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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, K. (2010a). Enacting proof in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351-382.

ABSTRACT: Discussions about school mathematics often address the importance of reasoning and proving for building students’ understanding of mathematics. However, there is little research examining how teachers enact tasks designed to engage students in justifying and proving in the classroom. This article presents results of a study investigating the processes and outcomes of implementing proof-related tasks in the classroom. Data collection consisted of observations of 7 middle school classrooms during implementation of proof-related tasks-tasks providing opportunities for students to produce generalizations, conjectures, or proofs-in the Connected Mathematics Project (CMP) curriculum by teachers experienced in using the materials. The findings suggest that students’ experiences with such tasks are insufficient for developing an understanding of what constitutes valid mathematical justification.

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Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71–80. doi:10.1016/j.ijer.2013.06.005

ABSTRACT: Over the past two decades, standards documents have emphasized the importance of developing students’ abilities to generate and critique mathematical arguments across all grade levels. However, little is known about the opportunities elementary textbooks provide for students to learn mathematical argumentation. We analyzed seven upper elementary (ages 9–11) mathematics textbooks published in the U.S., focusing specifically on reasoning-and-proving opportunities in written tasks, and found that the average percentage of such tasks was 3.7%. Further, analyses of the task purpose and type of justification warranted revealed distinctions between the text materials in terms of the kinds of reasoning-and-proving activities prompted and the placement of tasks in the lesson sections. Specifically, textbooks developed based on research and written to align with curriculum and instruction standards were more likely to have reasoning-and-proving tasks within the narrative and student exercise sections than other texts. We discuss implications for the opportunities to learn reasoning-and-proving in elementary classrooms.

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

Ellis, A. B. (2007). Connections between generalizing and justifying: Students reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194–229.

ABSTRACT: Research investigating algebra students’ abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students’ errors, less is known about what students do understand to be general and convincing. This study examines the ways in which seven middle school students generalized and justified while exploring linear functions. Students’ generalizations and proof schemes were identified and categorized in order to establish connections between types of generalizations and types of justifications. These connections led to the identification of four mechanisms for change that supported students’ engagement in increasingly sophisticated forms of algebraic reasoning: (a) iterative action/reflection cycles, (b) mathematical focus, (c), generalizations that promote deductive reasoning, and (d) influence of deductive reasoning on generalizing.

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Stylianides, G. J. (2007). Investigating the guidance offered to teachers in curriculum materials: The case of proof in mathematics. International Journal of Science and Mathematics Education, 6(1), 191 -215.

ABSTRACT: Despite widespread agreement that proof should be central to all students’ mathematical experiences, many students demonstrate poor ability with it. The curriculum can play an important role in enhancing students’ proof capabilities: teachers’ decisions about what to implement in their classrooms, and how to implement it, are mediated through the curriculum materials they use. Yet, little research has focused on how proof is promoted in mathematics curriculum materials and, more specifically, on the guidance that curriculum materials offer to teachers to enact the proof opportunities designed in the curriculum. This paper presents an analytic approach that can be used in the examination of the guidance curriculum materials offer to teachers to implement in their classrooms the proof opportunities designed in the curriculum. Also, it presents findings obtained from application of this approach to an analysis of a popular US reform-based mathematics curriculum. Implications for curriculum design and research are discussed.

Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11, 258–288.

ABSTRACT: Despite widespread agreement that the activity of reasoning-and-proving should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that teachers make about what tasks to implement in their classrooms and when and how to implement them are mediated by the textbooks they use. Yet, little is known about how reasoning-and-proving is promoted in school mathematics textbooks. In this article, I present an analytic/methodological approach for the examination of the opportunities designed in mathematics textbooks for students to engage in reasoning-and-proving. In addition, I exemplify the utility of the approach in an examination of a strategically selected American mathematics textbook series. I use the findings from this examination as a context to discuss issues of textbook design in the domain of reasoning-and-proving that pertain to any textbook series.

Wilson, Nazemi, Jackson, Wilhelm (2019). Investigating Teaching in Conceptually Oriented Mathematics Classrooms Characterized by African American Student Success. Journal for Research in Mathematics Education. Vol. 50, No. 4, 362-400

ABSTRACT: This article outlines several forms of instructional practice that distinguished middle-grades mathematics classrooms that were organized around conceptually oriented activity and marked by African American students’ success on state assessments. We identified these forms of practice based on a comparative analysis of teaching in (a) classrooms in which there was evidence of conceptually oriented instruction and in which African American students performed better than predicted by their previous state assessment scores and (b) classrooms in which there was evidence of conceptually oriented instruction but in which African American students did not perform better than predicted on previous state assessment scores. The resulting forms of practice can inform professional learning for preservice and in-service teachers.

NOTE: This study was done in CMP classrooms.