In a brain imaging study of children learning algebra, it is shown that the same regions are active in children solving equations as are active in experienced adults solving equations. As with adults, practice in symbol manipulation produces a reduced activation in prefrontal cortex area. However, unlike adults, practice seems also to produce a decrease in a parietal area that is holding an image of the equation. This finding suggests that adolescents' brain responses are more plastic and change more with practice. These results are integrated in a cognitive model that predicts both the behavioral and brain imaging results.T he study reported here integrates behavioral methods, functional brain imaging (functional MRI), and cognitive modeling to study how children learn to solve equations. In particular, the children were solving equations like the following: 7x ϩ 1 ϭ 29. Past research with adult college students (1) modeled algebra equation solving by the interaction of three cognitive modules in the adaptive control of thought-rational (ACT-R) cognitive architecture (2, 3). There was an imaginal module that held a representation of the equation and performed imagined transformations on the equations. There was a retrieval module that retrieved algebraic rules and arithmetic facts in the solution of this equation. Finally, there was a manual module that programmed the output of the answer by the hand. A region in the left parietal cortex, which has been associated with imagery (4-6) and spatial processing (7) in other studies, was found to correspond to the imaginal module. A region in the left prefrontal cortex, which has been associated with retrieval in other studies (8)(9)(10)(11)(12)(13)(14), was found to correspond to the retrieval module. Finally, a region in the left motor and sensory cortices, which controls the right hand, was found to correspond to the manual module.After having identified these regions in algebra equation solving, we performed a series of experiments to determine whether they were specifically involved in algebra or were also involved in nonmathematical information-processing tasks (1,15,16). Similar involvement of these regions was found in a nonmathematical isomorph of algebra (artificial algebra) (1). Subsequent research (15), in which college students practiced the isomorph, found a speed-up that could be accounted for entirely in terms of reduced retrieval time. This finding was reflected in reduced activation in the prefrontal region of interest. There was not a comparable reduction in either the motor or parietal region.The present research addresses the question of whether the brain activation patterns observed from adults will be shown in children learning algebra. Specifically, do children who are just learning equation solving show activation of the same regions as in adults' algebra (1) and will their improvement be explained in terms of reduction just in the prefrontal retrieval region shown in adults' artificial algebra learning (15)? There is reason to suspect that we...

This study examines the use of engineering design to facilitate science reasoning in high-needs, urban classrooms. The Design for Science unit utilizes scaffolds consistent with reform science instruction to assist students in constructing a design solution to satisfy a need from their everyday lives. This provides a meaningful context in which students could reason scientifically. Eighth grade students from two urban schools participated in the unit. Both schools contained large percentages of racial/ethnic minority and economically disadvantaged students. Students demonstrated statistically significant improvement on a paper-and-pencil, multiple-choice pre and post assessment. The results compare favorably with both a highquality inquiry science unit and a traditional textbook curriculum. Implications for the use of design-based curricula as a viable alternative for teaching science reasoning in high-needs, urban settings are discussed.

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She teaches design studios and lecture courses on developing creativity and research skills. Her current research focuses on identifying impacts of different factors on ideation of designers and engineers, developing instructional materials for design ideation, and foundations of innovation. She often conducts workshops on design thinking to a diverse range of groups including student and professional engineers and faculty member from different universities.