Mathematics teachers’ learning: a conceptual framework and synthesis of research

Abstract

How do practicing mathematics teachers continue to develop the knowledge and habits of mind that enable them to teach well and to improve their teaching over time? The question of how (and what) teachers learn lies at the crux of any effort to provide high-quality mathematics teaching for all students. This article reviews 106 articles written between 1985 and 2008 related to the professional learning of practicing teachers of mathematics. We offer a synthesis of this research, guided by Clarke and Hollingsworth’s (Teach Teach Educ 18(8):947–967, 2002) dynamic model of teacher growth. Their model emphasizes the recursive nature of teachers’ learning and suggests that growth in one aspect of teachers’ knowledge and practice may promote subsequent growth in other areas. We report the results in six major areas of teacher learning, identify several crosscutting themes in the literature, and make recommendations for future research aimed at understanding teachers’ professional learning.

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Fig. 1
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Notes

  1. 1.

    Findings related to teachers’ use of student outcome information were coded elsewhere. For example, we coded student outcomes results as Teachers’ Practice if the results indicated that student outcomes altered teachers’ practice. The “Student Outcome” category includes results that could not be coded in the other categories, for example, student outcome data presented as evidence of program effectiveness.

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Acknowledgments

This paper is based upon work supported by the National Science Foundation under grants DRL-0723340, DRL-0719627, and DRL-0722295. Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors thank four anonymous reviewers for their suggestions for strengthening this paper.

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Correspondence to Lynn T. Goldsmith.

Appendix: Articles included in the synthesis database

Appendix: Articles included in the synthesis database

Allinder, R. M., Bolling, R. M., Oats, R. G., & Gagnon, W. A. (2000). Effects of teacher self-monitoring on implementation of curriculum-based measurement and mathematics computation achievement of students with disabilities. Remedial and Special Education, 21(4), 219–226.

Anderson, C. R., & Hoffmeister, A. M. (2007). Knowing and teaching middle school mathematics: A professional development course for in-service teachers. School Science and Mathematics, 107(5), 193–203.

Arbaugh, F. (2003). Study groups as a form of professional development for secondary mathematics teachers. Journal of Mathematics Teacher Education, 6(2), 139–163.

Balfanz, R., Mac Iver, D. J., & Byrnes, V. (2006). The implementation and impact of evidence-based mathematics reforms in high-poverty middle schools: A multi-site, multi-year study. Journal for Research in Mathematics Education, 37(1), 33–64.

Barrett, J., Jones, G., Mooney, E., Thornton, C., Cady, J., Guinee, P., & Olson, J. (2002). Working with novice teachers: Challenges for professional development. Mathematics Teacher Education and Development, 4, 15–27.

Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412–446.

Borko, H., Davinroy, K. H., Bliem, C. L., & Cumbo, K. B. (2000). Exploring and supporting teacher change: Two third-grade teachers’ experiences in a mathematics and literacy staff development project. Elementary School Journal, 100(4), 273–306.

Borko, H., Jacobs, J., Eiteljorg, E., & Pittman, M.E. (2008). Video as a tool for fostering productive discussions in mathematics professional development. Teaching and Teacher Education, 24, 417–436.

Borko, H., Mayfield, V., Marion, S., Flexer, R., & Cumbo, K. (1997). Teachers’ developing ideas and practices about mathematics performance assessment: Successes, stumbling blocks, and implications for professional development. Teaching and Teacher Education, 13(3), 259–278.

Boyle, B., Lamprianou, I., & Boyle, T. (2005). A longitudinal study of teacher change: What makes professional development effective? Report of the second year of the study. School Effectiveness And School Improvement, 16(1), 1–27.

Bright, G. W., & Prokosch, N. E. (1995). Middle school mathematics teachers learning to teach with calculators and computers, part II: Teacher change. School Science and Mathematics, 95, 338–344.

Britt, M. S., Irwin, K. C., & Ritchie, G. (2001). Professional conversations and professional growth. Journal of Mathematics Teacher Education, 4(1), 29–53.

Brown, C. A., Stein, M. K., & Forman, E. A. (1996). Assisting teachers and students to reform the mathematics classroom. Educational Studies in Mathematics, 31(1–2), 63–93.

Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499–532.

Chaney-Cullen, T., & Duffy, T. M. (1999). Strategic teaching framework: Multimedia to support teacher change. Journal of The Learning Sciences, 8(1), 1–40.

Chapin, S. (1994). Implementing reform in school mathematics. Journal of Education, 176(1), 67–76.

Chapman, O. (1999). Inservice teacher development in mathematical problem solving. Journal of Mathematics Teacher Education, 2, 121–142.

Chazan, D., Ben-Chaim, D., & Gormas, J. (1998). Shared teaching assignments in the service of mathematics reform: Situated professional development. Teaching and Teacher Education, 14(7), 687–702.

Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18(8), 947–967.

Cohen, D. K., & Hill, H. C. (2000). Instructional policy and classroom performance: The mathematics reform in California. Teachers College Record, 102(2), 294–343.

Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers’ learning. The Elementary School Journal, 103(3), 287–311.

Confrey, J., Castro, J., & Wilhelm, J. (2000). Implementation research as a means to link systemic reform and applied psychology in mathematics education. Educational Psychologist, 35(3), 179–191.

Crockett, M. D. (2002). Inquiry as professional development: Creating dilemmas through teachers’ work. Teaching and Teacher Education, 18(5), 609–624.

Cwikla, J. (2007). The trials of a poor middle school trying to catch up in mathematics teachers’ multiple communities of practice and the boundary encounters. Education and Urban Society, 39(4), 554–583.

Dalgarno, N., & Colgan, L. (2007). Supporting novice elementary mathematics teachers’ induction in professional communities and providing innovative forms of pedagogical content knowledge development through information and communication technology. Teaching and Teacher Education, 23(7), 1051–1065.

Desimone, L. M., Porter, A. C., Garet, M. S., Yoon, K. S., & Birman, B. F. (2002). Effects of professional development on teachers’ instruction: Results from a three-year longitudinal study. Educational Evaluation and Policy Analysis, 24(2), 81–112.

Desimone, L. M., Smith, T. M., & Phillips, K. J. R. (2007). Does policy influence mathematics and science teachers’ participation in professional development? Teachers College Record, 109(5), 1086–1122.

Doerr, H. M., & English, L. D. (2006). Middle grade teachers’ learning through students’ engagement with modeling tasks. Journal of Mathematics Teacher Education, 9(1), 5–32.

Drake, C., Spillane, J., & Hufferd-Ackles, K. (2001). Storied identities: Teacher learning and subject-matter context. Journal of Curriculum Studies, 33(1), 1–23.

Edwards, T. G. (1996). Implications of a model for conceptualizing change in mathematics teachers’ instructional practices. Action in Teacher Education, 18(2), 19–30.

Edwards, T. G., & Hensien, S. M. (1999). Changing instructional practice through action research. Journal of Mathematics Teacher Education, 2(2), 187–206.

Etchberger, M. L., & Shaw, K. L. (1992). Teacher change as a progression of transitional images: A chronology of a developing constructivist teacher. School Science and Mathematics, 92(8), 411–417.

Fernandez, C. (2005). Lesson study: A means for elementary teachers to develop the knowledge of mathematics needed for reform-minded teaching? Mathematical Thinking and Learning, 7(4), 265–289.

Fisler, J., L., & Firestone, W. A. (2006). Teacher learning in a school-university partnership: Exploring the role of social trust and teaching efficacy beliefs. Teachers College Record, 108(6), 1155–1185.

Franke, M., Carpenter, T., Fennema, E., Ansell, E., & Behrend, J. (1998). Understanding teachers’ self-sustaining, generative change in the context of professional development. Teaching and Teacher Education, 14(1), 67–80.

Gabriele, A. J., & Joram, E. (2007). Teachers’ reflections on their reform-based teaching in mathematics: Implications for the development of teacher self-efficacy. Action in Teacher Education, 29(3), 60–74.

Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38(4), 915–945.

Gearhart, M., & Saxe, G. B. (2004). When teachers know what students know: Integrating mathematics assessment. Theory into Practice, 43(4), 304–313.

Gearhart, M., Saxe, G. B., Seltzer, M., Schlackman, J., Ching, C., Nasir, N., Fall, R., Bennett, T., Rhine, S., & Sloan, T. (1999). Opportunities to learn fractions in elementary mathematics classrooms. Journal for Research in Mathematics Education, 30(3), 286–315.

Gersten, R., & Kelly, B. (1992). Coaching secondary special education teachers in implementation of an innovative videodisc mathematics curriculum. Remedial and Special Education, 13(4), 40–51.

Glazer, E. (2004). From a caterpillar to a butterfly: The growth of a teacher in developing technology-enhanced mathematical investigations. Journal of Technology and Teacher Education, 12(1), 115–138.

Goos, M. (2005). A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology. Journal of Mathematics Teacher Education, 8(1), 35–59.

Grandau, L. (2005). Learning from self-study: Gaining knowledge about how fourth graders move from relational description to algebraic generalization. Harvard Educational Review, 75(2), 202–221.

Grant, S. G., Peterson, P. L., & Shojgreen-Downer, A. (1996). Learning to teach mathematics in the context of systemic reform. American Educational Research Journal, 33(2), 509–541.

Graven, M. (2004). Investigating mathematics teacher learning within an in-service community of practice: The centrality of confidence. Educational Studies in Mathematics, 57(2), 177–211.

Groth, R. E. (2007). Case studies of mathematics teachers’ learning in an online study group. Contemporary Issues in Technology and Teacher Education, 7(1), 490–520.

Halai, A. (1998). Mentor, mentee, and mathematics: A story of professional development. Journal of Mathematics Teacher Education, 1(3), 295–315.

Heck, D. J., Banilower, E. R., Weiss, I. R., & Rosenberg, S. L. (2008). Studying the effects of professional development: The case of the NSF’s local systemic change through teacher enhancement initiative. Journal for Research in Mathematics Education, 39(2), 113–152.

Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330–351.

Hodgen, J., & Askew, M. (2007). Emotion, identity and teacher learning: becoming a primary mathematics teacher. Oxford Review Of Education, 33(4), 469–487.

Horn, I. S. (2005). Learning on the job: A situated account of teacher learning in high school mathematics departments. Cognition and Instruction, 23(2), 207–236.

Izsak, A., & Sherin, M. G. (2003). Exploring the use of new representations as a resource for teacher learning. School Science and Mathematics, 103(1), 18–27.

Jaberg, P., Lubinski, C., & Yazujian, T. (2002). One teacher’s journey to change her mathematics teaching. Mathematics Teacher Education and Development, 4, 3–14.

Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258–288.

Jacobson, C., & Lehrer, R. (2000). Teacher appropriation and student learning of geometry through design. Journal for Research in Mathematics Education, 31(1), 71–88.

Jaworski, B. (1998). Mathematics teacher research: Process, practice and the development of teaching. Journal of Mathematics Teacher Education, 1(1), 3–31.

Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7(3), 203–235.

Kersaint, G., & Chappell, M. F. (2001). Helping teachers promote problem solving with young at-risk children. Early Childhood Education Journal, 29(1), 57–63.

Kimmel, H., Deek, F. P., Farrell, M. L., & O’Shea, M. (1999). Meeting the needs of diverse student populations: Comprehensive professional development in science, math, and technology for teachers of students with disabilities. School Science and Mathematics, 99(5), 241–249.

Kwon, N., & Orrill, C. H. (2007). Understanding a teacher’s reflections: A case study of a middle school mathematics teacher. School Science and Mathematics, 107(6), 246–257.

Lachance, A., & Confrey, J. (2003). Interconnecting content and community: A qualitative study of secondary mathematics teachers. Journal of Mathematics Teacher Education, 6(2), 107–137.

Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks . Educational Studies in Mathematics, 66(3), 349–371.

Lesh, R., & Kelly, A. E. (1997). Teacher’s evolving conceptions of one-to-one tutoring: A three-tiered teaching experiment. Journal for Research in Mathematics Education, 28(4), 398–430.

Lin, P. (2002). On enhancing teachers’ knowledge by constructing cases in classrooms. Journal of Mathematics Teacher Education, 5(4), 317–349.

Lin, X. (2001). Reflective adaptation of a technology artifact: A case study of classroom change. Cognition and Instruction, 19(4), 395–440.

Little, J. W. (2003). Inside teacher community: Representations of classroom practice. Teachers College Record, 105(6), 913–945.

Manouchehri, A. (2001). Collegial interaction and reflective practice. Action in Teacher Education, 22(4), 86–97.

Margolinas, C., Coulange, L., & Bessot, A. (2005). What can the teacher learn in the classroom? Educational Studies in Mathematics, 59(1–3), 205–234.

Miller, L. D. (1991). Constructing pedagogical content knowledge from students’ writing in secondary school. Mathematics Education Research Journal, 3(1), 30–44.

Nathan, M. J., & Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21(2), 175–207.

Peng, A. (2007). Knowledge growth of mathematics teachers during professional activity based on the task of lesson explaining. Journal of Mathematics Teacher Education, 10(4–6), 289–299.

Peressini, D. D., & Knuth, E. J. (1998). Why are you talking when you could be listening? The role of discourse and reflection in the professional development of a secondary mathematics teacher. Teaching and Teacher Education, 14(1), 107–125.

Peressini, D. D., Borko, H., Romagnano, L., Knuth, E. J., & Willis, C. (2004). A conceptual framework for learning to teach secondary mathematics: A situative perspective. Educational Studies in Mathematics, 56(1), 67–96.

Polettini, A. F. F. (2000). Mathematics teaching life histories in the study of teachers’ perceptions of change. Teaching and Teacher Education, 16(7), 765–783.

Puchner, L. D., & Taylor, A. R. (2006). Lesson study, collaboration and teacher efficacy: Stories from two school-based math lesson study groups. Teaching and Teacher Education, 22(7), 922–934.

Remillard, J. T. (2000). Can curriculum materials support teachers’ learning? Two fourth-grade teachers’ use of a new mathematics text. Elementary School Journal, 100(4), 331–350.

Remillard, J., & Bryans, M. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35(5), 352–388.

Ross, J. A., & Bruce, C. D. (2007a). Teacher self-assessment: A mechanism for facilitating professional growth. Teaching and Teacher Education, 23(2), 146–159.

Ross, J. A., & Bruce, C. D. (2007b). Professional development effects on teacher efficacy. Results of randomized field trial. Journal of Educational Research, 101(1), 50–60.

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Schorr, R. Y., & Koellner-Clark, K. (2003). Using a modeling approach to analyze the ways in which teachers consider new ways to teach mathematics. Mathematical Thinking and Learning, 5(2–3), 191–210.

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Goldsmith, L.T., Doerr, H.M. & Lewis, C.C. Mathematics teachers’ learning: a conceptual framework and synthesis of research. J Math Teacher Educ 17, 5–36 (2014). https://doi.org/10.1007/s10857-013-9245-4

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Keywords

  • Professional development
  • Mathematics
  • Teacher learning
  • In-service teachers