THIRD-YEAR HIGH SCHOOL MATHEMATICS CURRICULUM: EFFECTS OF CONTENT ORGANIZATION AND CURRICULUM IMPLEMENTATION

  • Óscar Chávez
  • James E. Tarr
  • Douglas A. Grouws
  • Victor M. Soria
Article

Abstract

We examined the effect of curriculum organization in US high schools where students could freely choose to study mathematics from textbooks that employed one of two types of content organization, an integrated approach or a (traditional) subject-specific approach. The study involved 2,242 high school students, enrolled in either Course 3 or Algebra 2, in 10 schools in 5 geographically dispersed states. Taking account of curriculum implementation and students’ prior mathematics learning, we analyzed two end-of-year outcome measures: a test of common objectives and a standardized achievement test. Our hierarchical linear models with three levels showed that students in the integrated curriculum scored significantly higher than those in the subject-specific curriculum on the common objectives test. In both outcome measures, gender and prior achievement were significant student-level predictors. In the standardized achievement test, ethnicity was a moderating factor. At the teacher-level, in addition to curriculum type, teachers’ orientation and free and reduced lunch eligibility were significant moderating factors. Opportunity to learn, implementation fidelity, teacher experience, and professional development were not significant predictors.

Keywords

curriculum comparison HLM high schools mathematics mathematics curriculum secondary curriculum textbooks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cai, J., Wang, N., Moyer, J. C., Wang, C. & Nie, B. (2011). Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal Project in the United States. International Journal of Educational Research, 50, 117–136.CrossRefGoogle Scholar
  2. Center for Mathematics Education (CME), P (2009) CME project: Algebra 2: Student edition. Boston: Pearson.Google Scholar
  3. Chávez, O., Papick, I., Ross, D. J., & Grouws, D. A. (2011). Developing fair tests for mathematics curriculum comparison studies: The role of content analyses. Mathematics Education Research Journal, 23(4), 397–416.Google Scholar
  4. Coxford, A. F., Fey, J. T., Hirsch, C. R., Schoen, H. L., Burrill, G., Hart, E. W. & Ritsema, B. (2003). Contemporary mathematics in context: A unified approach (course 3). Columbus: Glencoe/McGraw-Hill.Google Scholar
  5. Cuoco, A., Goldenberg, E. P. & Mark, J. (2010). Organizing a curriculum around mathematical habits of mind. Mathematics Teacher, 103, 682–688.Google Scholar
  6. Dossey, J., Halvorsen, K. & McCrone, S. (2008). Mathematics education in the United States 2008: A capsule summary book written for the eleventh International Congress on Mathematical Education (ICME-11). Reston: National Council of Teachers of Mathematics.Google Scholar
  7. Feldt, L. S., Forsyth, R. A., Ansley, T. N. & Alnot, S. D. (2003). Iowa Tests of Educational Development (Form B). Chicago: Riverside Publishing Company.Google Scholar
  8. Grouws, D. A., Smith, M. S. & Sztajn, P. (2004). The preparation and teaching practices of United States mathematics teachers: Grades 4 and 8. In P. Kloosterman, F. Lester & C. Brown (Eds.), Results and Interpretations of the 1990 through 2000 Mathematics Assessments of the National Assessment of Educational Progress (pp. 221–267). Reston: National Council of Teachers of Mathematics.Google Scholar
  9. Grouws, D. A., Tarr, J. E., Chávez, O., Sears, R., Soria, V., & Taylan, R. D. (2013). Curriculum and implementation effects on high school students’ mathematics learning from curricula representing subject-specific and integrated content organizations. Journal for Research in Mathematics Education, 44(2), 416–463.Google Scholar
  10. House, P. A. (2003). Integrated mathematics: An introduction. In S. A. McGraw (Ed.), Integrated mathematics: Choices and challenges (pp. 3–11). Reston: National Council of Teachers of Mathematics.Google Scholar
  11. Latterell, C. M. (2006). CPMP III versus Algebra II. Focus on Learning Problems in Mathematics, 28(2), 20–36.Google Scholar
  12. National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston: Author.Google Scholar
  13. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: Author.Google Scholar
  14. National Research Council (2002). Committee on understanding the influence of standards in K-12 Science, Mathematics, and Technology Education. In I. R. Weiss, M. S. Knapp, K. S. Hollweg & G. Burrill (Eds.), Investigating the influence of standards: A framework for research in mathematics, science, and technology education. Washington, DC: National Academy Press.Google Scholar
  15. National Research Council (2004). On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations. Washington, DC: National Academy Press.Google Scholar
  16. Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75, 211–246.CrossRefGoogle Scholar
  17. Remillard, J. T. & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35, 352–388.CrossRefGoogle Scholar
  18. Reys, R. & Reys, R. (2009). Two high school mathematics curricula paths—which one to take? Mathematics Teacher, 102(8), 568–570.Google Scholar
  19. Riverside Publishing (n.d.). Iowa tests of educational development. Retrieved from http://www.riversidepublishing.com/products/ited/details.html. Accessed 26 July 2012.
  20. Schoenfeld, A. H. (2006). What doesn’t work: The challenge and failure of the What Works Clearinghouse to conduct meaningful reviews of studies of mathematics curricula. Educational Researcher, 35(2), 13–21.CrossRefGoogle Scholar
  21. Senk, S., Thompson, D., Viktora, S., Usiskin, Z., Ahbel, N., Rubenstein, R. & Levin, S., et al. (2001). UCSMP Advanced Algebra. Englewood Cliffs: Prentice-Hall.Google Scholar
  22. Slavin, R. E. & Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research, 78(3), 427–515.CrossRefGoogle Scholar
  23. Stein, M. K., Remillard, J. & Smith, M. S. (2007). How curriculum influences student learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–370). Charlotte: Information Age Publishing.Google Scholar
  24. Stein, M. K. & Smith, M. S. (2010). The influence of curriculum on student learning. In B. Reys & R. Reys (Eds.), K-12 mathematics curriculum: Issues, trends and future directions (pp. 351–362). Reston: NCTM.Google Scholar
  25. Tarr, J. E., Grouws, D. A., Chávez, O., & Soria, V. (2013). The effects of content organization and curriculum implementation on students’ mathematics learning in second-year high school courses. Journal for Research in Mathematics Education 44(4), 683–729.Google Scholar
  26. Tarr, J. E., McNaught, M. D., & Grouws, D. A. (2012). The development of multiple measures of curriculum implementation in secondary mathematics classrooms: Insights from a three-year curriculum evaluation study. In: I. Weiss, D. Heck, K. Chval & S. Zeibarth (Eds.), Approaches to studying the enacted curriculum (pp. 89–115). Greenwich, CT: Information Age Publishing, Inc.Google Scholar
  27. Tarr, J. E., Reys, R. E., Reys, B. J., Chávez, O., Shih, J. & Osterlind, S. J. (2008). The impact of middle grades mathematics curricula on student achievement and the classroom learning environment. Journal for Research in Mathematics Education, 39(3), 247–280.Google Scholar
  28. Tarr, J. E., Ross, D. J., McNaught, M. D., Chávez, O., Grouws, D. A., Reys, R. E., & Sears, R. (2010). Identification of student- and teacher-level variables in modeling variation of mathematics achievement data. Paper presented at the Annual Meeting of the American Educational Research Association, Denver, CO, May 2010. Available for download from Educational Resources Information Center (ERIC): Paper ED510315.Google Scholar
  29. Usiskin, Z. (2003). The integration of the school mathematics curriculum in the United States: History and meaning. In S. A. McGraw (Ed.), Integrated mathematics: Choices and challenges (pp. 13–31). Reston: National Council of Teachers of Mathematics.Google Scholar
  30. Van Dormolen, J. (1986). Textual analysis. In B. Christiansen, A. G. Howson & M. Otte (Eds.), Perspectives on mathematics education (pp. 141–171). Dordrecht: D. Reidel Publishing Company.CrossRefGoogle Scholar

Copyright information

© National Science Council, Taiwan 2013

Authors and Affiliations

  • Óscar Chávez
    • 1
  • James E. Tarr
    • 2
  • Douglas A. Grouws
    • 2
  • Victor M. Soria
    • 2
  1. 1.University of Texas at San AntonioSan AntonioUSA
  2. 2.University of MissouriColumbiaUSA

Personalised recommendations