Blanton, M. L. (2008). Algebra and the Elementary Classroom: Transforming Thinking, Transforming Practice. Heinemann.

Blanton, M., Levi, L., Crites, T., & Dougherty, B. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3–5. In R. M. Zbiek (Series Ed.), Essential understanding series. National Council of Teachers of Mathematics

Blanton, M., Stephens, A., Knuth, E., Gardiner, A.M., Isler, L. & Kim, J. (2015). The development of children´s algebraic thinking: The impact of a comprehensive Early Algebra Intervention in Third Grade. Journal for Research in Mathematics Education 46(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039

Anderson, L. W., & Krathwohl, D. R. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives: complete edition. Addison Wesley Longman, Inc.

Baroody, A. J., Lai, M., Li, X., & Baroody, A. E. (2009). Preschoolers’ understanding of subtraction-related principles. Mathematical Thinking and Learning, 11, 41–60. https://doi.org/10.1080/10986060802583956

Article  Google Scholar 

Bastable, V. & Schifter, D. (2017). Classroom Stories: Examples of Elementary Students Engaged in Early Algebra. In J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the Early Grades (pp. 165-184). Lawrence Erlbaum Associates.

Bermejo, V., & Rodríguez, P. (1993). Children’s understanding of the commutative law of addition. Learning and Instruction, 20(1), 55-72. https://doi.org/10.1016/S0959-4752(09)80005-4

Article  Google Scholar 

Britt, M. S., & Irwin, K. C. (2011). Algebraic thinking with and without algebraic representation: A pathway for learning. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 137–159). Springer.

Chapter  Google Scholar 

Cai, J. & Howson, A. G. (2013). Toward an international mathematics curriculum. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & K.S. F. Leung (Eds.), Third international handbook of mathematics education research (pp. 949-978). Springer.

Google Scholar 

Canobi, K.H., Reeve, R.A., & Pattison, P.E. (2002). Young children’s understanding ofaddition concepts. Educational Psychology, 22, 513–532. https://doi.org/10.1080/0144341022000023608

Article  Google Scholar 

Carpenter, T. P. & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades. (Research Report No. 00–2). National Center for Improving Student Learning and Achievement in Mathematics and Science.

Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann.

Carpenter, T. P., Levi, L., Berman, P., & Pligge, M. (2005). Developing algebraic reasoning in the elementary school. In T. A. Romberg, T. P. Carpenter, & F. Dremock (Eds.), Understanding mathematics and science matters (pp. 81–98). Lawrence Erlbaum.

Google Scholar 

Carraher, D. W. & A. L. Schliemann (2007). Early algebra and algebraic reasoning. In F. Lester (ed.). Second Handbook of Research on Mathematics Teaching and Learning, Vol. 2 (pp. 669–705). Information Age Publishing, Inc. and NCTM.

Ching, B. H. H., & Nunes, T. (2017). Children’s understanding of the commutativity and complement principles: A latent profile analysis. Learning and Instruction, 47, 65-79. https://doi.org/10.1016/j.learninstruc.2016.10.008

Article  Google Scholar 

Confrey, J., & Lachance, A. (2000). Transformative teaching experiments through conjecture-driven research design. En A. E. Kelly y R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 231–265). Lawrence Erlbaum associates.

Cowan, R., & Renton, M. (1996). Do they know what they are doing? Children’s use of economic addition strategies and knowledge of commutativity. Educational Psychology, 16, 407–420. https://doi.org/10.1080/0144341960160405

Article  Google Scholar 

Crooks, N. M. & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Development Review, 34(4), 344–377. https://doi.org/10.1016/j.dr.2014.10.001

Di Martino, P. (2019). Pupils’ view of problems: the evolution from kindergarten to the end of primary school. Educational Studies in Mathematics, 100(3), 291-307. https://doi.org/10.1007/s10649-018-9850-3

Article  Google Scholar 

diSessa, A. (2007). An interactional analysis of clinical interviewing. Cognition and Instruction, 25(4), 523–565.

Article  Google Scholar 

Fujii, T. & Stephens, M. (2008). Using number sentences to introduce the idea of variable. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics: Seventieth yearbook of the National Council of Teachers of Mathematics (pp. 127–140). NCTM.

Ginsburg, H. P. (1997). Entering the child’s mind: The clinical interview in psychological research and practice. Cambridge University Press.

Book  Google Scholar 

Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Lawrence Erlbaum/Taylor & Francis Group; National Council of Teachers of Mathematics.

Kieran, C., Pang, J. S., Schifter, D., & Ng, S. F. (2016). Early algebra: Research into its nature, its learning, its teaching. Springer (open access eBook).

Mark-Zigdon, N., & Tirosh, D. (2017). What is a legitimate arithmetic number sentence? The case of kindergarten and first-grade children. In J. J. Kaput, M. Blanton, & D. Carraher (Eds.), Algebra in the Early Grades (pp. 201-210). Lawrence Erlbaum Associates.

Chapter  Google Scholar 

McGowen, M. (2017). Examining the Role of Prior Experience in the Learning of Algebra. In S. Stewart (Ed.) And the rest is just algebra (pp. 19-39). Springer International Publishing AG Switzerland.

Chapter  Google Scholar 

Merino, E., Cañadas, M. C. y Molina, M. (2013). Uso de representaciones y patrones por alumnos de Quinto de educación primaria en una tarea de generalización. EDMA 0–6: Educación Matemática en la Infancia, 21(1), 24–40. https://doi.org/10.24197/edmain.1.2013.24-40

Ministerio de Educación y Formación Profesional (2022). Real Decreto 157/2022, de 1 de mazo, por el que se establecen la ordenación y las enseñanzas mínimas de la Educación Primaria. BOE, 52 (24386- 24504). Author.

Molina, M., & Mason, J. (2009): Justifications-on-Demand as a Device to Promote Shifts of Attention Associated With Relational Thinking in Elementary Arithmetic, Canadian Journal of Science, Mathematics and Technology Education, 9:4, 224-242. https://doi.org/10.1080/14926150903191885

Article  Google Scholar 

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

Patel, P., & Canobi, K. H. (2010). The role of number words in preschoolers’ addition concepts and problem‐solving procedures. Educational Psychology, 30(2), 107-124. https://doi.org/10.1080/01443410903473597

Article  Google Scholar 

Robinson, K. M., Dubé, A. K., & Beatch, J. A. (2017). Children’s understanding of additive concepts. Journal of Experimental Child Psychology, 156, 16-28. https://doi.org/10.1016/j.jecp.2016.11.009

Article  Google Scholar 

Robinson, K. M., Price, J. A., & Demyen, B. (2018). Understanding arithmetic concepts: Does operation matter?. Journal of Experimental Child Psychology, 166, 421-436. https://doi.org/10.1016/j.jecp.2017.09.003

Article  Google Scholar 

Schifter, D. (2009). Representation-based proof in the elementary grades. In D. A. Stylianou, M. Blanton, & E. J. Knuth (Eds.), Teaching and learning proof across the grades: A K–16 perspective (pp. 71–86). Routledge/Taylor & Francis Group.

Google Scholar 

Schifter, D., Monk, S., Russell, S. J., & Bastable, V. (2008). Early algebra: What does understanding the laws of arithmetic mean in the early grades? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades, (pp. 413–448). Lawrence Erlbaum.

Google Scholar 

Schliemann, A., Lessa, M., Lima, A., & Siqueira, A. (2003). Young children’s understanding of equivalences. In A. Schliemann, D. Carraher & B. Brizuela (Eds.) Bringing out the algebraic character of arithmetic: From children’s ideas to classroom practice (pp. 37-56). Lawrence Erlbaum.

Google Scholar 

Skemp, R. (1987). The Psychology of Learning Mathematics Expanded American Edition. Lawrence Erlbaum & Associates, Publishers.

Star, J. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404–411.

Google Scholar 

Star, J. & Stylianides, G. (2013) Procedural and Conceptual Knowledge: Exploring the Gap Between Knowledge Type and Knowledge Quality, Canadian Journal of Science, Mathematics and Technology Education, 13:2, 169-181. https://doi.org/10.1080/14926156.2013.784828

Article  Google Scholar 

Stephens, A., Ellis, A., Blanton, M. L. & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. En J. Cai (Ed.), Compendium for research in mathematics education (pp. 386–420). Reston, VA: NCTM.

Vergnaud, G. (1996). The theory of conceptual fields. Theories of mathematical learning, 219–239.

Warren, E., Trigueros, M., & Ursini, S. (2016). Research on the learning and teaching of algebra. In A. Gutiérrez, G. C. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 73–108). Sense

Wittrock, M. (1990). La investigación de la enseñanza. III. Profesores y alumnos. Paidós Educador.