Common Core Standards for Mathematical Practice in the Algebra Strand of Six High School Textbook Series

• In Event: 14.043 - Roundtable Session 1
  In Roundtable Session: 14.043-14 - Analyzing the Common Core Standards for Mathematical Practice

Abstract

The following research question guides this investigation: To what extent are the CCSSM SMPs 1, 2, 3, 7, and 8 (National Governors Association Center for Best Practices and Council of Chief State School Officers, 2010) evident in the algebra strand of six high-school textbook series?

This study draws upon the framework, developed by Remillard and Heck (in press), which situates the enacted curriculum within a broad system of curriculum policy, design, and enactment that captures the relationships among different instantiations of curriculum. The relevant portion of this framework is shown in Figure 1. Textbooks are included in the rectangle labeled “instructional materials.”

Figure 1. Theoretical Framework (adapted from Remillard & Heck, in press)


Table 1 contains information about the six textbook series that are reported on in this study, including the number of items that have been coded in each.

Table 1
Textbooks Included in the Study

INTEGRATED
Core-Plus Mathematics Program (CPMP), n = 7,537.
Interactive Mathematics Program (IMP), n = 1,735.

SUBJECT SPECIFIC--Extensive Field Testing During Development
Center for Mathematics Education (CME), n = 12,795.
Discovering Mathematics (currently being coded).
University of Chicago School Mathematics Project (UCSMP), n = 13,675.

SUBJECT SPECIFIC -- Commercially Generated
Glencoe, n = 17,020.


The mathematical content of the textbooks is coded using the Survey of Enacted Curriculum (SEC) K-12 Mathematics Taxonomy (Wisconsin Center for Education Research, 2007). The cognitive behaviors expected of students as they engage with the mathematical content is coded using the categories of cognitive processes in the TIMSS Advanced 2008 Assessment Framework (Garden et al., 2006). The analytic frameworks are applied to every problem in the narrative and to every homework problem in the textbooks.

The study reported on here consists of secondary data analysis--examining the existing coding for evidence of the SMPs. In particular, for problems that are coded as involving the cognitive behavior domain reasoning, the corresponding textbook items are examined for evidence that the problems provide students with opportunities to:
● Make sense of problems and persevere in solving them (SMP1);
● Reason abstractly and quantitatively (SMP2);
● Construct viable arguments and critique the reasoning of others (SMP3);
● Look for and make use of structure (SMP7); and
● Look for and express regularity in repeated reasoning (SMP8).

Given the important role that CCSSM is playing in school mathematics, analysis like that provided in this paper will inform stakeholders of the extent to which their textbooks embody mathematical practices that involve higher-order reasoning. Because the SMPs are phrased in terms of mathematical behaviors of students, a challenge we are facing is translating them into a form that can be applied to textbook analysis. This issue will be discussed in this paper.

Authors

• Mary Ann Huntley, Cornell University

• Maria Terrell, Cornell University