Research

Current research

My research primarily concerns mathematical cognition, specifically the role of working memory and executive control in mathematical cognition. In my dissertation, I investigated the role of working memory in people's fraction strategies. Experiment 1 used an open-ended questioning approach to determine what types of strategies people tend to use when they are asked to mentally compare the size of two fractions. The data revealed reaction time differences between computational strategies (such as common denominators or cross multiplication) and concept-based strategies (such as benchmarking). However, it is not clear if these differences are due to the CHOICE of strategy or the EXECUTION of the selected strategy. Experiment 2 used the choice/no-choice methodology to investigate the roles of phonological and visuo-spatial working memory within these strategy types. I found that fraction comparison uses both visuo-spatial and, to a lesser extent, phonological resources. Perhaps surprisingly, the working memory load effect on computational strategies was greater than for conceptual strategies.

I am currently working to further the results of the dissertation by investigating the working memory load effects that result from varying the working memory load task (either a passive, recognition-based task, or an active, recall-based task).

Information

My curriculum vitae (pdf)

Various documents

Here are the slides to a talk given at the Research Council for Mathematics Learning in Rome, GA in March 2009.
This is a short note I wrote in a course on nonparametric statistics regarding a correction to a chapter in the NIST Stats Handbook. I think the chapter has since been corrected, but the note remains for those who are interested in the mathematics.