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Introducing Desirable Difficulty in Engineering Mathematics with Spaced Retrieval Practice

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2021 ASEE Virtual Annual Conference Content Access


Virtual Conference

Publication Date

July 26, 2021

Start Date

July 26, 2021

End Date

July 19, 2022

Conference Session

NSF Grantees Poster Session

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NSF Grantees Poster Session

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Campbell R. Bego University of Louisville Orcid 16x16

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An Assistant Professor with research in engineering education, Campbell R. Bego, PhD, PE, is interested
in improving STEM student learning and gaining understanding of STEM-specific learning mechanisms
through controlled implementations of evidence-based practices in the classroom. Dr. Bego has
an undergraduate Mechanical Engineering degree from Columbia University, a Professional Engineering
license in the state of NY, and a doctorate in Cognitive Science.

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Patricia A. Ralston University of Louisville

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Dr. Patricia A. S. Ralston is Professor and Chair of the Department of Engineering Fundamentals at the University of Louisville. She received her B.S., MEng, and PhD degrees in chemical engineering from the University of Louisville. Dr. Ralston teaches undergraduate engineering mathematics and is currently involved in educational research on the effective use of technology in engineering education, the incorporation of critical thinking in undergraduate engineering education, and retention of engineering students. She leads a research group whose goal is to foster active interdisciplinary research which investigates learning and motivation and whose findings will inform the development of evidence-based interventions to promote retention and student success in engineering. Her fields of technical expertise include process modeling, simulation, and process control.

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Keith B. Lyle University of Louisville


Jason Immekus University of Louisville

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Dr. Immekus is associate professor in the Department of Educational Leadership, Evaluation, and Organizational Development.

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Spaced retrieval practice is an evidence-based, memory-enhancing instructional technique in which students are asked to practice recall multiple times with temporal delays in between [1], [2]. Spacing out practice naturally increases the difficulty of retrieval and reduces immediate performance [3], but it improves memory in the long term [BLIND], [4]. The short-term costs and long-term benefits of spaced retrieval practice can be explained by the concept of desirable difficulty, which proposes that more difficult exercises during the early stages of learning can improve long-term retention [5]. Instructional techniques that improve learning are much needed in introductory engineering courses that establish foundational knowledge and abilities for first-year students. These courses often pose barriers to success in engineering [6]–[9]. Despite the efforts of the mathematics reform movement of 30 years ago to make calculus a pump instead of a filter [10], calculus continues to pose a challenge. To improve performance and retention in engineering mathematics courses, adopting research-based teaching practices such as spaced retrieval practice has the potential to improve learning in barrier courses and increase the number of STEM graduates.

Currently in the second year of a 3-year study (NSF Grant Award #BLIND), we are collecting student performance data from a spaced retrieval practice implementation in engineering mathematics, as well as 9 other undergraduate STEM barrier courses. The engineering mathematics course (Calculus I for Engineers) is a prerequisite for many engineering courses at BLIND university, and therefore it is imperative that students retain the course content. In all courses, we identified 24 target learning objectives in the first half of the semester. In 5 bi-weekly quizzes administered throughout the semester, we assigned each learning objective to either a massed (three questions on the same quiz) or spaced (three questions on three consecutive quizzes) condition. A fourth and final question for all objectives will be asked on a quiz at the end of the semester to measure learning. Our research design is within-subjects, which controls for differences in student ability and effort while giving all students experience with both massed and spaced retrieval practice. In addition, assignment of objectives to conditions is counterbalanced, which controls for differences in the difficulty of different objectives.

In this ASEE 2021 poster and full-length paper, we explore the difficulty introduced by spaced retrieval practice in engineering mathematics. Our research question is: How much does spaced retrieval practice impact short-term performance in engineering mathematics? We compare student performance on questions that are asked in either a massed or spaced condition. We expect that performance will be lower on spaced questions than massed questions. Although this analysis will not reveal whether we have induced desirable difficulty, since we are not assessing long-term learning at this time, it will indicate whether we have imposed additional difficulty with the manipulation of spacing. These intermediate results are important for our understanding of the mechanism by which spaced retrieval practice may enhance learning.

Bego, C. R., & Ralston, P. A., & Lyle, K. B., & Immekus, J. (2021, July), Introducing Desirable Difficulty in Engineering Mathematics with Spaced Retrieval Practice Paper presented at 2021 ASEE Virtual Annual Conference Content Access, Virtual Conference. 10.18260/1-2--37379

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