# 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.

Ball, D. L. (1996). Teacher learning and the mathematics reforms: What we think we know and what we need to learn. *Phi Delta Kappan*, 77(7), 500-508.

ABSTRACT: In order to improve mathematics education, a close examination of assumptions about teacher learning and the teaching of mathematics must be made. Teachers and others participating in the reform process will have to learn many new ideas and unlearn many previous assumptions.

Chval, K., Chávez, Ó., Reys, B., & Tarr, J. (2009). Considerations and limitations related to conceptualizing and measuring textbook integrity. In J. T. Remillard, B. A. HerbelEisenmann, & G. M. Lloyd (Eds.), *Mathematics teachers at work: Connecting curriculum materials and classroom instruction* (Studies in Mathematical Thinking and Learning Series, A. Schoenfeld, Ed.) (pp. 70-84). New York: Routledge.

Cobb, P., & Jackson, K. (2012). Analyzing educational policies: A learning design perspective. *The Journal of the Learning Sciences, 21*(4), 487-521.

ABSTRACT: In this article, we describe and illustrate an analytical perspective in which educational policies are viewed as designs for supporting learning. This learning design perspective is useful when designing policies, when adapting policies to particular school and district settings during implementation, and when revising policies after implementation to make them more effective. Analyzed from this perspective, a policy comprises the goals for the learning of members of the target group, the supports for their learning, and an often implicit rationale for why these supports might be effective. We clarify that this perspective on policies has broad generality. In addition, we illustrate that personnel at all levels of the US education system both formulate policies designed to influence others’ practices, and are practitioners targeted by others’ policies. The standard image of a single policy traveling down though an education system with more or less fidelity is therefore displaced by that of people at multiple levels of a system reorganizing their practices in school and district settings shaped by others’ policymaking efforts.

Collins, A. M. (2000). Yours is not to reason why. *Education Week, 20*(1), 60.

Hill, H. C. (2007). Mathematical knowledge of middle school teachers: Implications for the No Child Left Behind policy initiative. *Educational Evaluation and Policy Analysis, 29*(2), 95-114.

ABSTRACT: This article explores middle school teachers' mathematical knowledge for teaching and the relationship between such knowledge and teachers' subject matter preparation, certification type, teaching experience, and their students' poverty status. The author administered multiple-choice measures to a nationally representative sample of teachers and found that those with more mathematical course work, a subject-specific certification, and high school teaching experience tended to possess higher levels of teaching-specific mathematical knowledge. However teachers with strong mathematical knowledge for teaching are, like those with full credentials and preparation, distributed unequally across the population of U.S. students. Specifically, more affluent students are more likely to encounter more knowledgeable teachers. The author discusses the implications of this for current U.S. policies aimed at improving teacher quality.

Hill, H. C., & Charalambos, C. Y. (2012). Teacher knowledge, curriculum materials, and quality of instruction: Lessons learned and open issues. *Journal of Curriculum Studies, 44*(4), 559-576.

ABSTRACT: This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in the richness of the mathematical language employed during instruction, the explanations offered, the avoidance of errors, and teachers' capacity to highlight key mathematical ideas and use them to weave the lesson activities. By virtue of being ambitious, the curriculum materials set the stage for engaging students in mathematical thinking and reasoning; at the same time, they amplified the demands for enactment, especially for the low-MKT teachers. The analysis also helped develop three tentative hypotheses regarding the joint contribution of MKT and the curriculum materials: when supportive and when followed closely, curriculum materials can lead to high-quality instruction, even for low-MKT teachers; in contrast, when unsupportive, they can lead to problematic instruction, particularly for low-MKT teachers; high-MKT teachers, on the other hand, might be able to compensate for some of the limitations of the curriculum materials and offer high-quality instruction. This paper discusses the policy implications of these findings and points to open issues warranting further investigation.

Mac Iver, M. A., & Mac Iver, D. J. (2009). Urban middle-grade student mathematics achievement growth under comprehensive school reform. *Journal of Educational Research, 102*(3), 223–236.

ABSTRACT: Recognizing the need to implement standards based instructional materials with school wide coherence led some Philadelphia schools to adopt whole-school reform (WSR) models during the late 1990s. The authors report on the relation between mathematics achievement growth for middle-grade students on the Pennsylvania System of School Assessments and the number of years schools implemented either a WSR model with National Science Foundation-supported mathematics curriculum or a WSR model without a mathematics curriculum component, from 1997 to 2000. As the authors hypothesized, mathematics achievement gains (Grades 5–8) were positively related to the number of years those schools were implementing a specific mathematics curricular reform. Additional analyses indicated that the relation held for both computation skills and ability to apply mathematics concepts.

Monaghan, S. R. (2013). *Textbooks, teachers, and middle school mathematics student achievement* (Doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 1469609858)

ABSTRACT: The purpose of this study was to extend the research on textbook effectiveness to a situated investigation of a single large urban school district in which middle schools were given a choice in selecting from three textbooks for mathematics instruction: a reform textbook, a commercially produced textbook developed in response to mathematics standards, and a traditional textbook. Its genesis is rooted in the efforts in the mathematics education community to investigate the interaction of teachers and mathematics curriculum materials, but in light of the shift to an accountability policy climate in public education. In particular, this study sought to determine whether the type of textbook selected by a school, moderated by the human capital of the teachers teaching mathematics, and the interaction of those variables was associated with increased student mathematics achievement on the mathematics portion of the eighth grade statewide standardized test. Hierarchical linear modeling (HLM) was used to investigate models relating to textbook selection, components of teacher human capital, and their interaction. Contrary to the initial hypothesis, the interaction of textbook selection and components of human capital were not found to be significantly associated with student achievement. However, the selection of a reform mathematics textbook (CMP) over other more traditional texts was associated with student achievement, but accounted for very little of the variance in student test scores. To further explicate the interaction of textbook selection with school factors, logistic regression was used to investigate the association between school factors and the selection of a reform textbook. The demographics of the school (i.e. race, SES, ELL) were not associated with the school selecting a reform mathematics textbook. However, one component of teacher human capital, expertise (a component constructed from data about teacher certification, mathematics specialization, and participation in math focused professional development) was associated with the selection of a reform textbook. This study suggests there is a connection between teacher human capital, the use of reform texts and student achievement; however further investigation is needed to understand the mechanisms at work.

Phillips, E. (1995). *A response to “A research base supporting long-term algebra reform?”* Paper presented at the 17th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH.

ABSTRACT: This paper is a reaction to a plenary address, "A Research Base Supporting Long Term Algebra Reform?" by James Kaput (SE 057 182). The reactions fall into three categories: comments on Kaput's dimensions of algebra reform, a brief discussion of algebra and algebra reform from the viewpoint of a curriculum developer of the Connected Mathematics Project (CMP), and some concerns about Kaput's three stages of reform.

Ridgeway, J. E., Zawojewski, J. S., Hover, M. N., & Lambdin, D. V. (2003). Student attainment in the *Connected Mathematics* Curriculum. In S. L. Senk & D. R. Thompson (Eds.) *Standards-based school mathematics curricula: What are they? What do students learn?* (pp. 193-224). Hillsdale, NJ: Lawrence Erlbaum Associates.

Ridgeway, J. E., Zawojewski, J., & Hoover, M. (2000). Problematising evidence-based policy and practice. *Evaluation and Research in Education, 14*(3 & 4), 181-192.

ABSTRACT: Evidence-based policy and practice (EBPP) is widely advocated, and for good reason. Here, some challenges to EBPP are identified, illustrated by a large-scale evaluation of a major curriculum development project. Problems include: changes in educational goals, which necessitate the development of new measures of attainment; different time lines over which different patterns of result emerge; the challenge of defining a complex treatment, such as a new curriculum; and the variability of effect size in different classrooms. Several approaches are offered as responses to these challenges. The paper argues that much of the work on EBPP has focused on practice rather than on policy. Evidence-based policy will require detailed work on descriptions of systems and on systems change; more significantly, it will require the development of a new field of endeavor, associated with macro-systemic change, that is to say, the study of systems undergoing radical change.

Slavin, R., Lake, C., & Groff, C. (2007). Effective programs in middle and high school mathematics: A best-evidence synthesis. *Review of Educational Research, 79*(2), 839-911.

ABSTRACT: This article reviews research on the achievement outcomes of mathematics programs for middle and high schools. Study inclusion requirements include use of a randomized or matched control group, a study duration of at least 12 weeks, and equality at pretest. There were 100 qualifying studies, 26 of which used random assignment to treatments. Effect sizes were very small for mathematics curricula and for computer-assisted instruction. Positive effects were found for two cooperative learning programs. Outcomes were similar for disadvantaged and nondisadvantaged students and for students of different ethnicities. Consistent with an earlier review of elementary programs, this article concludes that programs that affect daily teaching practices and student interactions have more promise than those emphasizing textbooks or technology alone.

Smith III, J. P., & Star, J. R. (2007). Expanding the notion of impact of K-12 Standards-based mathematics and reform calculus programs. *Journal for Research in Mathematics Education, 38*(1), 3-34

ABSTRACT: Research on the impact of Standards-based, K-12 mathematics programs (i.e., written curricula and associated teaching practices) and of reform calculus programs has focused primarily on student achievement and secondarily, and rather ineffectively, on student attitudes. This research has shown that reform programs have competed well with traditional programs in terms of student achievement. Results for attitude change have been much less conclusive because of conceptual and methodological problems. We critically review this literature to argue for broader conceptions of impact that target new dimensions of program effect and examine interactions between dimensions. We also briefly present the conceptualization, design, and broad results of one study, the Mathematical Transitions Project (MTP), which expanded the range of impact along those lines. The MTP results reveal substantial diversity in students' experience within and between research sites, different patterns of experience between high school and university students, and surprising relationships between achievement and attitude for some students.

Star, J. R., & Hoffmann, A. J. (2002). Assessing students' conceptions of reform mathematics. In D. Mewborn, P. Sztajn, D. White, H. Wiegel, R. Bryant, & K. Nooney (Eds.), *Proceedings of the twenty-fourth annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education* (pp. 1729-1732). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

ABSTRACT: As the use of NSF-sponsored, reform-oriented mathematics curricula has become more prevalent across the US, an increasing number of researchers are attempting to study the "impact" of reform. In particular, mathematics educators are interested in determining whether reforms are having the desired effects on students, particularly with respect to the learning of mathematical content and the improvement of attitudes about mathematics. In this effort, researchers have used a variety of methods, and have looked at a variety of variables, in order to assess the impact of reform. In many cases, such research assesses reform by looking closely at students' scores on tests or their strategies for solving certain kinds of problems. For example, Riordan & Noyce (2001) assessed reform's impact by comparing students' scores on standardized achievement tests. Other researchers have used structured interviews, classroom observations, and more interpretive or ethnographic methods to assess the impact of reform (e.g., Boaler,1997). Both of these methodologies are useful in assessing the impact that reform mathematics curricula are having on students. An alternative evaluation of the impact of reform that has not been as widely used is through the use of survey instruments. Surveys have been widely and reliably used to assess students' motivation (Pintrich, Smith, Garcia, & McKeachie, 1993), beliefs and attitudes (Kenney & Silver, 1997), and interest (Köller, Baumert, & Schnabel, 2001). We propose to add to this literature by using a survey to study the impact of reform on students' conceptions of mathematics.

Star, J. R., & Hoffmann, A. J. (2005). Assessing the impact of Standards-based curricula: Investigating students’ epistemological conceptions of mathematics. *The Mathematics Educator, 15*(2), 25-34.

ABSTRACT: Since the advent of the NCTM Standards (1989), mathematics educators have been faced with the challenge of assessing the impact of Standards-based (or “reform”) curricula. Research on the impact of Standards-based curricula has predominantly focused on student achievement; here we consider an alternative: Students’ epistemological conceptions of mathematics. 297 participants were administered a Likert-scale survey instrument, the Conceptions of Mathematics Inventory. Of these, 163 had not experienced Standards-based curricula, while the rest had used a Standards-based curriculum for over three years. Our results indicate that students at the Standards-based site expressed more sophisticated epistemological conceptions of mathematics than those of the students from the non-Standards-based site. We interpret this result to suggest that implementation of Standards-based curricula may be having an effect on students’ epistemological conceptions of mathematics.

Star, J. R., Smith III, J. P., & Jansen, A. J. (2008). What students notice as different between reform and traditional mathematics programs. *Journal for Research in Mathematics Education, 39*(1), 9-32.

ABSTRACT: Research on the impact of Standards-based mathematics and reform calculus curricula has largely focused on changes in achievement and attitudes, generally ignoring how students experience these new programs. This study was designed to address that deficit. As part of a larger effort to characterize students' transitions into and out of reform programs, we analyzed how 93 high school and college students perceived Standards-based and reform calculus programs as different from traditional ones. Results show considerable diversity across and even within sites. Nearly all students reported differences, but high-impact differences, like Content, were not always related to curriculum type (reform or traditional). Students' perceptions aligned moderately well with those of reform curriculum authors, e.g., concerning Typical Problems. These results show that students' responses to reform programs can be quite diverse and only partially aligned with adults' views.