# All Published Research and Evaluation on CMP

A large body of literature exists that focuses on or is related to the *Connected Mathematics Project*. Here, you will find articles on CMP that we have compiled over the past thirty years. These include research, evaluation and descriptions from books, book chapters, dissertations, research articles, reports, conference proceedings, and essays. Some of the topics are:

- student learning in CMP classrooms
- teacher's knowledge in CMP classrooms
- CMP classrooms as research sites
- implementation strategies of CMP
- longitudinal effects of CMP in high school math classes
- students algebraic understanding
- student proportional reasoning
- student achievement
- student conceptual and procedural reasoning and understanding
- professional development and teacher collaboration
- comparative studies on different aspects of mathematics curricula
- the CMP philosophy and design, development, field testing and evaluation process for CMP

This list is based on thorough reviews of the literature and updated periodically. Many of these readings are available online or through your local library system. A good start is to paste the title of the publication into your search engine. Please contact us if you have a suggestion for a reading that is not on the list, or if you need assistance locating a reading.

Alibali, M. W., Stephens, A. C., Brown, A. N., Yvonne, S., & Nathan, M. J. (2014). M*iddle school students’ conceptual understanding of equations: Evidence from writing story problems. *International Journal of Educational Psychology, 3(3), 235–264. doi:10.4471/ijep.2014.13

ABSTRACT: This study investigated middle school students’ conceptual understanding of algebraic equations. 257 sixth- and seventh-grade students solved algebraic equations and generated story problems to correspond with given equations. Aspects of the equations’ structures, including number of operations and position of the unknown, influenced students’ performance on both tasks. On the story-writing task, students’ performance on two-operator equations was poorer than would be expected on the basis of their performance on one-operator equations. Students made a wide variety of errors on the story-writing task, including (1) generating story contexts that reflect operations different from the operations in the given equations, (2) failing to provide a story context for some element of the given equations, (3) failing to include mathematical content from the given equations in their stories, and (4) including mathematical content in their stories that was not present in the given equations. The nature of students’ story-writing errors suggests two main gaps in students’ conceptual understanding. First, students lacked a robust understanding of the connection between the operation of multiplication and its symbolic representation. Second, students demonstrated difficulty combining multiple mathematical operations into coherent stories. The findings highlight the importance of fostering connections between symbols and their referents.

Read Middle School Students Conceptual Understanding of Equations

Bouck, E. C., Kulkarni, G., & Johnson, L. (2011). *Mathematical performance of students with disabilities in middle school: Standards-based and traditional curricula. *Remedial and Special Education, 32(5), 429–443.

ABSTRACT: This study investigated the impact of mathematics curriculum (standards based vs. traditional) on the performance of sixth and seventh grade students with disabilities on multiple-choice and open-ended assessments aligned to one state’s number and operations and algebra standards. It also sought to understand factors affecting student performance on assessments: ability status (students with and without disabilities), curriculum (standards based vs. traditional), and assessment type (multiple choice vs. open ended). In all, 146 sixth grade students and 149 seventh grade students participated in the study. A linear mixed model for each grade revealed students with disabilities did not perform better in either curriculum. Furthermore, curriculum type was not a significant factor affecting student performance; however, ability status, time, and assessment type were. The implications of these results are discussed.

Cady, J. A., Hodges, T. E., & Collins, R. L. (2015). A comparison of textbooks’ presentation of fractions. *School Science & Mathematics, 115(*3), 105–116. doi:10.1111/ssm.12108.

ABSTRACT: In the United States, fractions are an important part of the middle school curriculum, yet many middle school students struggle with fraction concepts. Teachers also have difficulty with the conceptual understanding needed to teach fractions and rely on textbooks when making instructional decisions. This reliance on textbooks, the idea that teaching and learning of fractions is a complex process, and that fraction understanding is the foundation for later topics such as proportionality, algebra, and probability, makes it important to examine the variation in presentation of fraction concepts in U.S. textbooks, especially the difference between traditional and standards-based curricula. The purpose of this study is to determine if differences exist in the presentation of fractions in conventional and standards-based textbooks and how these differences align with the recommendations of National Council of Teachers of Mathematics, Common Core State Standards, and the research on the teaching and learning of fractions.

Kar, T., & Isik, C. (2015). Comparison of Turkish and American Seventh Grade Mathematics Textbooks in Terms of Addition and Subtraction Operations with Integers. Egitim ve Bilim, 40(177).

ABSTRACT: This study analyzes how addition and subtraction with integers are presented in Turkish and American mathematics textbooks. Analyses focus on how the concepts are given as well as the nature of the presented mathematical problems. It was found that both the Turkish and the American textbooks emphasized the relationships among different representations in teaching addition and subtraction with integers. It was found that the coordination among visual representation, verbal explanations and mathematical sentences was constructed in a more organized manner in the textbook named Connected Mathematics 2. It was found that operational skill oriented problems were proportionately featured more in the Turkish textbooks whereas the problems requiring high-level cognitive skills such as mathematical reasoning and problem posing were featured more in the American textbooks.

McNeil, N., Grandau, L., Knuth, E., Alibali, M., Stephens, A., Hattikudur, S., & Krill, D. (2006). Middle-school students' understanding of the equal sign: The books they read can't help. *Cognition and Instruction, 24*(3), 367-385.

ABSTRACT: This study examined how 4 middle school textbook series (2 skills-based, 2 Standards-based) present equal signs. Equal signs were often presented in standard operations equals answer contexts (e.g., 3 + 4 = 7) and were rarely presented in nonstandard operations on both sides contexts (e.g., 3 + 4 = 5 + 2). They were, however, presented in other nonstandard contexts (e.g., 7 = 7). Two follow-up experiments showed that students' interpretations of the equal sign depend on the context. The other nonstandard contexts were better than the operations equals answer context at eliciting a relational understanding of the equal sign, but the operations on both sides context was best. Results suggest that textbooks rarely present equal signs in contexts most likely to elicit a relational interpretation-an interpretation critical to success in algebra.

Muzheve, M. T. (2008). *Converting among fractions, decimals, and percents: An exploration of representational usage by middle school teachers.* (Unpublished doctoral dissertation). Texas A&M University, College Station, TX.

ABSTRACT: Using both quantitative and qualitative data collection and analyses techniques, this study examined representations used by sixteen (n = 16) teachers while teaching the concepts of converting among fractions, decimals, and percents. The classroom videos used for this study were recorded as part of the Middle School Mathematics Project (MSMP). The study also compared teacher-selected and textbook representations and examined how teachers‘ use of idiosyncratic representations influenced representational choices on the number test by the teachers‘ five hundred eighty-one (N = 581) students.

In addition to using geometric figures and manipulatives, a majority of the teachers used natural language such as the words nanny, north, neighbor, dog, cowboy, and house to characterize fractions and mathematical procedures or algorithms. Coding of teacher-selected representations showed that verbal representations deviated from textbook representations the most. Some teachers used the words or phrases bigger, smaller, doubling, tripling, breaking-down, and building-up in the context of equivalent fractions.

There was widespread use of idiosyncratic representations by teachers, such as equations with missing or double equal signs, numbers and operators written as superscripts, and numbers written above and below the equal sign. Although use of idiosyncratic representations by teachers influenced representational choices by students on the number test, no evidence of a relationship between representational forms and degree of correctness of solutions was found. The study did reveal though that teachers‘ use of idiosyncratic representations can lead to student misconceptions such as thinking that multiplying by a whole number not equal to 1 gives an equivalent fraction.

Statistical tests were done to determine if frequency of representation usage by teachers was related to the textbook, highest degree obtained by teacher, certification, number of years spent teaching mathematics, number of years teaching mathematics at grade level, number of hours completed on professional development related to their textbook, and total number of days spent on the Interagency Education Research Initiative (IERI) professional development. The results showed representation usage was related to all the above variables, except the highest degree obtained and the total number of days spent on the IERI professional development.