title: Detecting math problem solving strategies: an investigation into the use of retrospective self-reports, latency and fMRI data.
abstract: This research explores how to determine when mathematical problems are solved by retrieval versus computation strategies. Past research has indicated that verbal reports, solution latencies, and neural imaging all provide imperfect indicators of this distinction. Participants in the current study solved mathematical problems involving two distinct problem types, called 'Pyramid' and 'Formula' problems. Participants were given extensive training solving 3 select Pyramid and 3 select Formula problems. Trained problems were highly practiced, whereas untrained problems were not. The distinction between untrained and trained problems was observed in the data. Untrained problems took longer to solve, more often used procedural strategies and showed a greater activation in the horizontal intraparietal sulcus (HIPS) when compared to trained problems. A classifier fit to the neural distinction between trained-untrained problems successfully predicted training within and between the two problem types. We employed this classifier to generate a prediction of strategy use. By combining evidence from the classifier, problem solving latencies, and retrospective reports, we predicted the strategy used to solve each problem in the scanner and gained unexpected insight into the distinction between different strategies.
authors.affiliation: Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, United States. Electronic address: ctenison@andrew.cmu.edu.
authors.forename: Caitlin
authors.initials: C
authors.lastname: Tenison
authors.affiliation: Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, United States.
authors.forename: Jon M
authors.initials: JM
authors.lastname: Fincham
authors.affiliation: Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, United States.
authors.forename: John R
authors.initials: JR
authors.lastname: Anderson
mesh_terms: D001921:Brain / Q000502:physiology*; D001931:Brain Mapping; D005260:Female; D006801:Humans; D008279:Magnetic Resonance Imaging; D008297:Male; D055641:Mathematical Concepts; D011214:Practice, Psychological; D011340:Problem Solving / Q000502:physiology*; D057566:Self Report; D013997:Time Factors; D055815:Young Adult
keywords: Arithmetic; Problem solving; Strategy assessments; fMRI