Mathematical competency is vital to success in engineering. Competency requires not only short-term mastery of mathematical concepts, but also long-term retention. Research in cognitive psychology shows that the more times information is retrieved from memory, the more likely it is to be remembered over the long-term. Research also shows that increasing the amount of time between retrievals increases long-term retention. Which of these interventions—increasing the amount or the temporal spacing of retrieval practice—has the greater impact on long-term retention? Supported by NSF’s Improving Undergraduate STEM Education (IUSE) program, we answered this question by independently manipulating the amount and the spacing of retrieval practice in a precalculus course for engineering students. This was done by varying the number of quiz questions concerning key precalculus objectives (amount of practice) and varying whether those questions were massed on a single quiz or distributed across quizzes in multiple weeks (spacing of practice). Long-term retention was assessed in a test of precalculus knowledge administered one month after the end of the precalculus course. We found that students were significantly more likely to retain precalculus objectives when quiz questions had been spaced versus massed. Increasing the number of quiz questions did not significantly affect retention. These findings suggest that educators wishing to increase students’ long-term retention of mathematics knowledge should increase the spacing, rather than the amount, of retrieval practice in their courses.
Robin Hopkins is a graduate student in the Experimental Psychology PhD program at the University of Louisville. Her main research interests include learning in the classroom and eyewitness memory.
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.
Campbell Rightmyer Bego is currently pursuing a doctoral degree in Cognitive Science at the University of Louisville. She researches STEM learning with a focus on math learning, spatial representations, and active learning strategies. Ms. Bego is also assisting the Engineering Fundamentals Department in the Speed School in performing student retention research. She is particularly interested in interventions and teaching methods that alleviate working memory constraints and increase both learning retention and student retention in engineering. Ms. Bego is also a registered professional mechanical engineer in New York State.
Jeffrey L. Hieb is an Associate Professor in the Department of Engineering Fundamentals at the University of Louisville. He graduated from Furman University in 1992 with degrees in Computer Science and Philosophy. After 10 years working in industry, he returned to school, completing his Ph.D. in Computer Science Engineering at the University of Louisville’s Speed School of Engineering in 2008. Since completing his degree, he has been teaching engineering mathematics courses and continuing his dissertation research in cyber security for industrial control systems. In his teaching, Dr. Hieb focuses on innovative and effective use of tablets, digital ink, and other technology and is currently investigating the use of the flipped classroom model and collaborative learning. His research in cyber security for industrial control systems is focused on high assurance field devices using microkernel architectures.
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