# 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.

Bieda, Kristen N., Bowers, David, & Kuchle, Valentin A.B. (2019). The Genre(s) of Argumentation in School Mathematics. *Michigan Reading Journal. *(41)

Nie, B., Cai, J., & Moyer, J. (2009). How a Standards-based mathematics curriculum differs from a traditional curriculum: with a focus on intended treatments of the ideas of variable. *Zentralblatt fuer Didaktik der Mathematik (International Journal on Mathematics Education), 41*(6), 777-792.

ABSTRACT: Analyzing the important features of different curricula is critical to understand their effects on students’ learning of algebra. Since the concept of variable is fundamental in algebra, this article compares the intended treatments of variable in an NSF-funded standards-based middle school curriculum (CMP) and a more traditionally based curriculum (Glencoe Mathematics). We found that CMP introduces variables as quantities that change or vary, and then it uses them to represent relationships. Glencoe Mathematics, on the other hand, treats variables predominantly as placeholders or unknowns, and then it uses them primarily to represent unknowns in equations. We found strong connections among variables, equation solving, and linear functions in CMP. Glencoe Mathematics, in contrast, emphasizes less on the connections between variables and functions or between algebraic equations and functions, but it does have a strong emphasis on the relation between variables and equation solving.

Otten, S., & Soria, V. M. (2014). Relationships between students’ learning and their participation during enactment of middle school algebra tasks. *ZDM*, 46(5), 815–827. doi:10.1007/s11858-014-0572-4

ABSTRACT: This study examines a sequence of four middle school algebra tasks through their enactment in three teachers’ classrooms. The analysis centers on the cognitive demand—the kinds of thinking processes entailed in solving the task—and the participatory demand—the kinds of verbal contributions expected of students—of the task as written in the instructional materials, as set up by the three teachers, and as discussed by the teachers and their students. Relationships between the nature of the task enactments and students’ performance on a pre- and post-test are explored. Findings include the fact that the enacted tasks differed from the written tasks with regard to both the cognitive demand and the participatory demand, which related to students’ lack of success on the post-test. Specifically, cognitive demand declined in the enacted curriculum at different points for different classes, and the participatory demand during enactment tended to involve isolated mathematical terms rather than students verbally expressing mathematical relations.

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.

Star, J. R., Herbel-Eisenmann, B. A., & Smith III, J. P. (2000) Algebraic concepts: What's really new in new curricula?. *Mathematics Teaching in the Middle School, 5*(7). 446-451.

ABSTRACT: Examines 8th grade units from the Connected Mathematics Project (CMP). Identifies differences in older and newer conceptions, fundamental objects of study, typical problems, and typical solution methods in algebra. Also discusses where the issue of what is new in algebra is relevant to many other innovative middle school curricula.

Wasman, D. G. (2000). *An investigation of algebraic reasoning of seventh-and eighth-grade students who have studied from the Connected Mathematics Project curriculum.* (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 61(9). (ProQuest ID No. 727777811)

ABSTRACT: This study investigated algebraic reasoning of seventh and eighth graders' who have studied from the Connected Mathematics Project (CMP) materials. Algebraic reasoning was defined as the process of thinking logically about and applying algebraic concepts as described by NCTM's expectations for grades six through eight students described in the Patterns, Functions, and Algebra Standard outlined in the Principles and Standards for School Mathematics. The seventh and eighth graders represented 75% of the students at their grade level because the other 25% were enrolled in accelerated courses that did not use CMP. In order to document the extent and nature of the use of CMP, all sixth, seventh and eighth grade teachers completed a survey followed by researcher-conducted classroom observations. The Iowa Algebra Aptitude Test (IAAT) was administered to 100-seventh graders and 73-eighth graders. Five-seventh graders and six-eighth graders were randomly selected for individual interviews consisting of a series of twelve algebra tasks.

Students' performance on the IAAT and interview tasks demonstrated the well-developed nature of their understanding and use of algebraic ideas and strategies. Students demonstrated flexibility in their thinking and ability to describe linear relationships in a variety of representations. Students described rate of change arithmetically, algebraically, and/or geometrically in different situations. Students approached problems in a sense-making way, choosing a variety of different strategies (informal and formal) all of which led to correct solutions and reflected strong conceptual understanding of algebraic ideas. Eighth graders were more likely to use symbolic algebra methods to solve problems than the seventh graders, reflecting a natural development of more symbolic strategies. Context played an important role with regard to students' ability to interpret and symbolize mathematical ideas. Students were more likely to represent situations symbolically when they were embedded in a context-rich setting. Some students had difficulty translating from a recursive pattern to an explicit formula and interpreting a graph as a relationship between independent and dependent variables. These same weaknesses have been noted in other research studies indicating that these ideas may require more time or maturity to develop, regardless of the particular curriculum used.

Wu, Z. (2004). *The study of middle school teacher’s understanding and use of mathematical representation in relation to teachers’ zone of proximal development in teaching fractions and algebraic functions.* (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 65(7). (ProQuest ID No. 775173261)

ABSTRACT: This study examined teachers' learning and understanding of mathematical representation through the Middle School Mathematics Project (MSMP) professional development, investigated teachers' use of mathematics representations in teaching fractions and algebraic functions, and addressed patterns of teachers' changes in learning and using representation corresponding to Teachers' Zone of Proximal Development (TZPD). Using a qualitative research design, data were collected over a 2-year period, from eleven participating 6th and 7th grade mathematics teachers from four school districts in Texas in a research-designed professional development workshop that focused on helping teachers understand and use of mathematical representations. Teachers were given two questionnaires and had lessons videotaped before and after the workshop, a survey before the workshop, and learning and discussion videotapes during the workshop. In addition, ten teachers were interviewed to find out the patterns of their changes in learning and using mathematics representations. The results show that all teachers have levels of TZPD which can move to a higher level with the help of capable others. Teachers' knowledge growth is measurable and follows a sequential order of TZPD. Teachers will make transitions once they grasp the specific content and strategies in mathematics representation. The patterns of teacher change depend on their learning and use of mathematics representations and their beliefs about them. This study advocates teachers using mathematics representations as a tool in making connections between concrete and abstract understanding. Teachers should understand and be able to develop multiple representations to facilitate students' conceptual understanding without relying on any one particular representation. They must focus on the conceptual developmental transformation from one representation to another. They should also understand their students' appropriate development levels in mathematical representations. The findings suggest that TZPD can be used as an approach in professional development to design programs for effecting teacher changes. Professional developers should provide teachers with opportunities to interact with peers and reflect on their teaching. More importantly, teachers' differences in beliefs and backgrounds must be considered when designing professional development. In addition, professional development should focus on roles and strategies of representations, with ongoing and sustained support for teachers as they integrate representation strategies into their daily teaching.