Complexity of Curriculum Materials as Designed Artifacts: Implications and Future Directions

  • Janine T. RemillardEmail author
  • Ok-Kyeong Kim
Part of the Research in Mathematics Education book series (RME)


This chapter synthesizes and builds on findings from the previous chapters to consider what we have learned about mathematics curriculum materials as tools for teachers. Looking back at our analysis in Chaps.  2,  3,  4,  5,  6,  7, and  8, we briefly summarize our overall key findings and consider how these findings were influenced by key methodological decisions. We then discuss the complexity of curriculum materials as designed artifacts and the challenges associated with analyzing them. Using Hiebert and colleagues’ notion of a constellation of features that are needed to characterize classroom teaching, we argue that examining curriculum materials also involves considering a cluster of features. Using existing literature and our analysis in this volume, we also conceptualize curriculum materials as artifacts of design decisions comprised of multiple layers. We distinguish two main components, i.e., objectively given structures (what teachers see physically) and authors’ ideas and values, and discuss the relationship between them from curriculum authors’, the researchers’, and teachers’ perspectives. Finally, we provide some implications for teachers, curriculum designers, and researchers based on our findings and reflections on our work.


Curriculum analysis Mathematics curriculum materials Teacher’s guide Designed artifact Objectively given structure Constellation of features Design decisions Everyday Mathematics Investigations in Number, Data, and Space Math in Focus Math Trailblazers Scott Foresman–Addison Wesley Mathematics Author intentions Curriculum interpretations Teacher interpretations 


  1. Adler, J. (2019, September). Revisiting resources as a them in mathematics (teacher) education. Plenary address given at the Third International Conference on Mathematics Textbooks, Paderborn.Google Scholar
  2. Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is—Or might be—The role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–8.Google Scholar
  3. Ball, D. L., & Feiman-Nemser, S. (1988). Using textbooks and teachers’ guides: A dilemma for beginning teachers and teacher educators. Curriculum Inquiry, 18(4), 401–423.CrossRefGoogle Scholar
  4. Bezemer, J., & Kress, G. (2008). Writing in multimodal texts—A social semiotic account of designs for learning. Written Communication, 25(2), 166–195.CrossRefGoogle Scholar
  5. Bezemer, J., & Kress, G. (2016). Multimodality, learning and communication: A social semiotic frame. London: Routledge.Google Scholar
  6. Brown, M. W. (2009). Toward a theory of curriculum design and use: Understanding the teacher-tool relationship. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 17–36). New York: Routledge.Google Scholar
  7. Brown, S. A., Pitvorec, K., Ditto, C., & Kelso, C. R. (2009). Reconceiving fidelity of implementation: An investigation of elementary whole-number lessons. Journal for Research in Mathematics Education, 40(4), 363–395.Google Scholar
  8. Bruner, J. (1977). The process of education. Cambridge, MA: Harvard University Press.Google Scholar
  9. Charles, R. I., Crown, W., Fennell, F., et al. (2008). Scott Foresman–Addison Wesley Mathematics. Glenview, IL: Pearson.Google Scholar
  10. Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational Researcher, 34(3), 3–14.CrossRefGoogle Scholar
  11. Desimone, L. M., & Garet, M. S. (2015). Best practices in teacher’s professional development in the United States. Psychology, Society, & Education, 7(3), 252–263.CrossRefGoogle Scholar
  12. Fernandez, C., & Yoshida, M. (2004). Lesson study: A Japanese approach to improving mathematics teaching and learning. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  13. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel Publishing.Google Scholar
  14. Grossman, P., Wineburg, S., & Woolworth, S. (2001). Toward a theory of teacher community. Teachers College Record, 103, 942–1012.CrossRefGoogle Scholar
  15. Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218.CrossRefGoogle Scholar
  16. Gueudet, G., & Trouche, L. (2012). Communities, documents and professional geneses: Interrelated stories. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources (pp. 305–322). New York: Springer.CrossRefGoogle Scholar
  17. Hiebert, J., Stigler, J. W., Jacobs, J. K., Garnier, H., Smith, M. S., Hollingsworth, H., et al. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 Video Study. Educational Evaluation and Policy Analysis, 27(2), 111–132.CrossRefGoogle Scholar
  18. Kim, O. K. (2019). Teacher capacity for productive use of existing resources. In L. Trouche, G. Gueudet, & B. Pepin (Eds.), The ‘resource’ approach to mathematics education. New York: Springer.Google Scholar
  19. Leshota, M., & Adler, J. (2018). Disaggregating a mathematics teacher’s pedagogical design capacity. In L. Fan, L. Trouche, C. Qi, S. Rezat, & J. Visnovska (Eds.), Recent advances in research on mathematics teachers’ textbooks and resources (pp. 89–118). New York: Springer.CrossRefGoogle Scholar
  20. Little, J. W., & Horn, I. S. (2007). ‘Normalizing’ problems of practice: Converting routine conversation into a resource for learning in professional communities. In L. Stoll & K. S. Louis (Eds.), Professional learning communities: Divergence, detail and difficulties (pp. 79–92). Maidenhead: Open University Press.Google Scholar
  21. Lloyd, G. M. (1999). Two teachers’ conceptions of a reform-oriented curriculum: Implications for mathematics teacher development. Journal of Mathematics Teacher Education, 2(3), 227–252.CrossRefGoogle Scholar
  22. Marshall Cavendish International. (2010). Math in focus: The Singapore approach by Marshall Cavendish. Boston: Houghton Mifflin Harcourt.Google Scholar
  23. Melville, M. D. (2008). Kyozaikenkyu: An in-depth look into Japanese educators’ daily planning practices. Thesis, Brigham Young University.Google Scholar
  24. Munter, C., Stein, M. K., & Smith, M. S. (2015). Dialogic and direct instruction: Two distinct models of mathematics instruction and the debate(s) surrounding them. Teachers College Record, 117(11), 1–32.Google Scholar
  25. Otte, M. (1986). What is a text? In B. Christiansen, A. G. Howson, & M. Otte (Eds.), Perspectives on math education (pp. 173–202). Dordrecht: Kluwer.CrossRefGoogle Scholar
  26. Pepin, B., Gueudet, G., & Trouche, L. (2013). Re-sourcing teachers’ work and interactions: A collective perspective on resources, their use and transformations. ZDM – The International Journal on Mathematics Education, 45(7), 929–944.CrossRefGoogle Scholar
  27. Pepin, B., Gueudet, G., & Trouche, L. (2017). Refining teacher design capacity: Mathematics teachers’ interactions with digital curriculum resources. ZDM – Mathematics Education, 49(5), 799–812. Retrieved from Scholar
  28. Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246.CrossRefGoogle Scholar
  29. Remillard, J. T. (2012). Modes of engagement: Understanding teachers’ transactions with mathematics curriculum resources. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources (pp. 105–122). New York: Springer.Google Scholar
  30. Remillard, J. T. (2018). Examining teachers’ interactions with curriculum resource to uncover pedagogical design capacity. In L. Fan, L. Trouche, C. Qi, S. Rezat, & J. Visnovska (Eds.), Recent advances in research on mathematics teachers’ textbooks and resources (pp. 69–88). New York: Springer.CrossRefGoogle Scholar
  31. Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal of Research in Mathematics Education, 35(5), 352–388.CrossRefGoogle Scholar
  32. Remillard, J. T., & Kim, O. K. (2017). Knowledge of curriculum embedded mathematics: Exploring a critical domain of teaching. Educational Studies in Mathematics, 96(1), 65–81.CrossRefGoogle Scholar
  33. Remillard, J. T., & Taton, J. (2015). Rewriting myths about curriculum materials and teaching to new standards. In J. A. Supovitz & J. Spillane (Eds.), Challenging standards: Navigating conflict and building capacity in the era of the common core (pp. 49–58). Lanham, MD: Rowman & Littlefield.Google Scholar
  34. Shouffler, J. (2018). Teacher learning within United States lesson study: A study of a middle school mathematics lesson study team. Dissertation, University of Pennsylvania.Google Scholar
  35. Sleep, L. (2009). Teaching to the mathematical point: Knowing and using mathematics in teaching. Unpublished doctoral dissertation, University of Michigan.Google Scholar
  36. Sleep, L. (2012). The work of steering instruction toward the mathematical point a decomposition of teaching practice. American Educational Research Journal, 49(5), 935–970.CrossRefGoogle Scholar
  37. Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.CrossRefGoogle Scholar
  38. Stein, M. K., Grover, B. W., & Henningsen, M. A. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classroom. American Educational Research Journal, 33(2), 455–488.CrossRefGoogle Scholar
  39. TERC. (2008). Investigations in Number, Data, and Space (2nd edition). Glenview, IL: Pearson Education Inc.Google Scholar
  40. TIMS Project (2008). Math Trailblazers (3rd Edition). Dubuque, IA: Kendall/Hunt Publishing Company.Google Scholar
  41. Treffers, A. (1987). Three dimensions: A model of goal and theory description in mathematics instruction—The Wiskobas project. Dordrecht: Reidel Publishing.CrossRefGoogle Scholar
  42. University of Chicago School Mathematics Project. (2008). Everyday Mathematics (3rd Edition). Chicago, IL: McGraw-Hill.Google Scholar
  43. van Es, E. A. (2009). Participants’ roles in the context of a video club. The Journal of the Learning Sciences, 18, 100–137.CrossRefGoogle Scholar
  44. Watanabe, T., Takahashi, A., & Yoshida, M. (2008). Kyozaikenkyu: A critical step for conducting effective lesson study and beyond. In F. Arbaugh & P. M. Taylor (Eds.), Inquiry into mathematics teacher education (pp. 139–142). San Diego, CA: Association of Mathematics Teacher Educators.Google Scholar
  45. Wenger, E., McDermott, R. A., & Snyder, W. (2002). Cultivating communities of practice: A guide to managing knowledge. Boston, MA: Harvard Business School Press.Google Scholar
  46. Winsløw, C. (2012). A comparative perspective on teacher collaboration: The cases of lesson study in Japan and of multidisciplinary teaching in Denmark. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources (pp. 291–304). New York: Springer.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Graduate School of Education, University of PennsylvaniaPhiladelphiaUSA
  2. 2.Department of MathematicsWestern Michigan UniversityKalamazooUSA

Personalised recommendations