Solve it.

• Why did our manipulations fail to isolate the activity in these regions? • Explanation 1: These regions are not functionally distinct as characterized by ACT-R • Explanation 2: Our task manipulations failed to properly isolate retrieval and transformation • We designed two ACT-R models to determine the plausibility of Explanation 2 • Pure Model: Encompassed our initial assumptions about the design but failed to fit the RT data (R2 = .50) • Mixed Model: Assumed that both manipulations had retrieval and transformation components and fit the RT data well (R2 = .94) Using Cognitive Modeling to Understand the Roles of Prefrontal and Posterior Parietal Cortex in Algebra Problem Solving Jared F. Danker & John R. Anderson Department of Psychology and Center for the Neural Basis of Cognition, Carnegie Mellon University

[1]  John H. Flavell,et al.  Spontaneous verbal rehearsal in a memory task as a function of age , 1966 .

[2]  J. Rubin WHAT THE GOOD LANGUAGE LEARNER CAN TEACH US , 1975 .

[3]  Social processes and proofs of theorems and programs , 1977, POPL.

[4]  G. V. Nakamura,et al.  Memory Strategy Instruction with Children , 1982 .

[5]  Richard E. Mayer,et al.  The Teaching of Learning Strategies. , 1983 .

[6]  Mary W. Olson,et al.  Lessons from Champion Spellers , 1989 .

[7]  Michael Pressley,et al.  Strategies That Improve Children's Memory and Comprehension of Text , 1989, The Elementary School Journal.

[8]  Donald D. Deshler,et al.  An Instructional Model for Teaching Learning Strategies , 1991 .

[9]  J. Rubin,et al.  Can Strategy Instruction Improve Listening Comprehension , 1996 .

[10]  Sharon Vaughn,et al.  The Professional Knowledge Base on Instructional Practices That Support Cognitive Growth for English- Language Learners , 2000 .

[11]  M. Bock SODA Strategy , 2001 .

[12]  H. Lee Swanson,et al.  Instructing Adolescents with Learning Disabilities: A Component and Composite Analysis , 2001 .

[13]  Russell Gersten,et al.  Teaching Expressive Writing to Students with Learning Disabilities: A Meta-Analysis , 2001, The Elementary School Journal.

[14]  John R. Anderson,et al.  An information-processing model of the BOLD response in symbol manipulation tasks , 2003, Psychonomic bulletin & review.

[15]  S. Graham,et al.  Students with learning disabilities and the process of writing: A meta-analysis of SRSD studies. , 2003 .

[16]  N. Nguyen,et al.  An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .

[17]  John R. Anderson,et al.  Human Symbol Manipulation Within an Integrated Cognitive Architecture , 2005, Cogn. Sci..

[18]  John R. Anderson,et al.  The roles of prefrontal and posterior parietal cortex in algebra problem solving: A case of using cognitive modeling to inform neuroimaging data , 2007, NeuroImage.

[19]  J. Hesthaven,et al.  Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations , 2007 .

[20]  Olga Stasová,et al.  Convergence Analysis of Finite Volume Scheme for Nonlinear Tensor Anisotropic Diffusion in Image Processing , 2007, SIAM J. Numer. Anal..