An important component of the National Council of Teachers of Mathematics Standards is the equity principle: All students should have access to a coherent, challenging mathematics curriculum. Many in the mathematics reform community have maintained that this principle can be achieved through one well-designed curriculum. However, the extant research on equity—which focuses on either ethnic diversity or academic achievement—suggests that this principle is illusive. The current study compares the effectiveness of two curricula in teaching a range of math concepts to 53 (28 male; 25 female) middle school students at risk for special education services in math. The yearlong, quasi-experimental study involved achievement and attitudinal measures. Results indicated that students in the intervention group who used materials designed according to instructional principles described in the special education literature achieved higher academic outcomes ( p < .05, p < .001) and had more positive attitudes toward math (p < .001) than did students in the comparison group.
Get full access to this article
View all access options for this article.
References
1.
Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice Hall.
2.
Baxter, J., Woodward, J., & Olson, D. (2001). Effects of reform-based mathematics instruction in five third grade classrooms. Elementary School Journal , 101(5), 529—548.
3.
Baxter, J., Woodward, J., Wong, J., & Voorhies, J. (2002). We talk about it, but do they get it?Learning Disabilities Research and Practice, 17(3), 173—185.
4.
Butler, F., Miller, S., Crehan, K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research & Practice, 18(2), 99—111.
5.
Bush, G. (2001). No child left behind act. Washington, DC: U.S. Department of Education.
6.
Carey, D., Fennema, E., & Nelson, B. (1995). Equity and mathematics education. In W. Secada, E. Fennema, & L. Adajain (Eds.), New directions for equity in mathematics education (pp. 93—125). New York : Cambridge University Press.
7.
Cass, M., Cates, D., & Smith, M. (2003). Effects of manipulative instruction on solving area and perimeter problems by students with learning disabilities. Learning Disabilities Research & Practice, 18(2), 112—120.
8.
Covington, M. (1992). Making the grade: A self-worth perspective on motivation and school reform. Cambridge, NY: Cambridge University Press.
9.
Dweck, C. (2000). Self-theories: Their role in motivation, personality, and development. Philadelphia: Psychology Press.
10.
Fennema, E., Franke, M., Carpenter, T., & Carey, D. (1993). Using children's mathematical knowledge in instruction . American Educational Research Journal, 30(3), 555—583.
11.
Fuchs, L., & Fuchs, D. (2001). Principles for the prevention and intervention of mathematics difficulties. Learning Disabilities Research & Practice, 16(2), 85—95.
12.
Gamoran, A., Porter, A., Smithson, J., & White, P. (1997). Upgrading high school mathematics for low-achieving, low income youth. Educational Evaluation and Policy Analysis , 19(4), 325—338.
13.
Gamoran, A., & Weinstein, M. (1998). Differentiation and opportunity in restructured schools. American Journal of Education, 106(3), 385—415.
14.
Harris, K., & Graham, S. (1996). Constructivism and students with special needs: Issues in the classroom. Learning Disabilities Research and Practice, 11, 134—137.
15.
Jitendra, A., Hoff, K., & Beck, M. (1999). Teaching middle school students with learning disabilities to solve word problems using a schema-based approach. Remedial and Special Education, 20(1), 50—64.
16.
Kameenui, E., Carnine, D., Dixon, R., Simmons, D., & Coyne, M. (2002). E fective teaching strategies that accommodate diverse learners. Upper Saddle River, NJ: MerrillPrentice Hall.
17.
Moses, R. (2001). Radical equations. Boston: Beacon Press.
18.
McGraw-Hill. (2002). CTB terra nova. Monterrey, CA: CTB McGraw-Hill .
19.
Middleton, J., & Spanias, P. (1999). Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research. Journal for Research in Mathematics Education, 30(1), 65—88.
20.
National Academy of Sciences. (1993). Measuring what counts: A conceptual guide for mathematics assessment. Washington, DC: National Research Council.
21.
National Council of Teachers of Mathematics. ( 1989). Curriculum and evaluation NCTM Standards for school mathematics . Reston, VA: Author.
22.
National Council of Teachers of Mathematics. ( 1999). Teaching and learning mathematics in poor communities: A report to the board of directors of the National Council of Teachers of Mathematics. Reston, VA: Author .
23.
National Council of Teachers of Mathematics. ( 2000). Principles and NCTM Standards for school mathematics . Reston, VA: Author.
Prentice Hall. (2002). Connected mathematics program. New York: Author.
26.
Reys, R., Reys, B., Lapan, R., Holliday, G. & Wasman, D. (2003). Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement. Journal for Research in Mathematics Education, 34(1), 74—95.
27.
Ridgway, J., Zawaojewski, J., Hoover, M., & Lambdin, D. (2003). Student attainment in the Connect Mathematics curriculum. In S. Senk & D. Thompson (Eds.), Standards-based school mathematics curricula (pp. 193— 224). Mahwah, NJ: LEA.
28.
Riordan, J., & Noyce, P. (2001). The impact of two standards-based mathematics curricula on student achievement in Massachusetts. Journal for Research in Mathematics Education, 32(4), 368—398.
29.
Schoenfeld, A. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher , 31(1), 13—25.
30.
Secada, W.G. (1997). Instructional environment observation scales. Unpublished rating scale, University of Wisconsin, Madison.
31.
Secada, W., Fennema, E., & Adajain, L. (1995). New directions for equity in mathematics education . New York: Cambridge University Press.
32.
Semmel, M., & Gerber, M. (1990). If at first you don't succeed, bye, bye again: A response to general educators' views on the REI. Remedial and Special Education, 11(4), 53—59.
33.
Senk, S., & Thompson, D. (2002). Standards-oriented school mathematics curricula: What are they? What do students learn?Mahwah, NJ: Erlbaum.
34.
Shunk, D., & Pajares, F. (2001). The development of academic self efficacy. In A. Wigfield & J. Eccles (Eds.), Development of achievement motivation (pp. 16—32). San Diego, CA: Academic Press.
35.
Silver, E., Smith, M., & Nelson, B. (1995). The QUASAR project: Equity concerns meet mathematics education reform in the middle school. In W. Secada, E. Fennema, & L. Adajain (Eds.), New directions for equity in mathematics education (pp. 9—56). New York: Cambridge University Press.
van Garderen, D., & Montague, M. (2003). Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246—255.
38.
Weiner, B. (1986). An attributional theory of motivation and emotion . New York: Springer-Verlag.
39.
Witzel, B., Mercer, C., & Miller, D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18(2), 121—131.
40.
Woodward, J. (1999, February). Self-concept, self-esteem, and attributional issues in secondary math classes. Pacific Coast Research Conference, San Diego, CA.
41.
Woodward, J. (2005). Developing automaticity in math facts: Integrating strategies with controlled practice. (Technical Report 2005-1). Seattle, WA: Washington Research Institute.
42.
Woodward, J., & Baxter, J. (1997). The effects of an innovative approach to mathematics on academically low achieving students in mainstreamed settings. Exceptional Children, 63(3), 373—388.
43.
Woodward, J., Baxter, J., & Robinson, R. (1999). Rules and reasons: Decimal instruction for academically low achieving students. Learning Disabilities Research and Practice, 14(1), 15—24.
44.
Woodward, J., & Gersten, R. (1992). Innovative technology for secondary learning disabled students: A multi-faceted study of implementation. Exceptional Children, 58(4), 407—422.
45.
Woodward, J., & Howard, L. (1994). The misconceptions of youth: Errors and their mathematical meaning. Exceptional Children, 61(2), 126—136.
46.
Woodward, J., & Montague, M. (2002). Meeting the challenge of mathematics reform for students with learning disabilities. The Journal of Special Education, 36(2), 89—101.
