Overview

The goal of this project is to acquire systematic and reliable information about how algebra is represented in secondary school mathematics textbooks.

Research Question:  What is algebra, as defined by high-school mathematics textbooks?

a.      What is the content, including the breadth, sequence, and depth of topics covered?

b.      What sets of behaviors are expected of students as they engage with the content?

The six textbook series that are being analyzed are those with greatest market penetration (see below).  These represent a wide range of approaches to secondary mathematics.  For the integrated textbook series (CPMP and IMP) we are analyzing only the units within the first three years that have a major focus on algebra (as identified by the authors).  For the other series we are analyzing the Algebra 1 and Algebra 2 (Advanced Algebra) books.

 

Integrated	Subject Specific
	Extensive Field Testing during Development	Commercially Generated
Core-Plus Mathematics Program (CPMP), Glencoe/McGraw-Hill (2008-2009)	University of Chicago School Mathematics Project (UCSMP), Wright Group (2008/2009)	Glencoe Algebra 1 & 2 (2008)
Interactive Mathematics Program (IMP), Key Curriculum Press (2008-2009)	Discovering Mathematics, Key Curriculum Press (2007, 2004)
	EDC's Center for Mathematics Education Algebra 1 and 2, Pearson (2009)

Educational Significance

Curriculum materials are a strong determinant of what students have an opportunity to learn and what they learn (Begle, 1973; Robitaille & Travers, 1992; Schmidt, McKnight, & Raizen, 1997; Usiskin, 1985).  There is tremendous variation in the content of courses called “algebra” across educational jurisdictions, in the US and abroad (Kendal & Stacey, 2004).  As stated by Kieran (2007), “Since the mid-1980s, the content of school algebra has been experiencing a tug of war between traditional and reformist views” (p. 709).  Given the vast differences in commercially available mathematics textbooks, students have quite different opportunities for learning algebra.  It is important to be able to characterize and specify these differences in coherent, comprehensive, and commensurable ways so that curriculum decision makers and other stakeholders can compare textbooks and make informed decisions.

Data Collection Techniques and Analyses

The textbook analysis is based on two primary dimensions.  First, to analyze the mathematical content we have adopted the Survey of Enacted Curriculum (SEC) K-12 Mathematics Taxonomy (Wisconsin Center for Education Research, 2007).  This taxonomy consists of 16 general areas, each divided into 4-19 specific topics.  Second, to analyze the cognitive behaviors expected of students as they engage with the mathematical content, we are using the categories of cognitive processes articulated in the TIMSS Advanced 2008 Assessment Framework (Garden et al., 2006).  This framework is organized into three domains:  knowing (the facts, procedures, and concepts students need to know), applying (the ability of students to make use of this knowledge to select or create models and solve problems), and reasoning (the ability to use analytical skills, generalize, and apply mathematics to unfamiliar or complex contexts).  Other easily obtainable information is collected during the coding process; i.e., the percentage of problems in each curriculum that are set in real-world context, require use of calculators or computers, or require use of manipulatives.  Unlike projects that involve analyzing tables of contents, we are analyzing every item in the narrative (excluding worked-out examples) and every item in the exercises (homework problems).  This time and labor-intensive process is necessary in order to capture the sequencing of content and cognitive behaviors that authors build into their textbooks.

Four people are conducting the textbook analysis:  a mathematics educator, a mathematician, and two teachers with strong content knowledge and extensive teaching experience at the high-school level.  Each coding team consists of a teacher and either a university mathematics educator or mathematician.  A coding manual was written that outlines specific coding procedures.  A 2.5-day coder training session held during June 2009.  As follow-up to the coder training session, additional exercises were given to establish reliability of 85% across each coding dimension.  Since that meeting, periodic tests have been conducted to ensure that the coding teams maintain reliability.

Each item in a textbook is analyzed by two people working separately.  Through a process of negotiation the coding pair comes to agreement on the set of codes to apply to each item.  To date, four textbook series have been coded:  CPMP, Glencoe, IMP, and UCSMP.  By the time of the NCTM Research Presession, one additional textbook series will be analyzed (CME) and another will be in progress (Discovering Algebra).

Summary of Findings to Date

The data for CPMP, Glencoe, and UCSMP have been analyzed.  The content and cognitive profiles for Glencoe and UCSMP are quite similar to each other, and are in sharp contrast to the profile for CPMP.  Across the CPMP series there is considerably less emphasis on the SEC content categories of basic and advanced algebra, as compared with Glencoe and UCSMP.  The CPMP textbooks contain a heavy emphasis on functions, with that emphasis decreasing as one progresses from Course 1 to Course 3.  By contrast, there is less emphasis on functions in Glencoe and UCSMP, but the emphasis increases as one progresses from Algebra 1 to Algebra 2 (Advanced Algebra).  In terms of the cognitive dimension, according to the TIMSS framework, approximately the same percentage of items was classified as “applying” in the CPMP, Glencoe, and UCSMP books.  The most prominent difference is the considerably larger percentage of items in the CPMP books that are classified as reasoning, compared to Glencoe and UCSMP, which have noticeably more items classified as knowing.  The percentage of items in each curriculum that are set in real-world contexts is:  CPMP – 45%, Glencoe – 23%, and UCSMP – 28%.  The percentage of items in each curriculum that require use of calculators or computers is:  CPMP – 22%, Glencoe – 14%, and UCSMP – 20%.  Glencoe requires use of manipulatives on approximately 1% of the items, whereas the percentage for CPMP and UCSMP is less than 1%.

Timeline for the Session

• 15 minute overview of the study to entire audience, including reflections from a teacher collaborator
• Two 15 minute roundtable discussions in which we will present additional findings and seek feedback from the audience