Abstract
Drawing on evidence from the Longitudinal Investigation of the Effect of Curriculum on Algebra Learning (LieCal) Project, issues related to mathematics curriculum reform and student learning are discussed. The LieCal Project was designed to longitudinally investigate the impact of a reform mathematics curriculum called the Connected Mathematics Project (CMP) in the USA on teachers’ teaching and students’ learning. Using a three-level conceptualization of curriculum (intended, implemented, and attained), a variety of evidence from the LieCal Project is presented to show the impact of mathematics curriculum reform on teachers’ teaching and students’ learning. This paper synthesizes findings from the two longitudinal studies spanning 7 years of the LieCal Project both to show the kind of impact curriculum has on teachers’ teaching and students’ learning and to suggest powerful but feasible ways researchers can investigate curriculum effect on both teaching and learning.
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Australian Curriculum, Assessment and Reporting Authority. (2012). Australian curriculum: mathematics. Retrieved March 10, 2014 from www.australiancurriculum.edu.au/mathematics.
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. 14.
Barrows, H. S. (2000). Problem-based learning applied to medical education. Springfield: Southern Illinois University School of Medicine.
Basic Education Curriculum Material Development Center, Chinese Ministry of Education. (2001). National mathematics curriculum standards at the compulsory education level (draft for consultation) [in Chinese]. Beijing: Beijing Normal University.
Bednarz, N., Kieran, C., & Lee, L. (Eds.). (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht: Kluwer Academic Publishers.
Cai, J. (1995). A cognitive analysis of US and Chinese students’ mathematical performance on tasks involving computation, simple problem solving, and complex problem solving. Journal for Research in Mathematics Education, Monographs Series, 7, Reston, VA: National Council of Teachers of Mathematics.
Cai, J. (2010). Evaluation of mathematics education programs. In P. Peterson, E. Baker, & B. McGraw (Eds.), International encyclopedia of education (Vol. 3, pp. 653–659). Oxford: Elsevier.
Cai, J., & Howson, A. G. (2013). Toward an international mathematics curriculum. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & K.S. F. Leung (Eds.), Third international handbook of mathematics education research (pp. 949–978). Springer.
Cai, J., Lo, J. J., & Watanabe, T. (2002). Intended treatments of arithmetic average in U.S. and Asian school mathematics. School Science and Mathematics, 102(8), 391–404.
Cai, J., Nie, B., & Moyer, J. C. (2010). The teaching of equation solving: Approaches in Standards-based and traditional curricula in the United States. Pedagogies: An International Journal, 5(3), 170–186.
Cai, J., Wang, N., Moyer, J. C., Wang, C., & Nie, B. (2011). Longitudinal investigation of the curriculum effect: An analysis of student learning outcomes from the LieCal Project. International Journal of Educational Research, 50(2), 117–136.
Cai, J., Moyer, J. C., & Wang, N. (2013a). Longitudinal investigation of the effect of middle school curriculum on learning in high school. In A. Lindmeier & A. Heinze (Eds.), the Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (pp. 137–144). Kiel, Germany: PME
Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013b). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57–69.
Cockroft, W. H. (1982). Mathematics counts: Report of the committee of inquiry into the teaching of mathematics in school. London: Her Majesty’s Stationery Office (HMSO).
Cuban, L. (1992). Curriculum stability and change. In P. W. Jackson (Ed.), Handbook on research on curriculum (pp. 216–247). New York: Macmillan.
Darling-Hammond, L. (1993). Reframing the school reform agenda. Phi Delta Kappan, 74(10), 752–761.
Fan, L., & Zhu, Y. (2007). Representation of problem-solving procedures: a comparative look at China, Singapore, and US mathematics textbooks. Educational Studies in Mathematics, 66(1), 61–75.
Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16, 235–266.
Howson, A. G. (1991). National curricula in mathematics. Leicester: The Mathematical Association.
Howson, A. G. (1995). Mathematics textbooks: A comparative study of grade-8 texts. Vancouver: Pacific Educational Press.
Howson, G., Keitel, C., & Kilpatrick, J. (1981). Curriculum development for school mathematics. Cambridge: Cambridge University Press.
Husen, T. (1967). International study of achievement in mathematics: A comparison of twelve countries, Volume I & II. New York: Wiley.
Jackson, P. (1992). Handbook of research on curriculum. New York: Macmillan.
Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002). Moving straight ahead. Upper Saddle River: Prentice Hall.
Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234–241.
Mathematical Sciences Education Board. (1993). Measuring what counts: A conceptual guide for mathematics assessment. Washington, DC: National Academy Press.
Ministry of Education. (2009). Math curriculum for grades 7–9. Retrieved from http://meyda.education.gov.il/files/Tochniyot_Limudim/Math/Hatab/Mavo.doc (in Hebrew).
Ministry of Education, Culture, Sports, Science and Technology, Japan. (2008). The courses of study for elementary and lower secondary school. Retrieved from http://www.mext.go.jp/a_menu/shotou/new-cs/index.htm (in Japanese).
Ministry of Education, Science, and Technology, Korea. (2011). Mathematics curriculum. Seoul: Author.
Moyer, J. C., Cai, J., Nie, B., & Wang, N. (2012). Developing function sense in middle school: Approaches in standards-based and traditional Curricula. Paper presented at The 12th International Congress on Mathematical Education, Seoul, Korea, July 08–15, 2012
Moyer, J. C., Cai, J., Nie, B., & Wang, N. (2011). Impact of curriculum reform: Evidence of change in classroom instruction in the United States. International Journal of Educational Research, 50(2), 87–99.
National Commission on Excellence in Education (1983). A nation at risk. The imperative for education reform. U.S. Government Printing Office.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010). Common core state standards: Mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_MathStandards.pdf.
National Research Council. (2004). On evaluating curricular effectiveness: Judging the quality of K–12 mathematics evaluations. Washington, DC: National Academy Press.
National Research Council (2013). Mathematical sciences in 2025. The National Academies Press.
National Research Council. (2001). Knowing what students know: The science and design of educational assessment. In J. Pelligrino, N. Chudowsky, & R. Glaser (Eds.), Committee on the Foundations of Assessment. Washington, DC: National Academy Press.
National Science Board (NSB). (2010). Preparing the next generation of STEM innovators: Identifying and developing our nation’s human capital. Arlington: National Science Foundation.
Nie, B., Cai, J., & Moyer, J. (2009). How a standards-based mathematics curriculum differs from a traditional curriculum: With a focus on intended treatments of the ideas of variable. Zentralblatt fuer Didaktik der Mathematik (International Journal on Mathematics Education), 41(6), 777–792.
Nie, B., Freedman, T., Hwang, S., Wang, N., Moyer, J. C., & Cai, J. (2013). An investigation of teachers’ intentions and reflections for classroom instruction. ZDM—The International Journal on Mathematics Education, 45(5), 699–711.
Norman, G. R., & Schmidt, H. G. (1992). The psychological basis of problem-based learning: A review of the evidence. Academic Medicine, 67, 557–565.
Ravitch, D. (2000). Left back: A century of battles over school reform. New York: Touchstone.
Resnick, L. (1987). Education and learning to think. Washington, DC: National Academy Press.
Ridgway, J. E., Zawojewski, J. S., Hoover, M. N., & Lambdin, D. V. (2003). Student attainment in the Connected Mathematics curriculum. In S. L. Senk & D. R. Thompson (Eds.), Standards-based school mathematics curricula: What are they? What do students learn? Mahwah: Erlbaum.
Robitaille, D. F., & Garden, R. A. (1989). The IEA study of mathematics II: Contexts and outcomes of school mathematics. New York: Pergamon Press.
Senk, S. L., & Thompson, D. R. (Eds.). (2003). Standards-based school mathematics curricula: What are they? What do students learn? Mahwah: Erlbaum.
Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80.
Sternberg, R. J., & Ben-Zeev, T. (Eds.). (1996). The nature of mathematical thinking. Hillsdale: Erlbaum.
Usiskin, Z., & Willmore, E. (Eds.). (2008). Mathematics curriculum in Pacific Rim countries: China, Japan, Korea, and Singapore. Charlotte: Information Age Publishing.
Van den Heuvel-Panhuizen, M. (2001). Realistic mathematics education in the Netherlands. In J. Anghileri (Ed.), Principles and practices in arithmetic teaching: innovative approaches for the primary classroom (pp. 49–63). Buckingham: Open University Press.
Vernon, D. T., & Blake, R. L. (1993). Does problem-based learning work? A meta-analysis of evaluative research. Academic Medicine, 68, 550–563.
Vithal, R., & Volmink, J. (2005). Mathematics curriculum research: Roots, reforms, reconciliation and relevance. In R. Vithal, J. Adler, & C. Keitel (Eds.), Researching mathematics education in South Africa: Perspectives, practices and possibilities (pp. 3–27). Cape Town: Human Sciences Research Council.
Wong, N. Y. (2004). The CHC learner’s phenomenon: Its implications on mathematics education. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 503–534). Singapore: World Scientific.
Acknowledgments
Research reported in this paper has been supported by grants from the National Science Foundation (ESI-0454739 and DRL-1008536). Any opinions expressed herein are those of the author and do not necessarily represent the views of the National Science Foundation. This research was conducted in collaboration with John Moyer and Ning Wang. I am very grateful for the support from a number of researchers and research assistants, including, Bikai Nie, Maria Alyson, Pat Bolter, Darlene Boyle, Carole Bryan, Janis Freckmann, Tony Freedman, Tammy Garber, Joan Grampp, Yuichi Handa, Patrick Hopfensperger, Stephen Hwang, Connie Laughlin, Victorial Robison, Mark Roche, Maxwell Scheinfield, Chelsey Schwander, Steven Silber, Carly Toth, Matt Wells, Courtney White, Libby Wenner, and Yue Zeng. An earlier version of this paper was presented as a Regular Lecture at the International Congress of Mathematics Education, Seoul, South Korea, July 7–15, 2012. The author is grateful for the thorough editorial assistance provided by Stephen Hwang.
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Cai, J. Searching for evidence of curricular effect on the teaching and learning of mathematics: some insights from the LieCal project. Math Ed Res J 26, 811–831 (2014). https://doi.org/10.1007/s13394-014-0122-y
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DOI: https://doi.org/10.1007/s13394-014-0122-y