Spacing and Formative Assessment

• In Event: Bridging Research and Practice: From Cognitive Principles to Design Principles of Curriculum, Instruction, and Assessment

Abstract

Objectives and Purpose
Our work is focused on applying two cognitively-based instructional design principles: (1) spaced practice and (2) focused quizzing with feedback to the redesign of the Connected Mathematics Program 2 (CMP2) curriculum. Doing so requires a clear and consistent definition of “what” is to be learned and when it is introduced, practiced, assessed, and ostensibly mastered over the three-year span of the curriculum. Therefore, the purpose of our work is twofold: (1) to identify skills that are being practiced and assessed, when this occurs, and with what frequency, with recommendations for modifications, and (2) to conduct empirical studies of “optimal” patterns for the spacing of practice and feedback.

Theoretical Framework
The IES Practice Guide (2007) provides several research-based recommendations for improving instruction, including spacing learning over time and using focused quizzing. Considerable research has shown retention benefits when learners acquire knowledge over multiple points in time compared to learning via “massed” practice, a phenomenon dubbed “the spacing effect” (see Pashler, et al., 2007b; Rohrer & Taylor, 2007). Complementary to the “spacing effect” is a second instructional design principle focused on quizzing and assessment. Research on the “testing effect” (e.g., Roediger & Karpicke, 2006, Butler & Roediger, 2007) suggests that testing activities are successful compared to restudy in part because they prompt students to retrieve information, reflect on the state of their knowledge based on feedback, and offer opportunities to transfer knowledge to new problems or situations. Well-designed cycles of testing with feedback with opportunities for knowledge updating can support students in mastery and retention of desired skills (e.g., Pavlik et al., 2007).

Methods & Data Sources
To implement and test principles of spacing and testing we first identified the knowledge components to be mastered in CMP and traced the occurrences from initial mastery to subsequent opportunities for practice and assessment. The knowledge components—skills, context, procedures, and responses (see Figure 3) – consisted of 148 skills and about 70 prerequisite relationships among them. These were mapped within and across units from grade 6 to grade 8 by tagging all practice and test questions in the CMP2 curriculum. We then determined the practice frequency of specific skills as well as relationships between practice problems and assessment problems within and across CMP2 lessons and units.

Conclusions and Scholarly Significance
Our mapping of CMP2 reveals that the practice and assessment of skills does not follow any noticeable and consistent pattern, certainly not one often associated with effective spaced practice (see e.g., Figure 4; Karpicke & Roediger, 2010). This analysis suggests a variety of changes to the curricular materials at the “local” level of lessons and the “global” level of curricular units. Examples of such proposed changes will be presented. The work also supports the need for empirical studies to determine optimal patterns for the practice and assessment of specific skills, including whether skills varying in complexity and difficulty require differential practice and assessment plans to maximize student mastery and retention. Direct evaluation of these issues via within-classroom experiments will also be presented.

Authors

• Kevin Dietz, University of Illinois at Chicago

• Susan R. Goldman, University of Illinois at Chicago

• Neil T. Heffernan, Worcester Polytechnic Institute

• Cristina L. Heffernan, University of Pittsburgh

• James W. Pellegrino, University of Illinois at Chicago

• Deena Soffer Goldstein, University of Illinois at Chicago