ACT-R » Mathematical Problem Solving

Lee, H. S., Betts, S. & Anderson, J. R. (2017). Embellishing Problem-Solving Examples with Deep Structure Information Facilitates Transfer. The Journal of Experimental Education, 85(2),309-333.

Pyke, A. A., Fincham, J. M., & Anderson, J. R. (2017). When math operations have visuospatial meanings versus purely symbolic definitions: Which solving stages and brain regions are affected?. NeuroImage.

Lee, H.S., Betts, S. & Anderson,J.R. (2016) Learning Problem-Solving Rules as Search Through a Hypothesis Space. Cognitive Science, 40(5), 1036-1079.

Tenison, C., & Anderson, J. R. (2015, November 9). Modeling the Distinct Phases of Skill Acquisition. Journal of Experimental Psychology: Learning, Memory, and Cognition. Advance online publication. http://dx.doi.org/10.1037/xlm0000204

Lee, H. S., Fincham, J. M., & Anderson, J. R. (2015). Learning from examples versus verbal directions in mathematical problem solving. Mind, Brain, and Education, 9(4), 232-245.

Tenison, C., Fincham, J. M., & Anderson, J. R. (2014). Detecting math problem solving strategies: An investigation into the use of retrospective self-reports, latency and fMRI data. Neuropsychologia, 54, 41-52.

Anderson, J. R., Lee, H. S., & Fincham, J. M. (2014). Discovering the structure of mathematical problem solving. NeuroImage, 97, 163-177.

Lee, H. S., Fincham, J. M., Betts, S. & Anderson, J. R. (2014). An fMRI investigation of instructional guidance in mathematical problem solving. Trends in Neuroscience and Education, 3(2), 50–62.

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

Anderson, J. R., Betts, S. A., Ferris, J. L., & Fincham, J. M. (2013). 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 (pp. 299-324). Taylor and Francis: New York.

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.

Anderson, J. R., Betts, S. A., Ferris, J. L., & Fincham, J. M. (2012). Tracking children's mental states while solving algebra equations. Human Brain Mapping . 33(11), 2650-65.

Anderson, J. R., Betts, S. A., Ferris, J. L., Fincham, & J. M., Yang, J. (2012). Using Brain Imaging to Track Student Problem solving.IEEE Intelligent Systems, 60, 633-643.

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.

Anderson, J. R.,Betts, S. A., Ferris, J. L., & Fincham, J. M. (2011). Cognitive and metacognitive activity in mathematical problem solving: Prefrontal and parietal patterns.Cognitive, Affective, and Behavioral Neuroscience, 11, 52-67.

Anderson, J. R., Betts, S. A., Ferris, J. L., & Fincham, J. M (2011). Using Brain imaging to interpret student problem solving. In IEEE Intelligent Systems, 26(5), 22-29.

Lee, H. S., Anderson, A., Betts, S., & Anderson, J. R. (2011). When does provision of instruction promote learning? In L. Carlson, C. Hoelscher, & T. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 3518-3523). Austin, TX: Cognitive Science Society.

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.

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.

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

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.

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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.

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

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

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.

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.

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.

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.

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.

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.

Lovett, M. C. & Anderson, J. R. (1994). The effects of solving related proofs on memory and transfer in geometry problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20(2), 366-378.

Koedinger, K. & Anderson, J. R. (1993). Reifying implicit planning in geometry: Guidelines for model-based intelligent tutoring system design. In S. P. Lajoie & S. J. Derry (Eds.) Computers as cognitive tools (pp. 15-46). Hillsdale, NJ: Erlbaum.

Koedinger, K. & Anderson, J. R. (1991) Interaction of deductive and inductive reasoning strategies in geometry novices. In Proceedings of the 14th Annual Conference of the Cognitive Science Society, 780-784.

Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science, 14, 511-550.

Publications in Mathematical Problem Solving