Improving Mathematical Learning Outcomes Through Applying Principles of Spaced Practice and Assessment With Feedback

• In Event: Bridging Research and Practice: Findings From the National Center on Cognition and Mathematics Instruction

Abstract

This poster reviews two studies that investigate how applying the cognitive principles of spaced practice and assessment with feedback can improve mathematical learning outcomes. The first study investigates whether an online system that automatically reassesses student knowledge and provides relearning opportunities improves long-term retention for individual students and across specific mathematical skills. Over a single school year, 97 8th-grade students were pretested on a set of mathematical knowledge and skills that were previously learned and then subsequently practiced them until evidence of mastery was exhibited on each of the skills. After mastery, students received automatic online reassessment and relearning opportunities for half the skills, while the other half were not further assessed. End-of-year post-test results revealed better performance on the problem sets that were periodically reassessed and relearned if needed. Furthermore, reassessment and relearning was especially beneficial for students with low pre-test performance (poor retention of prior knowledge) and for more difficult skills.

The second study investigates whether the practice and reacquisition of mastery of relevant prior skills aid in the acquisition of new mathematical content. In redesigning the CMP curriculum, our work has largely focused on preparing students to learn new material in upcoming units by engaging in spaced practice with feedback on relevant concepts mastered in earlier units and grades. The determination of “relevant” previously mastered concepts was based upon our extensive mapping of CMP concepts from grade 6 to grade 8. The mapping identified the CMP concepts practiced or assessed in the context of the overall set of homework and assessment items found in the curriculum. We hypothesized that students who are provided opportunities to re-master relevant prior skills would be better prepared to learn new mathematical content and, therefore, would demonstrate higher levels of proficiency on these new skills compared to students who did not receive opportunities for re-mastery of relevant prior skills. Although the results differed depending on the mathematical content taught in each unit and the level of skill re-mastery before learning the new unit, there was evidence of a positive impact of prerequisite skill re-mastery on the acquisition of the new lesson content.

The educational implications of both studies will be discussed with respect to the role of distributed practice and reassessment of prior learning in the design of curriculum and instruction and the potential for positive impacts on student learning and retention of critical mathematical knowledge within and across academic years.

Authors

• Deena Soffer Goldstein, University of Illinois at Chicago

• James W. Pellegrino, University of Illinois at Chicago

• Susan R. Goldman, University of Illinois at Chicago

• Timothy Matthew Stoelinga, University of Illinois at Chicago

• Neil T. Heffernan, Worcester Polytechnic Institute

• Cristina Heffernan, Worcester Polytechnic Institute