomies: Competence viewed as a continuum. ZeitschriftF€ urPsychologie, 223(1), 3-13. https://doi.org/10.1027/2151-2604/a000194
Blömeke, S., Kaiser, G., König, J., & Jentsch, A. (2020). Profiles of mathematics teachers’ competence and their relation to instructional quality. ZDM Mathematics Education, 52, 329-342. https://doi.org/10.1007/s11858-020-01128-y
Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer. https://doi.org/10.1007/978-3-319-68072-9
Charalambous, C. Y., Philippou, G. N., & Kyriakides, L. (2008). Tracing the development of preservice teachers’ efficacy beliefs in teaching mathematics during fieldwork. Educational Studies in Mathematics, 67, 125-142. https://doi.org/10.1007/s10649-007-9084-2
Chen, H. (2023). The case study of improving pre-service teachers’ mathematical modeling teaching competence [PhD thesis, East China Normal University]. https://doi.org/10.27149/d.cnki.ghdsu.2023.004078
Condliffe, B., Quint, J., Visher, M. G., Bangser, M. R., Drohojowska, S., Saco, L., & Nelson, E. (2017). Project-based learning: A literature review. MDRC.
Copur-Gencturk, Y., & Tolar, T. (2022). Mathematics teaching expertise: A study of the dimensionality of content knowledge, pedagogical content knowledge, and content-specific noticing skills. Teaching and Teacher Education, 114, Article 103696. https://doi.org/10.1016/j.tate.2022.103696
Cormas, P. C. (2022). Preservice teachers’ beliefs in a mathematics/science course. Research in Science & Technological Education, 40(2), 234-250. https://doi.org/10.1080/02635143.2020.1784126
Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12-25. https://doi.org/10.1016/j.tate.2013.03.001
Döhrmann, M., Kaiser, G., & Blömeke, S. (2012). The conceptualization of mathematics competencies in the international teacher education study TEDS-M. ZDM Mathematics Education, 44(3), 325-340. https://doi.org/10.1007/s11858-012-0432-z
Ekawati, R., Lin, F. L., & Yang, K. L. (2015). Developing an instrument for measuring teachers’ mathematics content knowledge on ratio and proportion: A case of Indonesian primary teachers. International Journal of Science and Mathematics Education, 13, 1-24. https://doi.org/10.1007/s10763-014-9532-2
Ekawati, R., Rosyidi, A. H., Prawoto, B. P., Prahmana, R. C. I., & Lin, F. L. (2022). Developing a constructive conceptual framework of a pre-service mathematics teachers’ content knowledge instrument on space and shape. Mathematics, 10(1), Article 137. https://doi.org/10.3390/math10010137
Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249-253). Falmer.
Fang, Y., Paine, L., & Huang, R. (2022). Continuity and change: Chinese lesson study redefined in the context of key competencies-based reform. International Journal for Lesson & Learning Studies, 11(2), 49-59. https://doi.org/10.1108/IJLLS-04-2022-0057
Fisher, D., Kusumah, Y. S., & Dahlan, J. A., 2020. Project-based learning in mathematics: A literature review. Journal of Physics: Conference Series, 1657(1), Article 012032. https://doi.org/10.1088/1742-6596/1657/1/012032
Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466-491. https://doi.org/10.1037/1082-989X.9.4.466
Francis, D. C., Rapacki, L., & Eker, A. (2014). The individual, the context, and practice: A review of the research on teachers’ beliefs related to mathematics. In H. Fives, & M. G. Gill (Eds.), International handbook of research on teachers’ beliefs (pp. 336-352). Lawrence Erlbaum Associates Publishers.
Han, S., Rosli, R., Capraro, M. M., & Capraro, R. M. (2016). The effect of science, technology, engineering and mathematics (STEM) project-based learning (PjBL) on students’ achievement in four mathematics topics. Journal of Turkish Science Education, 13(special), 3-29.
Herro, D., Quigley, C., & Abimbade, O. (2021). Assessing elementary students’ collaborative problem-solving in makerspace activities. Information and Learning Sciences, 122(11/12), 774-794. https://doi.org/10.1108/ILS-08-2020-0176
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30. https://doi.org/10.1086/428763
Hofer, B. K. (2004). Epistemological understanding as a metacognitive process: Thinking aloud during online searching. Educational Psychologist, 39(1), 43-55. https://doi.org/10.1207/s15326985ep3901_5
Hofer, B. K., & Pintrich, P. R. (1997). The development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning. Review of Educational Research, 67(1), 88-140. https://doi.org/10.3102/00346543067001088
Holmes, V. L., & Hwang, Y. (2016). Exploring the effects of project-based learning in secondary mathematics education. The Journal of Educational Research, 109(5), 449-463. https://doi.org/10.1080/00220671.2014.979911
Hoy, A. W., Davis, H., & Pape, S. J. (2006). Teacher knowledge and beliefs. In P. A. Alexander, & P. H. Winne (Eds.), Handbook of educational psychology (pp. 715-737). Lawrence Erlbaum Associates Publishers.
Hsieh, F. J. (2013). Strengthening the conceptualization of mathematics pedagogical content knowledge for international studies: A Taiwanese perspective. International Journal of Science and Mathematics Education, 11, 923-947. https://doi.org/10.1007/s10763-013-9425-9
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, 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, 369-387. https://doi.org/10.1007/s10763-015-9616-7
Kim, S., Jang, Y., Choi, S., Kim, W., Jung, H., Kim, S., & Kim, H. (2021). Analyzing teacher competency with TPACK for K-12 AI education. KI-Künstliche Intelligenz, 35(2), 139-151. https://doi.org/10.1007/s13218-021-00731-9
Klieme, E., Hartig, J., & Rauch, D. (2008). The concept of competence in educational contexts. In J. Hartig, E. Klieme, & D. Leutner (Eds.), Assessment of competencies in educational contexts (pp. 3-22). Hogrefe & Huber.
Kokotsaki, D., Menzies, V., & Wiggins, A. (2016). Project-based learning: A review of the literature. Improving Schools, 19(3), 267-277. https://doi.org/10.1177/1365480216659733
König, J., Blömeke, S., & Kaiser, G. (2015). Early career mathematics teachers’ general pedagogical knowledge and skills: Do teacher education, teaching experience, and working conditions make a difference? International Journal of Science and Mathematics Education, 13(2), 331-350. https://doi.org/10.1007/s10763-015-9618-5
König, J., Blömeke, S., Klein, P., Suhl, U., Busse, A., & Kaiser, G. (2014). Is teachers’ general pedagogical knowledge a premise for noticing and interpreting classroom situations? A video-based assessment approach. Teaching and Teacher Education, 38, 76-88. https://doi.org/10.1016/j.tate.2013.11.004
König, J., Blömeke, S., Paine, L., Schmidt, W. H., & Hsieh, F. J. (2011). General pedagogical knowledge of future middle school teachers: On the complex ecology of teacher education in the United States, Germany, and Taiwan. Journal of Teacher Education, 62(2), 188-201. https://doi.org/10.1177/0022487110388664
Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716-725. https://doi.org/10.1037/0022-0663.100.3.716
Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., & Neubrand, M. (2013). Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV project. Springer. https://doi.org/10.1007/978-1-4614-5149-5
Le Deist, F. D., & Winterton, J. (2005). What is competence? Human Resource Development International, 8(1), 27-46. https://doi.org/10.1080/1367886042000338227
Li, R., Cevikbas, M., & Kaiser, G. (2024). Mathematics teachers’ beliefs about their roles in teaching mathematics: Orchestrating scaffolding in cooperative learning. Educational Studies in Mathematics, 117(3), 357-377. https://doi.org/10.1007/s10649-024-10359-9
Liljedahl, P., Rösken, B., & Rolka, K. (2021). Changes to preservice elementary teachers’ beliefs about mathematics and the teaching and learning of mathematics: How and why? Journal of Adult Learning, Knowledge and Innovation, 4(1), 20-30. https://doi.org/10.1556/2059.03.2019.09
Lo, W. Y. (2020). Unpacking mathematics pedagogical content knowledge for elementary number theory: The case of arithmetic word problems. Mathematics, 8(10), Article 1750. https://doi.org/10.3390/math8101750
Löfström, E., & Pursiainen, T. (2015). Knowledge and knowing in mathematics and pedagogy: A case study of mathematics student teachers’ epistemological beliefs. Teachers and Teaching, 21(5), 527-542. https://doi.org/10.1080/13540602.2014.995476
Markham, T., Larmer, J., & Ravitz, J (2003). Project based learning handbook: A guide to standards-focused project based learning for middle and high school teachers (2nd ed.). Buck Institute for Education.
Meyer, D. K., Turner, J. C., & Spencer, C. A. (1997). Challenge in a mathematics classroom: Students’ motivation and strategies in project-based learning. The Elementary School Journal, 97(5), 501-521. https://doi.org/10.1086/461878
Ministry of Education. (2022, April 8). Mathematics Curriculum Standards for Compulsory Education. Retrieved August 20, 2024, from http://www.moe.gov.cn/srcsite/A26/s8001/202204/t20220420_619921.html
Neubrand, M. (2018). Conceptualizations of professional knowledge for teachers of mathematics. ZDM Mathematics Education, 50, 601-612. https://doi.org/10.1007/s11858-017-0906-0
Pagiling, S. L., Palobo, M., & Mayasari, D. (2021). Preservice teacher belief on nature of mathematics and mathematics teaching and learning: A quantitative study. Journal of Physics: Conference Series, 1806, Article 012111. https://doi.org/10.1088/1742-6596/1806/1/012111
Ravitz, J. (2010). Beyond changing culture in small high schools: Reform models and changing instruction with project-based learning. Peabody Journal of Education, 85(3), 290-312. https://doi.org/10.1080/0161956X.2010.491432
Rehman, N., Huang, X., Mahmood, A., AlGerafi, M. A., Javed, S. (2024). Project-based learning as a catalyst for 21st-century skills and student engagement in the math classroom. Heliyon, 10(23), Article e39988. https://doi.org/10.1016/j.heliyon.2024.e39988
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), Handbook of research on teacher education (2nd ed., pp. 102-119). Macmillan.
Russo, J., Bobis, J., Downton, A., Hughes, S., Livy, S., McCormick, M., & Sullivan, P. (2020). Elementary teachers’ beliefs on the role of struggle in the mathematics classroom. The Journal of Mathematical Behavior, 58, Article 100774. https://doi.org/10.1016/j.jmathb.2020.100774
Saadati, F., Cerda, G., Giaconi, V., Reyes, C., & Felmer, P. (2019). Modeling Chilean mathematics teachers’ instructional beliefs on problem solving practices. International Journal of Science and Mathematics Education, 17, 1009-1029. https://doi.org/10.1007/s10763-018-9897-8
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11, 107-125. https://doi.org/10.1007/s10857-007-9063-7
Suh, J. M., Matson, K., & Seshaiyer, P. (2018). Mathematical modeling competencies essential for elementary teachers: The case of teachers in transition. In T. E. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), Proceedings of the 40^th Annual Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education (pp. 1122-1125). University of South Carolina and Clemson University.
Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Rowley, G., Peck, R., Bankov, K., Rodriguez, M., & Reckase, M. (2012). Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries. Findings from the IEA teacher education and development study in mathematics (TEDS-M). IEA.
Thomas, J. W. (2000). A review of research on project-based learning. Autodesk.
Thompson, A. (1992). Teacher’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 127-146). IAP.
Tschannen-Moran, M., & Hoy, A. W. (2001). Teacher efficacy: Capturing an elusive construct. Teaching and Teacher Education, 17(7), 783-805. https://doi.org/10.1016/S0742-051X(01)00036-1
Tschannen-Moran, M., Hoy, A. W., & Hoy, W. K. (1998). Teacher efficacy: Its meaning and measure. Review of Educational Research, 68(2), 202-248. https://doi.org/10.3102/00346543068002202
Voss, T., Kleickmann, T., Kunter, M., & Hachfeld, A. (2013). Mathematics teachers’ beliefs. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV project (pp. 249-271). Springer. https://doi.org/10.1007/978-1-4614-5149-5_12
Wan, H., & Gao, X. Y. (2023). Project-based learning teachers: Role cognitions and competence elements. Teacher Education Research, 35(2), 63-68. https://doi.org/10.13445/j.cnki.t.e.r.2023.02.001
Weinert, F. E. (2001). Concept of competence: A conceptual clarification. In D. S. Rychen, & L. H. Salganik (Eds.), Defining and selecting key competencies (pp. 45-65). Hogrefe & Huber Publishers.
Wess, R., Klock, H., Siller, H. S., & Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modeling: A test instrument. In G. Kaiser, G. A. Stillman, M. S. Biembengut, W. Blum, H. Doerr, P. Galbraith, T. Ikeda, M. Niss, & J. Xie (Eds.), International perspectives on the teaching and learning of mathematical modeling (pp. 249-260). Springer. https://doi.org/10.1007/978-3-030-78071-5_3
Weyers, J., König, J., Rott, B., Greefrath, G., Vorhölter, K., & Kaiser, G. (2023). Mathematics teachers’ professional noticing: Transfer of a video-based competence assessment instrument into teacher education for evaluation purposes. Zeitschrift für Erziehungswissenschaft, 26(3), 627-652. https://doi.org/10.1007/s11618-023-01159-7
Xenofontos, C. (2018). Greek-Cypriot elementary teachers’ epistemological beliefs about mathematics. Teaching and Teacher Education, 70, 47-57. https://doi.org/10.1016/j.tate.2017.11.007
Yang, X., & Kaiser, G. (2022). The impact of mathematics teachers’ professional competence on instructional quality and students’ mathematics learning outcomes. Current Opinion in Behavioral Sciences, 48, Article 101225. https://doi.org/10.1016/j.cobeha.2022.101225
Yang, X., Kaiser, G., König, J., & Blömeke, S. (2018). Measuring Chinese teacher professional competence: Adapting and validating a German framework in China. Journal of Curriculum Studies, 50(5), 638-653. https://doi.org/10.1080/00220272.2018.1502810
Yang, X., Schwarz, B., & Leung, I. K. (2022). Pre-service mathematics teachers’ professional modeling competencies: A comparative study between Germany, Mainland China, and Hong Kong. Educational Studies in Mathematics, 109(2), 409-429. https://doi.org/10.1007/s10649-021-10064-x
Ye, B. X., Sang, G. Y., & Wang, X. Y. (2021). Teacher competence in project-based learning: Framework construction based on mixed surveys. Journal of Shanghai Educational Research, 10, 23-29. https://doi.org/10.16194/j.cnki.31-1059/g4.2021.10.006
Yunita, Y., Juandi, D., Kusumah, Y. S., & Suhendra, S. (2021). The effectiveness of the project-based learning (PjBL) model in students’ mathematical ability: A systematic literature review. Journal of Physics: Conference Series, 1882(1), Article 012080. http://doi.org/10.1088/1742-6596/1882/1/012080
Zeeb, H., Ibach, A., Voss, T., & Renkl, A. (2023). How does teachers’ noticing of students’ fixed mindsets relate to teachers’ knowledge, beliefs, and experience? An exploratory study. Teaching and Teacher Education, 130, 104170. https://doi.org/10.1016/j.tate.2023.104170
Zhang, W. L., & Yang, X. Q. (2021). The structure and connotation of teacher competence for project-based teaching based on the national curriculum. Educational Information Technology, Z2, 3-7.
Zhou, Z., Peverly, S. T., & Xin, T. (2006). Knowing and teaching fractions: A cross-cultural study of American and Chinese mathematics teachers. Contemporary Educational Psychology, 31(4), 438-457. https://doi.org/10.1016/j.cedpsych.2006.02.001

How to cite this article

APA

Li, S., Qi, C., & Li, R. (2025). The conceptualization of mathematics teachers’ professional competence in project-based learning contexts. Eurasia Journal of Mathematics, Science and Technology Education, 21(7), em2660. https://doi.org/10.29333/ejmste/16562

Vancouver

Li S, Qi C, Li R. The conceptualization of mathematics teachers’ professional competence in project-based learning contexts. EURASIA J Math Sci Tech Ed. 2025;21(7):em2660. https://doi.org/10.29333/ejmste/16562

AMA

Li S, Qi C, Li R. The conceptualization of mathematics teachers’ professional competence in project-based learning contexts. EURASIA J Math Sci Tech Ed. 2025;21(7), em2660. https://doi.org/10.29333/ejmste/16562

Chicago

Li, Sha, Chunxia Qi, and Ruisi Li. "The conceptualization of mathematics teachers’ professional competence in project-based learning contexts". Eurasia Journal of Mathematics, Science and Technology Education 2025 21 no. 7 (2025): em2660. https://doi.org/10.29333/ejmste/16562

Harvard

Li, S., Qi, C., and Li, R. (2025). The conceptualization of mathematics teachers’ professional competence in project-based learning contexts. Eurasia Journal of Mathematics, Science and Technology Education, 21(7), em2660. https://doi.org/10.29333/ejmste/16562

MLA

Li, Sha et al. "The conceptualization of mathematics teachers’ professional competence in project-based learning contexts". Eurasia Journal of Mathematics, Science and Technology Education, vol. 21, no. 7, 2025, em2660. https://doi.org/10.29333/ejmste/16562