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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.

Star, J. R. (2001). Re-conceptualizing procedural knowledge: Innovation and flexibility in equation solving. (Doctoral dissertation). Retrieved from Dissertation Abstracts International, 62(10). (ProQuest ID No. 726024271)

ABSTRACT: The studies described in this thesis explore the development of students' knowledge of mathematical procedures. Students' tendency to develop rote knowledge of procedures has been widely commented on and is generally attributed to a lack of connection to principled knowledge. I postulate an alternative endpoint for the development of procedural knowledge, one that Ryle (1949) called an “intelligent performance" and Skemp (1976) described as "relational." Students demonstrate this capacity when they are able to flexibly use mathematical procedures, especially when they choose to deviate from established solving patterns on particular problems for greater efficiency. The purposes of these studies were (a) to demonstrate that students could develop the ability to execute mathematical procedures "intelligently," and (b) to explore the instructional conditions that facilitate the emergence of this outcome. In three studies, students with no prior knowledge of formal linear equation solving techniques were taught the basic transformations of this domain. After instruction, students engaged in problem-solving sessions in two conditions. In the treatment group, students completed "alternative ordering tasks," where they were asked to re-solve previously completed problems but using a different ordering of steps. When the treatment group engaged in such tasks, the control group instead solved structurally isomorphic equations. In Study 1, 10 students worked individually with the experimenter for 4, 30-minute problem-solving sessions. Eight of the 10 students became very successful solvers of linear equations, discovering sub-goal knowledge and also developing an efficient and consistently used solving heuristic. In Study 2, 36 students engaged in 4 one-hour individual problem-solving sessions. The treatment group students became more innovative and more flexible solvers. Study 3 replicated Study 2 using a classroom rather than an individualized learning environment; similar results were obtained.

These results suggest that alternative ordering tasks may help to support the development of flexible knowledge of procedures. Flexibility is an advantage for acquiring more advanced knowledge and also for solving specific problems most efficiently. With training on considering alternative solutions, students can be assisted in avoiding rote learning of procedures and in developing a rich understanding of why procedures work.

Wilhelm, A. G. (2015). Mathematics teachers’ enactment of cognitively demanding tasks: Investigating links to teachers’ knowledge and conceptions. Journal for Research in Mathematics Education, 45(5), 636–674.

ABSTRACT: This study sought to understand how aspects of middle school mathematics teachers’ knowledge and conceptions are related to their enactment of cognitively demanding tasks. I defined the enactment of cognitively demanding tasks to involve task selection and maintenance of the cognitive demand of high-level tasks and examined those two dimensions of enactment separately. I used multilevel logistic regression models to investigate how mathematical knowledge for teaching and conceptions of teaching and learning mathematics for 213 middle school mathematics teachers were related to their enactment of cognitively demanding tasks. I found that teachers’ mathematical knowledge for teaching and conceptions of teaching and learning mathematics were contingent on one another and significantly related to teachers’ enactment of cognitively demanding tasks.

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