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Integrating Cognitive Principles to Redesign a Middle School Math Curriculum

Integrating Cognitive Principles to Redesign a Middle School Math Curriculum Jodi L. Davenport (jdavenp@wested.org) WestEd STEM Program, 300 Lakeside Drive, 25 th Floor Oakland, CA 94612 USA Yvonne S. Kao (ykao@wested.org) WestEd STEM Program, 400 Seaport Court, Suite 222 Redwood City, CA 94063 USA Steven A. Schneider (sschnei@wested.org) WestEd STEM Program, 400 Seaport Court, Suite 222 Redwood City, CA 94063 USA principles to redesign Connected Mathematics Project 2 (CMP2), a widely-used middle school (grades 6-8) mathematics curriculum. The Math Center team selected cognitive-based principles shown to improve student learning: 1) integrating visual with verbal information to promote the integration of concepts, 2) prompting for self- explanation of correct and incorrect worked examples, 3) carefully spacing the learning of critical content and skills over time, and 4) using quizzes to provide focused feedback and adjust instruction to the needs of students. The CMP2 curriculum is an NSF-funded, research-based curriculum for grades 6-8 that covers topics emphasized in both national and state standards and aligns well with key ideas from the NCTM (2006) Focal Points. Key features of the curriculum are that it (1) is organized around important mathematics ideas and processes, e.g., number sense, symbolic reasoning, and probability, (2) is problem- centered, and (3) builds and connects concepts across problems, units, and grades. Each year of the curriculum is divided into eight units; each unit includes a student booklet and accompanying teacher materials to support instructional practice. Applying the principles to revise instructional materials (e.g., the print curriculum) and instructional practice (e.g., what happens in the classroom) required expertise across many fields. Teams devoted to cognition research, mathematics, professional development, and production collaborated to ensure that the revised materials were grounded in the research findings, were mathematically accurate and appropriate (in terms of student development and curriculum standards), were clearly specified for teachers, and were produced with a high level of technical quality. The iterative, multi-layered design process that we have developed for integrating the cognitive principles with the CMP2 curriculum applies not only in the context of mathematics instruction, but also to bridging research with instructional design across content areas. Abstract Does a middle school mathematics curriculum that is redesigned using principles based in cognitive research improve student outcomes? To test whether research can be effectively translated into practice, the Connected Mathematics Project 2 (CMP2) curriculum was revised according to four principles 1) integrating visual with verbal information, 2) prompting for self-explanation of correct and incorrect worked examples, 3) spacing learning over time, and 4) using formative assessment. This study of 6 th grade and 8 th grade mathematics education addresses the research question: “Do students who are exposed to specific redesigned CMP2 curriculum modules (treatment) exhibit greater improvements in mathematics performance in the module-specific content area than their counterparts exposed to the regular CMP2 curriculum (control)?” Preliminary analyses show statistically significant effects of the redesigned CMP2 units in three of the four curricular units in this study. Keywords: cognitive psychology; mathematics; math education; education; spaced learning; formative assessment; worked examples; visual representations Introduction Lab-based research in cognitive and learning sciences has led to a number of recommendations for improving learning and instruction (e.g., Pashler et al., 2007). Tightly controlled experiments have shown that learning can be enhanced with strategies such as mapping between visual representations, prompting for explanation of worked examples, using quizzing to promote learning and spacing practice opportunities over time. The vast majority of studies focus on specific strategies in isolation rather than how principles may be combined. If these research findings are to be meaningfully applied to classrooms, the synergistic effects of the strategies must be tested in real-world settings. In the current paper, we describe a large-scale effort of the National Center on Cognition and Mathematics Instruction (Math Center) in the United States to bridge research and practice by applying cognitive principles to redesign an existing mathematics curriculum and testing the efficacy of these materials. To test the synergistic effects of research-based instructional strategies, the Math Center applied four The Principles The following four principles were selected as they have demonstrated effectiveness in student learning, have broad