National Research & Development Center on Cognition and Mathematics Instruction

Topic: Cognition and Mathematics Instruction

Purpose: The National Center for Cognition and Mathematics Instruction has a core goal of redesigning components of a widely-used middle school mathematics curriculum—Connected Mathematics Project (CMP), and evaluating the efficacy of the redesigned curriculum materials.

Bringing together leading experts in cognition, instruction, assessment, research design and measurement, mathematics education, and teacher professional development, the Center team will apply research-based design principles to revise mathematics curricular materials for the grade span of 6 to 8, when fundamental concepts required for algebra and advanced mathematics are addressed. The redesign will be based upon principles derived from experimental studies in classrooms and controlled laboratory settings to enhance the conditions of instruction and improve learning outcomes for students. The Math Center will conduct an integrated series of design studies; develop and test practical guidelines that will enable mathematics teachers, curriculum developers, and publishers to apply the design guidelines; as well as conduct supplementary studies on important issues in mathematics teaching and learning. The Math Center will first complete a series of controlled experiments (RCTs) aimed at examining the effects of revised curricular units with 50 participating teachers, and then a large-scale, school-level random assignment efficacy study to examine the effects of the redesigned CMP in 78 schools. The Math Center will also widely disseminate findings and provide leadership to the education field.

Established through a five-year, $10.0 million grant from the Institute of Education Sciences (IES) of the U.S. Department of Education, the National Center on Cognition and Mathematics Instruction is housed at WestEd, and operated in collaboration with partners at the University of Illinois at Chicago, Carnegie Mellon University, Temple University, University of Wisconsin-Madison, and Worcester Polytechnic Institute.

Key Personnel: Steven Schneider, James Pellegrino, Ken Koedinger, Neil Heffernan, Julie Booth, Mitchell Nathan, Martha Alibali, Susan Goldman, Diane Briars, Shandy Hauk, Jodi Davenport, Kim Vivani

Center Website: http://www.iesmathcenter.org

IES Program Contact: Dr. Elizabeth Albro
Email: Elizabeth.Albro@ed.gov
Telephone: (202) 219-2148

Publications from this project:

Journal articles

Alibali, M. W., Stephens, A. C., Brown, A. N., Kao, Y. S., and Nathan, M. J. (2014). Middle School Students' Conceptual Understanding of Equations: Evidence from Writing Story Problems. International Journal of Educational Psychology, 3 (3), 235–264.

Booth, J.E., and Davenport, J. L. (2013). The Role of Conceptual Encoding and Feature Knowledge in Algebraic Equation-Solving. Journal of Mathematical Behavior, 32, 415–423.

Booth, J. L., McGinn, K. M., Young, L. K., and Barbieri, C. (2015). Simple Practice Doesn't Always Make Perfect Evidence From the Worked Example Effect. Policy Insights from the Behavioral and Brain Sciences, 2 (1), 24–32.

Clinton, V., Alibali, M.W., and Nathan, M.J. (2016). Learning About Posterior Probability: Do Diagrams and Elaborative Interrogations Help? Journal of Experimental Education, 84, 579–599. doi: 10.1080/00220973.2015.1048847

Clinton, V., Morsanyi, K., Alibali, M.W., and Nathan, M.J. (2016). Learning About Probability from Text and Tables: Do Color Coding and Labeling Through an Interactive User Interface Help? Applied Cognitive Psychology, 30, 440–453. doi: 10.1002/acp.3223.

Goldman, S.R., and Pellegrino, J.W. (2015). Research on Learning and Instruction: Implications for Curriculum, Instruction, and Assessment. Policy Insights from the Behavioral and Brain Sciences, Vol. 2 (1) 33–41.

Heffernan, N. T., and Heffernan, C. L. (2014). The ASSISTMENTS Ecosystem: Building a Platform that Brings Scientists and Teachers Together for Minimally Invasive Research on Human Learning and Teaching. International Journal of Artificial Intelligence in Education, 24(4), 470–497.

Young, L.K., and Booth, J.L. (2015). Student Magnitude Knowledge of Negative Numbers. Journal of Numerical Cognition, 1(1), 38–55.

Conference proceedings

Adjei, S. A., Botelho, A. F., and Heffernan, N. T. (2016, April). Predicting Student Performance on Post-Requisite Skills Using Prerequisite Skill Data: An Alternative Method for Refining Prerequisite Skill Structures. In Proceedings Of The Sixth International Conference On Learning Analytics and Knowledge (Pp. 469–473). ACM.

Booth, J. L., Begolli, K. N., Mccann, N. F. (In Press). The Effect of Student Learning and Error Anticipation in Algebra. In The Thirty-Eighth Meeting of the North American Chapter of the International Group gor the Psychology of Mathematics Education. Tucson, AZ.

Gu, J., Cai, H., and Beck, J. E. (2014, June). Investigate Performance Of Expected Maximization on the Knowledge Tracing Model. In International Conference on Intelligent Tutoring Systems (Pp. 156–161). Springer International Publishing.

Hawkins, W. J., Heffernan, N. T., and Baker, R. S. (2014, June). Learning Bayesian Knowledge Tracing Parameters with a Knowledge Heuristic and Empirical Probabilities. In International Conference on Intelligent Tutoring Systems (pp. 150–155). Springer International Publishing.

Kehrer, P., Kelly, K. M., and Heffernan, N. T. (2013). Does Immediate Feedback While Doing Homework Improve Learning?. In FLAIRS Conference.

Kelly, K. M., and Heffernan, N. T. (2016, April). Optimizing the Amount of Practice in an On-Line Platform. In Proceedings of the Third (2016) ACM Conference On Learning@ Scale (Pp. 145–148). ACM.

Koedinger, K.R. and Mclaughlin, E.A. (2016). Closing the Loop with Quantitative Cognitive Task Analysis. In T. Barnes, M. Chi and M. Feng (Eds.), Proceedings of the 9th International Conference On Educational Data Mining (pp. 412–417). Raleigh, NC.

Koedinger, K. R., Stamper, J. C., Mclaughlin, E. A., and Nixon, T. (2013). Using Data-Driven Discovery of Better Student Models to Improve Student Learning. In Proceedings Of The 16th International Conference on Artificial Intelligence In Education (Pp .421–430). Memphis, TN.

Li, N., Stampfer, E., Cohen, W.W., and Koedinger, K.R. (2013) General and Efficient Cognitive Model Discovery Using A Simulated Student. In M. Knauff, M. Pauen, N. Sebanz, and I. Wachsmuth (Eds.), Proceedings of the 35th Annual Conference of the Cognitive Science Society (pp. 894–899). Austin, TX: Cognitive Science Society.

Liu, R., Koedinger, K. R., and Mclaughlin, E. A. (2014). Interpreting Model Discovery And Testing Generalization To A New Dataset. In Stamper, J., Pardos, Z., Mavrikis, M., Mclaren, B.M. (Eds.) Proceedings of the 7th International Conference on Educational Data Mining (pp.107–113). London, UK.

Lomas, J. D., Forlizzi, J., Poonwala, N., Patel, N., Shodhan, S., Patel, K., ... and Brunskill, E. (2016, May). Interface Design Optimization as a Multi-Armed Bandit Problem. In Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems (Pp. 4142–4153). ACM.

Ostrow, K., Donnelly, C., Adjei, S., and Heffernan, N. (2015). Improving Student Modeling Through Partial Credit and Problem Difficulty. In Proceedings of the Second (2015) ACM Conference On Learning@ Scale (Pp. 11–20). ACM.

Ostrow, K., and Heffernan, N. (2014). Testing the Multimedia Principle in the Real World: A Comparison of Video vs. Text Feedback in Authentic Middle School Math Assignments. In Educational Data Mining 2014.

Ostrow, K., Heffernan, N., Heffernan, C., and Peterson, Z. (2015). Blocking vs. Interleaving: Examining Single-Session Effects Within Middle School Math Homework. In International Conference on Artificial Intelligence In Education (pp. 338–347). Springer International Publishing.

Ostrow, K. S., Selent, D., Wang, Y., Van Inwegen, E. G., Heffernan, N. T., and Williams, J. J. (2016). The Assessment of Learning Infrastructure (ALI): The Theory, Practice, and Scalability of Automated Assessment. In Proceedings of the Sixth International Conference on Learning Analytics and Knowledge (pp. 279–288). ACM.

Selent, D., and Heffernan, N. (2014). Reducing Student Hint Use by Creating Buggy Messages from Machine Learned Incorrect Processes. In International Conference on Intelligent Tutoring Systems (pp. 674–675). Springer International Publishing.

Stampfer, E. and Koedinger, K.R. (2013a). When Seeing Isn't Believing: Influences of Prior Conceptions and Misconceptions. In M. Knauff, M. Pauen, N. Sebanz, and I. Wachsmuth (Eds.), Proceedings of the 35th Annual Conference of the Cognitive Science Society (pp. 1384–1389). Austin TX: Cognitive Science Society.

Stampfer, E., and Koedinger, K.R. (2013b). Conceptual Scaffolding to Check One's Procedures. In H.C. Lane, K. Yacef, J. Mostow, and P. Pavlik (Eds.), Proceedings of the 16th International Conference on Artificial Intelligence In Education (Pp. 916–919).

Van Inwegen, E., Adjei, S., Wang, Y., and Heffernan, N. (2015, March). An Analysis of the Impact of Action Order on Future Performance: The Fine-Grain Action Model. In Proceedings of the Fifth International Conference on Learning Analytics and Knowledge (pp. 320–324). ACM.

Wang, Y., and Heffernan, N. T. (2014, June). The Effect Of Automatic Reassessment And Relearning On Assessing Student Long-Term Knowledge In Mathematics. In International Conference On Intelligent Tutoring Systems (pp. 490–495). Springer International Publishing.

Wang, Y., Ostrow, K., Beck, J., and Heffernan, N. (2016, April). Enhancing the Efficiency and Reliability of Group Differentiation Through Partial Credit. In Proceedings of the Sixth International Conference on Learning Analytics and Knowledge (Pp. 454–458). ACM.

Wiese, E.S. and Koedinger, K.R. (2014a) Investigating Scaffolds for Sense Making in Fraction Addition and Comparison. In P. Bello, M. Guarini, M. McShane, and B. Scassellati (Eds.), Proceedings Of The 36th Annual Conference Of The Cognitive Science Society (pp. 1515–1520) Quebec City, Canada.

Wiese, E.S. and Koedinger, K.R. (2014b) Toward Sense Making with Grounded Feedback. Proceedings of the 12th International Conference on Intelligent Tutoring Systems (pp. 695–697).

Wiese, E.S., Patel, R., Olsen, J., and Koedinger, K.R. (2015) Transitivity is not Obvious: Probing Prerequisites for Learning. In D. C. Noelle, R. Dale, A. S. Warlaumont, J. Yoshimi, T. Matlock, C.D. Jennings, and P. P. Maglio, (Eds.), Proceedings of the 37th Annual Meeting of the Cognitive Science Society (pp. 2655–2660). Austin, TX: Cognitive Science Society.