Batanero, C., Navarro-Pelayo, V., & Godino, J. (1997). Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educational Studies in Mathematics, 32, 181–199.
Carlson, M. P., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33(5), 352–378.
Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 3–20.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.
Eizenberg, M. M., & Zaslavsky, O. (2004). Students’ verification strategies for combinatorial problems. Mathematical Thinking and Learning, 6(1), 15–36.
Ellis, A., Lockwood, E., & Celik, A. (2022). Empirical re-conceptualization: bridging from empirical generalizations to insight and understanding. Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2021.100928.
Ellis, A. B., Lockwood, E., Tillema, E., & Moore, K. (2021). Generalization across multiple mathematical domains: relating, forming, and extending. Cognition and Instruction. https://doi.org/10.1080/07370008.2021.2000989.
English, L. D. (1991). Young children’s combinatorics strategies. Educational Studies in Mathematics, 22, 451–547.
Fischbein, E., Pampu, I., & Manzat, I. (1970). Effects of age and instruction on combinatory ability in children. British Journal of Educational Psychology, 40, 261–270.
Goldin, G. A. (2014). Mathematical representations. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer.
Harel, G. (2008). A DNR perspective on mathematics curriculum and instruction. Part II: With reference to teacher’s knowledge base. ZDM Mathematics Education, 40, 893–907.
Kramer, S. L., & Keller, R. (2008). A brief report: An existence proof: Successful joint implementation of the IMP curriculum and a 4× 4 block schedule at a suburban US high school. Journal for Research in Mathematics Education, 39(1), 2–8.
Lockwood, E., & Caughman, J. S. (2016). Set partitions and the multiplication principle. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 26(2), 143–157.
Lockwood, E., & De Chenne, A. (2020). Using conditional statements in Python to reason about sets of outcomes in combinatorial problems. International Journal of Research in Undergraduate Mathematics Education, 6, 303–346. https://doi.org/10.1007/s40753-019-00108-2
Lockwood, E., Wasserman, N. H., & McGuffey, W. (2018). Classifying combinations: Do students distinguish between different categories of combination problems? International Journal of Research in Undergraduate Mathematics Education, 4(2), 305–322. https://doi.org/10.1007/s40753-018-0073-x
Maher, C. A., Powell, A. B., & Uptegrove, E. B. (Eds.). (2011). Combinatorics and reasoning: representing, justifying, and building isomorphisms. Springer.
Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children. W. W. Norton & Company Inc.
Reed, Z., & Lockwood, E. (2021). Leveraging a categorization activity to facilitate productive generalizing activity and combinatorial reasoning. Online First Cognition and Instruction. https://doi.org/10.1080/07370008.2021.1887192
Steffe, L., & Thompson, P. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education. Lawrence Erlbaum Associates.
Tillema, E. S. (2013). A power meaning of multiplication: Three eighth graders’ solutions of Cartesian product problems. Journal of Mathematical Behavior, 32(3), 331–352. https://doi.org/10.1016/j.jmathb.2013.03.006