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Teaching Mathematics Using Standards-Based and Traditional Curricula: A Case of Variable Ideas

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Mathematics Curriculum in School Education

Part of the book series: Advances in Mathematics Education ((AME))

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Abstract

This chapter discusses approaches to teaching algebraic concepts like variables that are embedded in a Standards-based mathematics curriculum (CMP) and in a traditional mathematics curriculum (Glencoe Mathematics). Neither the CMP curriculum nor Glencoe Mathematics clearly distinguishes among the various uses of variables. Overall, the CMP curriculum uses a functional approach to teach equation solving, while Glencoe Mathematics uses a structural approach to teach equation solving. The functional approach emphasizes the important ideas of change and variation in situations and contexts. The structural approach, on the other hand, avoids contextual problems in order to concentrate on developing the abilities to generalize, work abstractly with symbols, and follow procedures in a systematic way. This chapter reports part of the findings from the larger LieCal research project. The LieCal Project is designed to investigate longitudinally the impact of a Standards-based curriculum like CMP on teachers’ classroom instruction and student learning. This chapter tells part of the story by showing the value of a detailed curriculum analysis in characterizing curriculum as a pedagogical event.

Research reported in this chapter is supported by grants from the National Science Foundation (ESI-0454739 and DRL-1008536). Any opinions expressed herein are those of the authors and do not necessarily represent the views of the National Science Foundation.

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Notes

  1. 1.

    In 2006 and 2009, the CMP authors published revised editions of the CMP curriculum under the name CMP2. CMP3 was published in 2013. This article is based on the original CMP curriculum because the students in the LieCal project used CMP, not CMP2 or CMP3.

References

  • Algebra Working Group to the National Council of Teachers of Mathematics (1997). A framework for constructing a vision of algebra: a discussion document. Reston: NCTM.

    Google Scholar 

  • Bailey, R., Day, R., Frey, P., Howard, A. C., Hutchens, D. T., McClain, K., et al. (2006a). Mathematics: applications and concepts. Columbus: The McGraw-Hill Company (teacher wraparound edition), course 1.

    Google Scholar 

  • Bailey, R., Day, R., Frey, P., Howard, A. C., Hutchens, D. T., McClain, K., et al. (2006b). Mathematics: applications and concepts. Columbus: The McGraw-Hill Company (teacher wraparound edition), course 2.

    Google Scholar 

  • Bailey, R., Day, R., Frey, P., Howard, A. C., Hutchens, D. T., McClain, K., et al. (2006c). Mathematics: applications and concepts. Columbus: The McGraw-Hill Company (teacher wraparound edition), course 3.

    Google Scholar 

  • 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.

    Google Scholar 

  • Bednarz, N., Kieran, C., & Lee, L. (Eds.) (1996). Approaches to algebra: perspectives for research and teaching. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Cai, J., Lo, J. J., & Watanabe, T. (2002). Intended treatment of arithmetic average in U.S. and Asian school mathematics textbooks. School Science and Mathematics, 102(8), 391–404.

    Article  Google Scholar 

  • Cai, J., Nie, B., & Moyer, J. (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.

    Google Scholar 

  • Cai, J., Ni, Y., & Lester, F. K. Jr. (2011a). Curricular effect on the teaching and learning of mathematics: findings from two longitudinal studies in China and the United States. International Journal of Educational Research, 50(2), 63–64.

    Article  Google Scholar 

  • Cai, J., Wang, N., Moyer, J. C., Wang, C., & Nie, B. (2011b). 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.

    Article  Google Scholar 

  • Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (in press). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics.

    Google Scholar 

  • Doyle, W. (1992). Curriculum and pedagogy. In P. W. Jackson (Ed.), Handbook of research on curriculum (pp. 486–516). New York: Macmillan.

    Google Scholar 

  • Janvier, C. (1996). Modeling and the initiation to algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: perspectives for research and teaching (pp. 225–236). Dordrecht: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.

    Article  Google Scholar 

  • Kieran, C., Boileau, A., & Garançon, M. (1996). Introducing algebra by means of a technology supported functional approach. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: perspectives for research and teaching (pp. 257–293). Dordrecht: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002a). Variables and patterns. Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002b). Moving straight ahead. Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002c). Getting to know connected mathematics: an implementation guide. Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002d). Lesson planner for grades 6, 7, and 8. Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002e). Data about us. Upper Saddle River: Prentice Hall.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics (1995). Assessment standards for school mathematics. Reston: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: Author.

    Google Scholar 

  • Nemirovsky, R. (1996). Mathematical narratives, modeling and algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra. Perspectives for research and teaching (pp. 197–220). Dordrecht: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Nie, B., Cai, J., & Moyer, J. C. (2009). How a standards-based mathematics curriculum differs from a traditional curriculum: with a focus on intended treatments of the ideas of variable. ZDM—International Journal on Mathematics Education, 41(6), 777–792.

    Article  Google Scholar 

  • Schoenfeld, H. A., & Arcavi, A. (1988). On the meaning of variable. The Mathematics Teacher, 81(6), 420–427.

    Google Scholar 

  • Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford (Ed.), The ideas of algebra, K-12 (pp. 8–19). Reston: NCTM.

    Google Scholar 

  • Wheeler, D. (1996). Backwards and forwards: reflections on different approaches to algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: perspectives for research and teaching (pp. 317–325). Dordrecht: Kluwer Academic Publishers.

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Delaware, Newark, USA

    Jinfa Cai & Bikai Nie

  2. Marquette University, Milwaukee, USA

    John C. Moyer

  3. Widener University, Chester, USA

    Ning Wang

Authors
  1. Jinfa Cai
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  2. Bikai Nie
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  3. John C. Moyer
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  4. Ning Wang
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Corresponding author

Correspondence to Jinfa Cai .

Editor information

Editors and Affiliations

  1. Texas A & M University Dept. Teaching, Learning & Culture, College Station, Texas, USA

    Yeping Li

  2. Michigan State University, East Lansing, Michigan, USA

    Glenda Lappan

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Cai, J., Nie, B., Moyer, J.C., Wang, N. (2014). Teaching Mathematics Using Standards-Based and Traditional Curricula: A Case of Variable Ideas. In: Li, Y., Lappan, G. (eds) Mathematics Curriculum in School Education. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7560-2_19

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