Abstract
Textbooks are a major factor in creating opportunities for learning in high school mathematics. However, teachers sometimes skip or modify lessons in the textbook. Thus, the enacted curriculum can be quite different from the intended curriculum of the textbook. This chapter describes a study of the intended, enacted, and attained curriculum conducted in ten matched pairs of Algebra 2 classes in five high schools in the United States. In particular, because functions are a major content strand of high school mathematics across the world, we discuss relationships between students’ achievement on items testing their knowledge of functions and the opportunities to learn provided by their textbooks and teachers.
The original evaluation study from which the research in this report is drawn was funded by the University of Chicago School Mathematics Project.
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- 1.
In about 90 % of U.S. high schools, the mainstream curriculum consists of a sequence of three full-year courses, Algebra 1-Geometry-Algebra 2 or Algebra 1-Algebra 2-Geometry, which students begin in either Grade 8, 9, or 10 (Dossey et al. 2008). Other high schools use some version of integrated curricula combining topics from algebra, geometry, and other mathematical subjects.
- 2.
The UCSMP is a curriculum research and development project for Grades K-12 that was established in the United States in 1983. With funding from both private and public foundations, it is one of the longest lasting curriculum projects in the history of the United States (Usiskin 2003).
- 3.
As of March 2012, 45 of the 50 states and several U.S. territories had adopted these standards.
- 4.
The items are available through the NAEP Questions Tool v4.0, downloaded from http://nces.ed.gov/nationsreportcard/itmrlsx/search.aspx?subject=mathematics on February 17, 2012.
- 5.
In addition to the five schools described in this chapter, five additional schools that either did not have comparison classes or had comparisons between the second and third editions of UCSMP Advanced Algebra were involved in the evaluation study. In this chapter, we include only those schools in which comparison classes used a non-UCSMP textbook.
- 6.
The Cronbach alpha measures reported here were obtained using test results only from the students in this sample.
- 7.
Cronbach alpha reliability measures were run again for only those items comprising each subtest.
- 8.
We acknowledge that this method potentially overcounts the number of lessons related to functions in some textbooks. However, a detailed look at every lesson in each textbook to determine whether function concepts were explicitly addressed was beyond the scope of this secondary analysis.
- 9.
During the year the comparison teacher in School 28 taught linear relations and functions, linear systems including linear programming, polynomials including quadratics and factoring, arithmetic and geometric sequences and series. The teacher did not teach exponential, logarithmic, rational or radical functions.
- 10.
A dependent measures t-test on the mean of the differences of the class means provides a method to test the overall effect of the two curricula (Gravetter and Wallnau 1985, p. 373).
- 11.
Effect size was determined using measures appropriate for matched groups. The effect size is \(d=t_{c}\cdot\sqrt{\frac{2(1-r)}{n}}\), where d=effect size, t c is based on the difference of the pair means, r is the correlation between the pair means, and n is the number of matched pairs (Dunlap et al. 1996).
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Appendix: Textbooks Used in the Study
Bellman, A. E., Bragg, S. C., Charles, R. I., Handlin, W. G. Sr., & Kennedy, D. (2004). Algebra 2. Needham: Prentice Hall.
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Larson, R., Boswell, L., Kanold, T. D., & Stiff, L. (2001). Algebra 2. Evanston: McDougal Littell.
Lial, M. L., & Hornsby, J. (2000). Intermediate algebra (8th ed.). Reading: Addison Wesley Longman.
Schultz, J. E., Ellis, W. Jr., Hollowell, K., & Kennedy, P. A. (2001). Algebra 2. Austin: Holt, Rinehart and Winston.
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Senk, S.L., Thompson, D.R., Wernet, J.L.W. (2014). Curriculum and Achievement in Algebra 2: Influences of Textbooks and Teachers on Students’ Learning about Functions. 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_24
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