Applying Cognitive Principles of "Spacing" and "Testing" in the Context of a Curriculum

• In Event: 66.026 - Scaling Up Cognitive Learning Principles to Redesign a Mathematics Curriculum for Improved Learning

Abstract

Consistent with the theme of this symposium, this paper will focus on the challenges of understanding two research-based principles: spacing of practice (e.g., Cepeda, et al., 2006) and focused quizzing (e.g., Butler & Roediger, 2007), in the context of redesign of the Connected Mathematics 2 (CMP2) curriculum. Translating and applying these principles to redesign of CMP2 required that we first grapple with appropriately defining what is being practiced or assessed and when. Thus, we began by mapping the concepts and skills targeted in CMP2 to: (1) trace occurrences from initial mastery to subsequent opportunities for practice and assessment; (2) guide proposed changes in the curricular materials and teacher instructional practices; and (3) guide the design of empirical studies to test effects of altering distribution of practice and assessment opportunities.

All homework and assessment problems were mapped with regard to content knowledge, the context in which the knowledge is tapped (e.g., word problem, graph), the procedure involved in answering (e.g. draw, compute, explain), and the type of response required (e.g. diagram, text, algebraic equation). We identified over 150 “skills” and about 70 prerequisite relationships between them, as well as practice frequency and relationships between the contexts of practice and assessment. Table 1 provides a portion of the mapping of knowledge components to elements of the curriculum with frequencies of occurrence. Overall, we observed considerable variability in how and how much a knowledge component is practiced and assessed in CMP2. The mapping results constrain the redesign changes to the curriculum to better implement both spacing and testing. They also suggested the need for empirical data to better understand optimization of spacing effects over an entire curriculum, especially when prior skills are used in mastering subsequent ones.

One constraint on redesign was that implementation was limited to paper and pencil curricular materials. We supplemented information provided to teachers in the Teacher’s Guide in the form of information about the prerequisite skills for the new skills-to-be-taught in each unit in CMP2. We recommended assessment on these prerequisites prior to beginning a unit, with targeted practice for those where student performance was weak and provided an assessment of tool for each unit. Thus, the redesign was intended to result in teachers evaluating students’ retention of prior skills relevant for the upcoming unit, and providing feedback and additional assessment and practice on prior skills before beginning the new unit.

Simultaneously, we pursued studies where the ASSISTments web-based system allowed for controlled tests of the benefits of various practice and assessment activities. Results in one study suggested that providing assessment and practice of highly relevant and ostensibly mastered prerequisite skills increases students’ acquisition of new material. Another study revealed significant benefits of providing feedback during homework practice.
Our discussion will focus on the conceptual and pragmatic benefits of attempting to translate principles from cognitive research in the context of actual curriculum materials, as well as some inherent constraints on implementation, optimization, and hypothesis testing.

Authors

• Deena Soffer Goldstein, University of Illinois at Chicago

• Cristina Heffernan, Worcester Polytechnic Institute

• Neil T. Heffernan, Worcester Polytechnic Institute

• James W. Pellegrino, University of Illinois at Chicago

• Susan R. Goldman, University of Illinois at Chicago

• Kim Kelly

• Vinoadharen Nair Das, University of Illinois at Chicago