Educational Studies in Mathematics

, Volume 102, Issue 3, pp 319–342 | Cite as

Scaling up innovative learning in mathematics: exploring the effect of different professional development approaches on teacher knowledge, beliefs, and instructional practice

  • Daniel J. Heck
  • Courtney L. Plumley
  • Despina A. StylianouEmail author
  • Adrienne A. Smith
  • Gwendolyn Moffett


Professional learning experiences (PLEs) provide teachers with opportunities to improve their understanding of mathematics content and teaching practices. However, PLEs are often conducted in person and in small groups—hence costly and localized. The purpose of the current study was to explore different ways for teachers to engage in PLEs and how these approaches might enable the field to scale up these efforts in a sustainable manner. We compared the impact of three PLE formats on the early algebra knowledge and teaching practices of elementary mathematics teachers: (1) a facilitated summer workshop, (2) a multimedia course completed on teachers’ own time, and (3) learning resources provided in the algebra curriculum unit that teachers used individually. Our findings suggest that all three formats can be mapped against a set of principles for quality professional learning. Analysis of pre- and post-treatment measures indicate that participating teachers’ knowledge of algebra content and best practices significantly increased, regardless of the PLE format with which they engaged. Interviews with a subset of the teachers from the three groups point to the key features of each of the formats that can be capitalized on by designers of PLEs.


Large-scale implementation Professional development Elementary mathematics Algebraic reasoning Professional learning experiences 



This research was supported by the National Science Foundation under Grant No. 0822034. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We acknowledge the contributions of Catherine T. Fosnot who was the Principal Investigator of project DELTA (Digital Environments for the Learning and Teaching of Algebra) as well as Maarten Dolk, Kara Imm and Bill Jacob who facilitated workshops for teachers and wrote the units and workshop materials. We also acknowledge the work of former DELTA project staff and advisory board: Maria Blanton, Loren Pitt, Marty Simon, Eve Torrence, and Murray Wickwire.


  1. Arias, A., Smith, S., Davis, E., Marino, J., & Palincsar, A. (2017). Justifying predictions: Connecting use of educative curriculum materials to students’ engagement in science argumentation. Journal of Science Teacher Education, 28, 11–35.Google Scholar
  2. Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373–397.Google Scholar
  3. Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport, CT: Ablex.Google Scholar
  4. Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–31). San Fransisco, CA: Jossey-Bass.Google Scholar
  5. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.Google Scholar
  6. Banilower, E. R., Smith, P. S., Weiss, I. R., Malzahn, K. A., Campbell, K. M., & Weis, A. (2012). Report of the 2012 National Survey of Science and Mathematics Education. Chapel Hill, NC: Horizon Research, Inc.Google Scholar
  7. Beyer, C. J., Delgado, C., Davis, E. A., & Krajcik, J. (2009). Investigating teacher learning supports in high school biology curricular programs to inform the design of educative curriculum materials. Journal of Research in Science Teaching, 46, 977–998.Google Scholar
  8. Blanchard, M. R., LePrevost, C. E., Tolin, A. D., & Gutierrez, K. S. (2016). Investigating technology-enhanced teacher professional development in rural, high-poverty middle schools. Educational Researcher, 45, 207–220.Google Scholar
  9. Borko et al. (2010). Contemporary approaches to teacher professional development. In P. Peterson, E. Baker, & B. McGaw (Eds.), International encyclopedia of education (Vol. 7, pp. 548–556). Oxford, United Kingdom: Elsevier.Google Scholar
  10. Borko, H., Koellner, K., & Jacobs, J. (2014). Examining novice teacher leaders’ facilitation of mathematics professional development. The Journal of Mathematical Behavior, 33, 149–167.Google Scholar
  11. Cai, J., Morris, A., Hwang, S., Hohensee, C., Robinson, V., & Hiebert, J. (2017). Improving the impact of educational research. Journal for Research in Mathematics Education, 48, 2–6.Google Scholar
  12. Center for Research in Mathematics and Science Teacher Development. (2005). Information packet for diagnostic mathematics assessments for elementary school teachers. Louisville, KY: College of Education and Human Development, University of Louisville.Google Scholar
  13. Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  14. Cohen, D. K., & Hill, H. C. (2000). Instructional policy and classroom performance: The mathematics reform in California. Teachers College Record, 102, 294–343.Google Scholar
  15. Dajani, M. (2017). Introducing science stories in Palestinian elementary classrooms: Facilitating teacher learning. Journal of Science Teacher Education, 28, 73–91.Google Scholar
  16. Darling-Hammond, L., Wei, R., Andree, A., Richardson, N., & Orphanos, S. (2009). Professional learning in the learning profession: A status report on teacher development in the United States and abroad. National Staff Development Council.Google Scholar
  17. Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational Researcher, 34, 3–14.Google Scholar
  18. Dede, C., Ketelhut, D. J., Whitehouse, P., Breit, L., & McCloskey, E. M. (2009). A research agenda for online teacher professional development. Journal of Teacher Education, 60, 8–19.Google Scholar
  19. Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181–199.Google Scholar
  20. Donna, J. D., & Hick, S. R. (2017). Developing elementary preservice teacher subject matter knowledge through the use of educative science curriculum materials. Journal of Science Teacher Education, 28, 92–110.Google Scholar
  21. Elmore, R. F. (2002). Bridging the gap between standards and achievement: The imperative for professional development in education. Washington, DC: Albert Shanker Institute.Google Scholar
  22. Fennema, E., Carpenter, T., Franke, M., Levi, L., Jacobs, V., & Empson, S. (1996). Learning to use children’s thinking in mathematics instruction: A longitudinal study. Journal for Research in Mathematics Education, 27, 403–434.Google Scholar
  23. Fisher, J. B., Schumaker, J. B., Culbertson, J., & Deshler, D. D. (2010). Effects of a computerized professional development program on teacher and student outcomes. Journal of Teacher Education, 61, 302–312.Google Scholar
  24. Fishman, B., Konstantopoulos, S., Kubitskey, B. W., Vath, R., Park, G., Johnson, H., & Edelson, D. C. (2013). Comparing the impact of online and face-to-face professional development in the context of curriculum implementation. Journal of Teacher Education, 64, 426–438.Google Scholar
  25. Fosnot, C., & Lent, P. (2007). Trades, jumps, and stops: Early algebra. Portsmouth, NH: Heinemann.Google Scholar
  26. 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, 915–945.Google Scholar
  27. Guskey, T. R., & Sparks, D. (2002). Linking professional development to improvements in student learning. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.Google Scholar
  28. Guskey, T. R., & Yoon, K. S. (2009). What works in professional development? Phi Delta Kappan, 90, 495–500.Google Scholar
  29. Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105, 11–30.Google Scholar
  30. Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371–406.Google Scholar
  31. Hill, H. C., Beisiegel, M., & Jacob, R. (2013). Professional development research: Consensus, crossroads, and challenges. Educational Researcher, 42, 476–487.Google Scholar
  32. Imm, K., Fosnot, C., Dolk, M., Jacob, B., & Stylianou, D. A. (2012). Young mathematicians at work resource package: Early algebra. Portsmouth, NH: Heinemann.Google Scholar
  33. Jacob, B., & Fosnot, C. T. (2007). The California frog-jumping contest. Portsmouth, NH: Heinemann.Google Scholar
  34. Kennedy, M. M. (1999). Form and substance in mathematics and science professional development (NISE Brief Vol. 3, No. 2). Madison, WI: University of Wisconsin-Madison, National Institute for Science Education.Google Scholar
  35. Kennedy, M. M. (2016). How does professional development improve teaching? Review of Educational Research, 86, 945–980.Google Scholar
  36. Kennedy, M., Rodgers, W., Romig, J., Lloyd, J., & Brownell, M. (2017). Effects of a multimedia professional development package on inclusive science teachers’ vocabulary instruction. Journal of Teacher Education, 68, 213–230.Google Scholar
  37. Krajcik, J., & Delen, I. (2017). The benefits and limitations of educative curriculum materials. Journal of Science Teacher Education, 28, 1–10.Google Scholar
  38. Little, J. W. (1987). Teachers as colleagues. In V. Richardson-Koehler (Ed.), Educators’ handbook: A research perspective (pp. 491–518). New York: Longman.Google Scholar
  39. Loucks-Horsley, S., Love, N., Stiles, K., Mundry, S., & Hewson, P. (2003). Designing professional development for teachers of science and mathematics. Thousand Oaks, CA: Corwin Press.Google Scholar
  40. Meiers, M., & Ingvarson, L. (2005). Investigating the links between teacher professional development and student learning outcomes. Retrieved from:
  41. Moon, J., Passmore, C., Reiser, B. J., & Michaels, S. (2014). Beyond comparisons of online versus face-to-face PD: Commentary in response to Fishman et al., “Comparing the impact of online and face-to-face professional development in the context of curriculum implementation”. Journal of Teacher Education, 65, 172–176.Google Scholar
  42. Penuel, W. R., Fishman, B. J., Yamaguchi, R., & Gallagher, L. P. (2007). What makes professional development effective? Strategies that foster curriculum implementation. American Educational Research Journal, 44, 921–958.Google Scholar
  43. Philipp, R. (2007). Mathematics teachers’ beliefs and affect. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–318). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  44. Pringle, R., Mesa, J., & Hayes, L. (2017). Professional development for middle school science teachers: Does an educative curriculum make a difference? Journal of Science Teacher Education, 28, 57–72.Google Scholar
  45. Remillard, J. T. (2000). Can curriculum materials support teachers’ learning? Two fourth-grade teachers’ use of a new mathematics text. The Elementary School Journal, 100(4), 331–350.Google Scholar
  46. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.Google Scholar
  47. Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  48. Stigler, J., & Hiebert, J. (1997). Understanding and improving classroom mathematics, instruction: An overview of the TIMSS video study. Phi Delta Kappan, 79(1), 12–21.Google Scholar
  49. Stipek, D., Givvin, K., Salmon, J., & MacGyvers, V. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17, 213–226.Google Scholar
  50. Stylianides, G. J. (2008). Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics. International Journal of Science and Mathematics Education, 6, 191–215.Google Scholar
  51. Sztajn, P., Marrongelle, K., & Smith, M. (2012). Supporting implementation on the common core state standards for mathematics: Recommendations for professional development. Raleigh, NC: Friday Institute for Educational Innovation at North Carolina State University.Google Scholar
  52. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.Google Scholar
  53. Yoon, K. S., Duncan, T., Lee, S. W., Scarloss, B., & Shapley, K. L. (2007). Reviewing the evidence on how teacher professional development affects student achievement. Issues and answers report, REL 2007 No. 033. Washington, DC: US. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southwest 2007. Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Horizon Research, Inc.Chapel HillUSA
  2. 2.The City College of New YorkNew YorkUSA
  3. 3.Cynosure ConsultingApexUSA

Personalised recommendations