Ayala-Altamirano, C., & Molina, M. (2020). Meanings attributed to letters in functional contexts by primary school students. International Journal of Science and Mathematics Education, 18(7), 1271-1291.

Article  Google Scholar 

Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. Mathematics, Teachers and Children, 216, 235.

Google Scholar 

Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In L. I. Tatsien (Ed.), Proceedings of the International Congress of Mathematicians, Vol. III (pp. 907–920). Beijing: Higher Education.

Becker, J. R., & Rivera, F. D. (2006). Sixth graders’ figural and numerical strategies for generalizing patterns in algebra (1). In Alatorre, S., Cortina, J.L., Sáiz, M., and Méndez, A. (Eds.), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 95 – 101). Mérida, México: Universidad Pedagógica Nacional.

Blanton, M., Gardiner, A., Ristroph, I., Stephens, A., Stroud, R., & Knuth, E. (2022). Progressions in young learners’ understandings of parity arguments. Mathematical Thinking and Learning, 1–31. https://doi.org/10.1080/10986065.2022.2053775

Blanton, M., Levi, L., Crites, T., Dougherty, B., & Zbiek, R. M. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in Grades 3–5. Series in essential understandings. ERIC.

Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 412–446.

Breiteig, T., & Grevholm, B. (2006). The transition from arithmetic to algebra: To reason, explain, argue, generalize and justify. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 225–232). Prague, Czechovslovakia: Charles University.

Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM, 40, 3-22. https://doi.org/10.1007/s11858-007-0067-7

Article  Google Scholar 

Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32, 9-13.

Article  Google Scholar 

Cooper, T. J., & Warren, E. (2008). The effect of different representations on Years 3 to 5 students’ ability to generalise. ZDM, 40(1), 23-37.

Article  Google Scholar 

Dörfler, W. (2008). En route from patterns to algebra: Comments and reflections. ZDM Mathematics Education, 40, 143 – 160.

Article  Google Scholar 

Ellis, A. B. (2005). Justification as a support for generalizing: Students’ reasoning with linear relationships. In G. M. Lloyd, M. R. Wilson, J. L. M. Wilkins, & S. L. Behm (Eds.), Proceedings of the 27th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Eugene, OR: All Academic.

Ellis, A. B. (2007). Connections between generalizing and justifying: Students’ reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194–229. Retrieved from http://www.jstor.org/stable/30034866

Ellis, A. B. (2011). Generalizing-promoting actions. Journal in Research in Mathematics Education, 42(4), 308-345.

Article  Google Scholar 

Ellis, A. B., Lockwood, E., Tillema, E., & Moore, K. (2022). Generalization across multiple mathematical domains: Relating, forming, and extending. Cognition and Instruction, 40(3), 351-384.

Article  Google Scholar 

Fujii, T., & Stephens, M. (2001). Fostering an understanding of algebraic generalisation through numerical expressions: The role of quasi-variables. Proceedings of the 12th ICMI Study Conference: The Future of the teaching and learning of algebra, 1, pp. 258–264.

Hiebert, J. (1997). Making sense: Teaching and learning mathematics with understanding. Heinemann, Portsmouth, NH.

Google Scholar 

Initiative, C. C. (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.

Kaput, J. (1999). Teaching and learning a new algebra with understanding. In E. Fennema, & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Mahwah, NJ: Erlbaum.

Google Scholar 

Kaput, J. J. (2000). Teaching and Learning a New Algebra with Understanding. ERIC.

Lannin, J. K. (2005). Generalization and Justification: The Challenge of Introducing Algebraic Reasoning Through Patterning Activities. Mathematical Thinking and Learning, 7, 231-258. https://doi.org/10.1207/s15327833mtl07033

Article  Google Scholar 

Leron, U., & Zaslavsky, O. (2013). Generic proving: Reflections on scope and method. For the Learning of Mathematics, 33(3), 24–30.

Google Scholar 

Lobato, J., Ellis, A. B., & Muñoz, R. (2003). How “focusing phenomena” in the instructional environment support individual students’ generalizations. Mathematical Thinking and Learning, 5, 1-36.

Article  Google Scholar 

Mason, J. H. (2001). Tunja sequences as examples of employing students’ powers to generalize. The Mathematics Teacher, 94(3), 164-168.

Article  Google Scholar 

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. Reston, VA: Author.

Radford, L. (1996). Some reflections on teaching algebra through generalization. In L. Lee (Ed.), Approaches to algebra: Perspectives for research and teaching (pp. 107–111). Dordrecht, The Netherlands: Kluwer.

Chapter  Google Scholar 

Russell, S. J., Schifter, D., & Bastable, V. (2011). Developing algebraic thinking in the context of arithmetic. In Early algebraization (pp. 43–69). Springer.

Schifter, D. (2010). Representation-based proof in the elementary grades. In Teaching and learning proof across the grades (pp. 71–86). Routledge.

Steffe, L. P. (2004). PSSM from a constructivist perspective. In Clements, D. H., Sarama, J., & DiBiase, A. M. (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 221-251). Mahwah, NJ: Lawrence Erlbaum Associates.

Google Scholar 

Stephens, A., Blanton, M., Knuth, E., Isler, I., & Gardiner, A. M. (2015). Just Say Yes to Early Algebra! Teaching Children Mathematics, 22, 92–101. Retrieved from http://www.jstor.org/stable/10.5951/teacchilmath.22.2.0092

Stephens, A. C., Ellis, A. B., Blanton, M., & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.), Third Handbook of Research on Mathematics Teaching and Learning (pp. 386–420). Reston, VA: National Council of Teachers of Mathematics.

Strachota, S., Blanton, M., & Knuth, E. (2018). Cycles of Generalizing Activity in the Classroom. In Carolyn Kieran (Ed.) Teaching and Learning Algebraic Thinking with 5- to 12-year-olds: The Global Evolution of an Emerging Field of Research and Practice. (pp. 351-378). Cham: Switzerland, Springer International Publishing.

Chapter  Google Scholar 

Strachota, S., Stephens, A., Morton, K., Veltri-Torres, R., Blanton, M., Gardiner A., Sung, Y., Stroud R., & Knuth, E. (2023). The Role of Tools in Supporting Students’ Generalizing About Evens and Odds. Mathematics Education Research Journal, 1–26.

Stylianides, A. J. (2016). Proving in the elementary mathematics classroom. Oxford University Press.

Book  Google Scholar 

Witzel, B. S., & Little, M. E. (2016). Teaching elementary mathematics to struggling learners. The Guilford Press.

Google Scholar