Investigating Changes in Students’ Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra (NSF #1651571)

This project is examining how learning about a new STEM concept changes students’ reasoning about concepts that are not new to them and focuses mainly on mathematics concepts. We also examine how to teach new concepts in ways that enhance students’ reasoning about not-new concepts.

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Target Audience: 
Algebra Students and Teachers
STEM Discipline(s): 
Mathematics
What Issue(s) in STEM Education is your Project Addressing?: 

The main issue our project addresses is how students’ reasoning about concepts that are not new to them changes when learning about a new concept, and we call this phenomenon backward transfer. We specifically focus on mathematics, but believe our backward transfer research is highly relevant within and across STEM content domains more broadly. For instance, this research is relevant to how learning about the relationships between position, velocity, and acceleration in physics could influence students’ reasoning about derivatives and integrals in calculus, and vice versa.

One way our project has been innovative is by being the first to use contrasting cases to examine backward transfer (i.e., comparing distinctly different instructional environments). By comparing backward transfer across contrasting cases (e.g., business-as-usual classroom environments, summer math camps), we have gained insights into backward transfer we would not have gained had we examined a single instructional environment alone. Another way our project has been innovative is by being the first to develop and test mathematics activities designed to teach students new concepts, while simultaneously enhancing their reasoning about concepts that are not new to them.

What are your Findings?: 

One finding relevant to STEM education is that teaching students about a new concept with a business-as-usual instructional approach led to extensive and varied unintended backward-transfer effects. A second finding is that, compared to a business-as-usual approach, when a new concept was taught using an approach designed to simultaneously produce particular backward-transfer effects, fewer unintended backward transfer effects associated with the not-new concept were realized. A third finding is that the types of changes in reasoning that students exhibited about a not-new concept after learning about a new concept, were related to their level of understanding of the not-new concept.

PI: 
Charles Hohensee