Publications about Mathematical Problem Solving

Anderson, J. R. (2005) Human symbol manipulation within an integrated cognitive architecture. Cognitive Science, 29(3), 313-341. [] [info]

Anderson, J. R. (2007). The Algebraic Brain. In Gluck, M. A., Anderson, J. R , & Kosslyn, S. M. (Eds.). Memory and Mind: A Festschrift for Gordon H. Bower. New Jersey: Lawrence Erlbaum Associates. [] [info]

Anderson, J. R., Betts, S. A., Ferris, J. L., & Fincham, J. M. (2009). Can neural imaging investigate learning in an educational task? In proceedings of the 36th Annual Carnegie Symposium on Cognition, June 2-3, Carnegie Mellon University. [Document] [][Model] [info]

Anderson, J. R., Betts, S. A., Ferris, J. L., & Fincham, J. M. (in press). Can neural imaging be used to investigate learning in an educational task? In J. Stazewski (Ed.) Expertise and skill acquisition: The impact of William G. Chase. [info]

Anderson, J. R.,Betts, S. A., Ferris, J. L., & Fincham, J. M. (in press). Cognitive and metacognitive activity in mathematical problem solving: Prefrontal and parietal patterns.Cognitive, Affective, and Behavioral Neuroscience, 11, 52-67. [] [HTML] [info]

Anderson, J. R., Betts, S. A., Ferris, J. L., & Fincham, J. M. (in press). Tracking children's mental states while solving algebra equations. Human Brain Mapping . [][Mindreading HMM files and data] [info]

Anderson, J. R., Betts, S. A., Ferris, J. L., Fincham, & J. M., Yang, J. (in press). Using Brain Imaging to Track Student Problem solving.IEEE Intelligent Systems. [info]

Baker, R. S., Corbett, A. T., Koedinger, K. R. (2001) Toward a model of learning data representations. In Proceedings of the Twenty-Third Annual Conference of the Cognitive Science Society, (pp. 45-50). Mahwah, NJ: Erlbaum. [] [info]

Danker, J. F. & Anderson, J. R. (2007). The roles of prefrontal and posterior parietal cortex in algebra problem-solving: A case of using cognitive modeling to inform neuroimaging data. Neuroimage, 35, 1365-1377. [][Models] [info]

Danker, J. F. & Anderson, J. R. (2007). Using cognitive modeling to understand the roles of prefrontal and posterior parietal cortex in algebra problem solving. In Proceedings of the Society for Cognitive Neuroscience. New York, New York. [] [info]

Danker, J. M. & Anderson, J. R. (2007). The Roles of Prefrontal and Posterior Parietal Cortex in Algebra Problem Solving: A Case of Using Cognitive Modeling to Inform Neuroimaging Data. NeuroImage. 35, 1365-1377. [info]

Fincham, J. M., & Anderson, J. R. (2007). An fMRI study of the neural correlates of performance and learning in an algebraic isomorph task. In Proceedings of the Annual Meeting of the Cognitive Neuroscience Society. New York, NY, p. 271 [info]

Gluck, K. A. (2000). An ACT-R/PM model of algebra symbolization. In N. Taatgen & J. Aasman (Eds.), Proceedings of the Third International Conference on Cognitive Modeling (pp. 134-141). Veenendaal: Universal Press. [] [info]

Gunzelmann, G., Gluck, K. A., Kershner, J., Van Dongen, H. P. A., & Dinges, D. F. (2007). Understanding decrements in knowledge access resulting from increased fatigue. In The 29th Annual Conference of the Cognitive Science Society. Nashville, Tennessee, USA. [] [info]

Haverty, L. A., Koedinger, K. R., Klahr, D., & Alibali, M. W. (2000). Solving induction problems in mathematics: Not-so-trivial pursuit. Cognitive Science, 24, (2), 249-298. [] [info]

Jastrzembski, T. S., Gluck, K. A., & Gunzelmann, G. (2006). Mathematical models of spacing effects in memory: Applications in education and training. In Proceedings of the Society for Mathematical Psychology annual meeting: Vancouver, Canada. [] [info]

Kao, Y. & Anderson, J. R. (2006). What are they thinking? Decomposing a complex task. In proceedings of the 28th Annual Conference of the Cognitive Science Society (pp. 2523) . Vancouver, British Columbia, Canada. [] [info]

Kao, Y. S., Douglass, S. A., Fincham, J. M., & Anderson, J. R. (in revision). Traveling the Second Bridge: Using fMRI to Assess an ACT-R Model of Geometry Proof. [][Model] [info]

Kase, S. E., Ritter, F. E., Schoelles, M. (2009). Caffeine's effect on appraisal and mental arithmetic performance: A cognitive modeling approach tells us more. In Proceedings of the 9th International Conference of Cognitive Modeling (paper 252), Manchester, United Kingdom. [info]

Koedinger, K. R., & MacLaren, B. A. (1997). Implicit strategies and errors in an improved model of early algebra problem solving. In Shafto, M. G. & Langley, P. (Eds.) Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society, (pp. 382-387). Hillsdale, NJ: Erlbaum. [] [info]

Koedinger, K. R. & MacLaren, B. A. (2002). Developing a pedagogical domain theory of early algebra problem solving. CMU-HCII Tech Report 02-100. [] [info]

Koedinger, K. R. & Terao, A. (2002). A cognitive task analysis of using pictures to support pre-algebraic reasoning. In C. D. Schunn & W. Gray (Eds.), Proceedings of the Twenty-Fourth Annual Conference of the Cognitive Science Society, 542-547. Mahwah, NJ: Lawrence Erlbaum Associates [] [info]

Lee, H. S., Betts, S. A. & Anderson, J. R. (2011). How can we design effective instructions to promote transfer? paper to be presented at the annual meetings of the Society for Research on Educational Effectiveness (SREE), September 8-11, 2011, Washington, D.C. [info]

Lee, H. S., Betts, S. & Anderson, J. R. (under review). Revealing hidden structure by explicit rule-instruction versus scaffolded example. [Document][Model][Model] [info]

MacLaren, B. & Koedinger, K. R. (2002). Instructional experiments with ACT-R "SimStudents". In S.A. Cerri, G. Gouarderes, & F. Paraguacu (Eds.), Proceedings of the 6th International Conference on Intelligent Tutoring Systems, 355-356. Berlin: Springer-Verlag. [] [info]

Ravizza, S. M., Anderson, J. R., & Carter, C. S. (2008). Errors of mathematical processing: The relationship of accuracy to neural regions associated with retrieval or representation of the problem state. Brain Research, 1238, 118-126. [] [info]

Ritter, S., Anderson, J. R., Koedinger, K. R., & Corbett, A. (2007) Cognitive Tutor: Applied research in mathematics education. Psychonomic Bulletin & Review, 14, 249-255. [] [info]

Rittle-Johnson, B. & Koedinger, K. R. (2001). Using cognitive models to guide instructional design: The case of fraction division. In Proceedings of the Twenty-Third Annual Conference of the Cognitive Science Society, (pp. 857-862). Mahwah, NJ: Erlbaum. [] [info]

Rosenberg-Lee, M., Lovett, M., & Anderson, J. R. (2009). Neural correlates of arithmetic calculation strategies. Cognitive, Affective, & Behavioral Neuroscience, 9(3), 270-285. [] [Document][Model] [info]

Stocco, A., & Anderson, J. R. (2007). Endogenous control in algebraic problem solving: An fMRI study. In Proceedings of the Annual Meeting of the Cognitive Neuroscience Society. New York, NY, p. 271. [] [info]

Stocco, A. & Anderson, J. R. (2008) Endogenous control and task representation: An fMRI study in algebraic problem solving. Journal of Cognitive Neuroscience, 20(7), 1300-1314. [][Model] [info]

Terao, A., Koedinger K., Sohn, M-H., Anderson, J. R., & Carter, C. S. (2004). An fMRI study of the interplay of visual-spatial systems in mathematical reasoning. In Proceedings of the 26th Annual Conference of the Cognitive Science Society (pp. 1327-1332). August 4-7, Chicago, USA. [] [info]

Wintermute, S., Betts, S. A., Ferris, J. L., Fincham, J. M., & Anderson, J. R. (2012). Brain Networks Supporting Execution of Mathematical Skills versus Acquisition of New Mathematical Competence. Public Library of Science (PLOS) ONE. [Document][Pyramid Data] [info]