
How do different notations and representations impact the way people think about proportion?
Learning fractions is extremely difficult for many children (and adults!), but recent work by me and by others suggests that learning fractions is extremely important for later math learning, especially algebra.
One of the things that makes learning about fractions so difficult is the many ways it can be talked about and represented. In my work, I'm interested in how different aspects of fraction information (for example: ratio, proportion, partwhole relationships, magnitude information, etc.) are understood using different notations and representations (for example: fractions, decimals, pie charts, number lines, discrete items, etc.). In particular, I'm interested in which notations/representations may be best matched for teaching specific types of fraction concepts, and not good for teaching other concepts. This helps us learn more about how our minds work to mentally represent information and communicate it to others (through notation and symbols). Also, if we have a better understanding of how children and adults think about fractions and use different representations, we may be able to construct curricula that better match the way children learn. 
How can we improve people's attitudes toward math problem solving and persistence?
The number of Science, Technology, Engineering, and Math graduates is staggeringly low, even though these fields are becoming more and more important.
In my work, I'm interested in what kind of subjective factors influence people's decisions to pursue math and computer science fields. In particular, we are looking at how people's ideas about problemsolving and "debugging" as normal aspects of their math and computer science activities impacts their persistence and interest in these fields more generally. 