Skip to main content
Log in

Mathematics instructor actions and knowledge integration: utilizing resources in mathematics courses for teachers

  • Original Paper
  • Published:
ZDM – Mathematics Education Aims and scope Submit manuscript

Abstract

Future mathematics teachers must integrate their knowledge of mathematics, pedagogy, and learners to effectively teach mathematics. Historically, these different forms of knowledge were taught separately in teacher preparation and left to the preservice teacher to integrate on their own. This raises the question; what resources can be leveraged to promote knowledge integration in mathematics courses for teachers? In this study, we identified six instructional actions that were associated with potential knowledge integration when implemented within the environment of a mathematics course for preservice teachers. We posit these instructional actions can be implemented in concise and minimally invasive ways in a variety of mathematics content courses. Further unpacking of these instructional actions and considerations for implementation are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Anderson, R. C., Reynolds, R. E., Schallert, D. L., & Goetz, E. T. (1977). Frameworks for comprehending discourse. American Education Research Journal 14(4). 367–381.

  • Arbaugh, F., Graysay, D., Konuk, N., & Freeburn, B. (2019). The three-minute-rehearsal cycle of enactment and investigation: Preservice secondary mathematics teachers learning to elicit and use evidence of student thinking. Mathematics Teacher Educator, 8(1), 22–48.

    Article  Google Scholar 

  • Ball, D. L. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3), 241–247.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Barker, D. D., Lannin, J. K., Winsor, M. S., & Kirwan, J. V. (2019). Integrating knowledge for instruction: A tale of two teachers. The Mathematics Enthusiast, 16(1), 331–358.

    Article  Google Scholar 

  • Barker, D. D., Winsor, M. S., Kirwan, J. V., & Rupnow, T. J. (2020). Searching for the key to knowledge integration. In T. Lehmann (Ed.), International Perspectives on Knowledge Integration: Theory, research, and good practice in pre-service teacher and higher education (pp. 59–78). Brill Sense.

  • Bartlett, F. C. (1932). Remembering: A study in experimental and social psychology. Cambridge University Press.

  • Battista, M. T. (1999). Fifth graders enumeration of cubes in 3D arrays: Conceptual progress in an inquiry-based classroom. Journal for Research in Mathematics Education, 30, 417–448.

    Article  Google Scholar 

  • Blömeke, S., Gustafsson, J. E., & Shavelson, R. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift für Psychologie, 223, 3–13. https://doi.org/10.1027/2151-2604/a000194

    Article  Google Scholar 

  • Chamberlin, M. (2009). Teacher’s reflections on their mathematical learning experiences in a professional development course. Mathematics Teacher Education and Development, 11, 22–35.

    Google Scholar 

  • Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. American Education Research Journal 25(2). 119–142.

  • Conference Board of the Mathematical Sciences [CBMS] (2001). The mathematical education of teachers Providence, RI and Washington, DC: American Mathematical Society and Mathematical Association of America.

  • Conference Board of the Mathematical Sciences [CBMS] (2012). The Mathematical Education of Teachers II. Providence, RI: American Mathematical Society.

  • Feldman, A. (2003). Validity and quality in self-study. Educational Research, 32, 26–28.

    Article  Google Scholar 

  • Frykohlm, J. A. (1999). The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education, 2, 79–105.

    Article  Google Scholar 

  • Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. New Brunswick, NJ: Aldine Transaction.

    Google Scholar 

  • Glesne, C. (2011). Becoming qualitative researchers. Boston, MA: Pearson.

    Google Scholar 

  • Gottein, H. P. (2020). Closing the gap: An innovative learning environment for enabling pre-service teachers to put theoretical knowledge into action. In T. Lehmann (Ed.), International perspectives on knowledge integration: Theory, research, and good practice in preservice teacher and higher education (pp. 231–254). Brill Sense.

  • Graziano, M. S. A. (2022). A conceptual framework for consciousness. Pnas, 19(18), e2116933119. https://doi.org/10.1073/pnas.2116933119

    Article  Google Scholar 

  • Harr, N., Eichler, A., & Renkyl, A. (2014). Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics. Frontiers in Psychology, Article 924, https://doi.org/10.3389/fpsyg.2014.00924. 5.

  • Harr, N., Eichler, A., & Renkyl, A. (2015). Integrated learning: Ways of fostering the applicability of teachers’ pedagogical and psychological knowledge. Frontiers in Psychology, Article 738, https://doi.org/10.3389/fpsyg.2015.00738. 6.

  • Herman, W. E. (1998). Promoting pedagogical reasoning as preservice teachers analyze case vignettes. Journal of Teacher Education, 49(5), 391–397.

    Article  Google Scholar 

  • Hiebert, J., Gallimore, R., & Stigler, J. W. (2002). A knowledge base for the teaching profession: What would it look like and how can we get one? Educational Researcher, 31(5), 3–15.

    Article  Google Scholar 

  • Janssen, N., & Lazonder, A. W. (2016). Supporting pre-service teachers in designing technology-infused lesson plans. Journal of Computer Assisted Learning, 32(5), 456–467.

    Article  Google Scholar 

  • Klein, F. (2016). Elementary mathematics from a higher standpoint: Arithmetic, algebra, analysis. Trans.). Springer. (Original work published 1924)G. Schubring.

  • Kontorovich, I., & Ovadiya, T. (2023). How narratives about the secondary-tertiary transition shape undergraduate tutors’ sense-making of their teaching. Educational Studies in Mathematics, 113, 125–146.

    Article  Google Scholar 

  • Lee, J., & Turner, J. E. (2017). Extensive knowledge integration strategies in pre-service teachers: The role of perceived instrumentality, motivation, and self-regulation. Educational Studies, 44(5), 505–520.

    Article  Google Scholar 

  • Lehmann, T. (2020). What is knowledge integration of multiple domains and how does it relate to teachers’ professional competence? In T. Lehmann (Ed.), International Perspectives on Knowledge Integration: Theory, research, and good practice in pre-service teacher and higher education (pp. 9–29). Brill Sense.

  • Lehmann, T., Rott, B., & Schmidt-Borcherding, F. (2019). Promoting pre–service teachers’ integration of professional knowledge: Effects of writing tasks and prompts on learning from multiple documents. Instructional Science, 47, 99–126. https://doi.org/10.1007/s11251-018-9472-2

    Article  Google Scholar 

  • Lehmann, T., Pirnay-Dummer, P., & Schmidt-Borcherding, F. (2020). Fostering integrated mental models of different professional knowledge domains: Instructional approaches and model-based analyses. Education Tech Research Development, 68, 905–927. https://doi.org/10.1007/s11423-019-09704-0

    Article  Google Scholar 

  • Levasseur, K., & Cuoco, A. (2003). Mathematical habits of mind. In H. Schoen, & R. Charles (Eds.), Teaching mathematics through problem solving: Grades 6–12 (pp. 27–38). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Lindmeier, A. (2011). Modeling and measuring knowledge and competences of teachers. Münster: Waxmann.

    Google Scholar 

  • Lindmeier, A., Seemann, S., Kuratli-Geeler, S., Wullschleger, A., Dunekacke, S., Leuchter, M., Vogt, F., Moser Opitz, E., & Heinze, A. (2020). Modeling early childhood teachers’ mathematics-specific professional competence and its differential growth through professional development—an aspect of structural validity. Research in Mathematics Education, 22(2), 168–187.

    Article  Google Scholar 

  • Lortie, D. C. (1975). Schoolteacher: A sociological study. University of Chicago Press.

  • Loughran, J. (2007). Researching teacher education practices: Responding to the challenges, demands and expectations of self-study. Journal of Teacher Education, 58, 12–20.

    Article  Google Scholar 

  • Marshall, S. P. (1995). Schemas in problem solving. New York, NY: Cambridge University Press.

    Book  Google Scholar 

  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook. Thousand Oaks, CA: Sage Publications.

    Google Scholar 

  • Nickerson, C. (2021). December 6). The role of a Schema in psychology. Simply Psychology. https://www.simplypsychology.org/what-is-a-schema.html

  • Rumelhart, D. E., & Norman, D. A. (1976). Accretion, tuning, and restructuring: Three modes of learning Report No. 7602. (ED134902) ERIC. https://files.eric.ed.gov/fulltext/ED134902.pdf

  • Schön, D. A. (1983). The reflective practitioner: How professionals think in action. New York, NY: Basic Books.

    Google Scholar 

  • Sherman, U. P., & Morley, M. J. (2015). On the formation of the psychological contract: A schema theory perspective. Group & Organization Management, 40(2), 160–192.

    Article  Google Scholar 

  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.

    Article  Google Scholar 

  • Steele, M., & Hillen, A. (2012). The content-focused methods course: A model for integrating pedagogy and mathematics content. Mathematics Teacher Educator, 1, 53–70.

    Article  Google Scholar 

  • van Leeuwen, A., & Janssen, J. (2019). A systematic review of teacher guidance during collaborative learning in primary and secondary education. Educational Research Review, 27, 71–98.

    Article  Google Scholar 

  • Vanassche, E., & Keltchermans, G. (2016). Facilitating self-study of teacher education practices: Toward a pedagogy of teacher educator professional development. Professional Development in Education, 42, 100–122.

    Article  Google Scholar 

  • Voss, T., Kunter, M., & Baumert, J. (2011). Assessing teacher candidates’ general pedagogical/psychological knowledge: Test construction and validation. Journal of Educational Psychology, 103(4), 952–969. https://doi.org/10.1037/a0025125

    Article  Google Scholar 

  • Wäschle, K., Lehmann, T., Brauch, N., & Nückles, M. (2015). Prompted journal writing supports preservice history teachers in drawing on multiple knowledge domains for designing learning tasks. Peabody Journal of Education, 90(4), 546–559.

    Article  Google Scholar 

  • Widmayer, S. A. (2001). Schema theory: An introduction. Retrieved December 16, 2022. https://docplayer.net/21424460-Schema-theory-an-introduction-sharon-alayne-widmayer-george-mason-university.html

  • Winsor, M., Kirwan, J. V., & Ssebaggala, L. (2018). What do we know about secondary mathematics teacher preparation in the United States? The Mathematics Educator, 27(2), 73–106.

    Google Scholar 

  • Winsor, M. S., Barker, D. D., & Kirwan, J. V. (2020). Promoting knowledge integration in teacher education programs. In T. Lehmann (Ed.), International Perspectives on Knowledge Integration: Theory, research, and good practice in pre-service teacher and higher education (pp. 349–369). Brill Sense.

  • Zazkis, R., & Kontorovich, I. (2016). A curious case of superscript (-1): Prospective secondary mathematics teachers explain. The Journal of Mathematical Behavior, 43, 98–110.

    Article  Google Scholar 

  • Zeichner, Z. (1996). Designing Educative Practicum Experiences for prospective teachers. In K. Zeichner, S. Melnick, & M. L. Gomez (Eds.), Currents of reform in preservice teacher education (pp. 215–234). New York, NY: Teachers College Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Vince Kirwan.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kirwan, J.V., Winsor, M.S. & Barker, D.D. Mathematics instructor actions and knowledge integration: utilizing resources in mathematics courses for teachers. ZDM Mathematics Education 55, 837–849 (2023). https://doi.org/10.1007/s11858-023-01502-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-023-01502-6

Keywords

Navigation