Role Project

The goal of this project is to examine how students solve mathematical problems and manipulate concepts. In the context of the ACT-R theory of human cognition (Anderson & LeBiere, 1998), which allows us to produce computational models of cognition, our research is concerned with mathematical problem solving and its inter-relationship to working memory abilities and cognitive control. Using fMRI, we study brain activation markers of the course of mathematical problem solving and learning as well as those associated with more general attributes such as memory span. We focus on patterns of activation associated with more or less effective strategies for problem solving as well as changes in activation associated with: a) the acquisition of skill related to mathematical problem solving, b) improved memory function, and c) increased attentional capacity.

As any math teacher will attest, students produce frequent errors when solving mathematical problems. Indeed, the number and types of errors can be an important source of information for teachers in determining where students need further instruction. A number of behavioral studies have closely examined the types of errors that occur when solving equations, however, very few studies have determined whether neural regions associated with mathematical processing are important for successful performance. Our goal is to assess whether errors in mathematical performance are associated with activity in neural regions known to instantiate processes required for problem-solving. For example, retrieval efficiency and visuospatial representational abilities may both be associated with greater accuracy. If so, regions undertaking those processes should be engaged to a greater degree when equations are solved correctly than when errors are committed. These studies will help in refining a computerized algebra tutor used to improve mathematical learning in many schools nationwide.


	Role Project The goal of this project is to examine how students solve mathematical problems and manipulate concepts. In the context of the ACT-R theory of human cognition (Anderson & LeBiere, 1998), which allows us to produce computational models of cognition, our research is concerned with mathematical problem solving and its inter-relationship to working memory abilities and cognitive control. Using fMRI, we study brain activation markers of the course of mathematical problem solving and learning as well as those associated with more general attributes such as memory span. We focus on patterns of activation associated with more or less effective strategies for problem solving as well as changes in activation associated with: a) the acquisition of skill related to mathematical problem solving, b) improved memory function, and c) increased attentional capacity. As any math teacher will attest, students produce frequent errors when solving mathematical problems. Indeed, the number and types of errors can be an important source of information for teachers in determining where students need further instruction. A number of behavioral studies have closely examined the types of errors that occur when solving equations, however, very few studies have determined whether neural regions associated with mathematical processing are important for successful performance. Our goal is to assess whether errors in mathematical performance are associated with activity in neural regions known to instantiate processes required for problem-solving. For example, retrieval efficiency and visuospatial representational abilities may both be associated with greater accuracy. If so, regions undertaking those processes should be engaged to a greater degree when equations are solved correctly than when errors are committed. These studies will help in refining a computerized algebra tutor used to improve mathematical learning in many schools nationwide.
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