La construcción y justificación de ideas matemáticas generales por un niño de 5 años: el rol de las representaciones manipulativas

Referencias

AMIT, M.; NERIA, D. “Rising to the challenge”: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM, Dordrecht, v. 40, n. 1, p. 111–129, 2008. BAROODY, , A. J. How and when should place-value concepts and skills be taught? Journal for Research in Mathematics Education, v. 21, n 4, p. 281-286, 1990. BAROODY, A. The developmental bases for early childhood number and operations standards. In: CLEMENTS, D. H.; SARAMA, J. (Eds.), Engaging young children in mathematics: standards for early childhood mathematics. Mahwah, NJ, Lawrence Erlbaum Associates. 2004. p. 173–219. BASTABLE, V.; SCHIFTER, D.. Classroom stories: Examples of elementary students engaged in early algebra. In: KAPUT, J. J.; BLANTON, M. L.; CARRAHER, D. W. (Eds.), Algebra in the early grades. Mahwah, NJ, Lawrence Erlbaum Associates. 2008. p. 165–184. BLANTON, M. L.; OTÁLORA, Y.; BRIZUELA, B.; GARDINER, A.; SAWREY, K.; GIBBINS, A.; KIM, Y. Exploring Kindergarten Students’ Early Understandings of the Equal Sign. Mathematical Thinking and Learning, v. 20, n. 3, p. 167–201, 2018. BLANTON, M. L. Algebra and the elementary classroom. Transforming thinking, transforming practice. Portsmouth, NH. 2008. BLANTON, M. L. Algebraic reasoning in grades 3-5. In: BATTISTA, M. T. (Ed.), Reasoning and sense making in the mathematics classroom. Grades 3-5. Reston, VA, NCTM, 2017. p. 67–102. BLANTON, M. L., BRIZUELA, B., STEPHENS, A., KNUTH, E., ISLER, I., GARDINER, A., STROUD, R., FONGER, N., STYLIANOU. Implementing a Framework for Early Algebra. In: KIERA, C. (Ed.), Teaching and Learning Algebraic Thinking with 5-to-12-Year-Olds, Dordrecht. 2018. p. 27–49. BLANTON, Maria L. e KAPUT, James J. Elementary grade students’ capacity for functional thinking. 2004, [S.l: s.n.], 2004. p. 135–142. BLANTON, Maria L. e KAPUT, James J. Generalizing and progressively formalizing in a third-grade mathematics classroom: Conversations about even and odd numbers. 2000, Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education., 2000. p. 115–119. BOALER, J.; HUMPHREYS, C. Connecting mathematical ideas. Middle school video cases to support teaching and learning. Portsmouth, NH, Heinemann, 2005. CAI, J.; MOYER, J. C. Developing Algebraic Thinking in Earlier Grades : Some Insights from International Comparative Studies. In: GREENES, C. E.; RUBENSTEIN, R. (Eds.), Algebra and algebraic thinking in school mathematics. Reston, VA, NCTM, 2008. p. 169–192. CAÑADAS, M. C.; CASTRO, E. A proposal of categorisation for analysing inductive reasoning. PNA, Granada, v. 1, n. 2, p. 67-78, 2007. CAÑADAS, M. C.; MOLINA, M. Una aproximación al marco conceptual y principales antecedentes del pensamiento funcional en primeras edades. In CASTRO, E. (Ed.), Investigación en Educación Matemática. Homenaje a Luis Rico. Granada, España: Comares, 2016. p. 209–218. CARRAHER, D. W.; SCHLIEMANN, A. D. Algebraic reasoning in elementary school classrooms. In: LAMBDIN, D.; LESTER, F. (Eds.), Teaching and learning mathematics: Traslating research to the classroom. Reston, VA, NCTM, 2010. p. 23– 29. CARRAHER, D. W.; SCHLIEMANN, A. D. Powerful ideas in elementary school mathematics. In: ENGLISH, L.; KIRSHNER, D (Eds.), Handbook of International Research in Mathematics Education: Third Edition, n. 2, p. 191–218, 2015. CARRAHER, D. W.; SCHLIEMANN, A. D. Early algebra and algebraic generalization. Handbook of research on mathematics education, p. 669–705, 2007. CASTRO, E.; CAÑADAS, M. C.; MOLINA, M. Pensamiento funcional mostrado por estudiantes de Educación Infantil. Edma, Madrid, v. 6, n. 2, p. 1–13, 2017. CASTRO, E.; CASTRO, E. Enseñanza y aprendizaje de las matemáticas en educación infantil. Granada, España, Pirámide, 2016. COHEN, L.; MANION, L.; MORRISON, K. Research methods in education (Octava edición). Nueva York, NY, Routledge, 2018. CORNEJO-MORALES, C.; ALSINA, Á. La argumentación en los currículos de educación matemática infantil. Edma 0-6: Eduación Matemática en la Infancia, Madrid, v. 9, n. 1, p. 12–30, 2020. ELLIS, A. B. A taxonomy for categorizing generalizations: Generalizing actions and reflection generalizations. Journal of the Learning Sciences, v. 16, n. 2, p. 221–262, 2007. FUSON, K. C. Pre-K to grade 2 goals and standards: Achieving 21st century mastery for all. In: CLEMENTS, D. H.; SARAMA, J. (Eds.), Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics. Mahwah, NJ, Erlbaum, 2004. p. 105–148. GINSBURG, H. Entering the child’s mind: The clinical interview in psychological research and practice. Nueva York, NY, Cambridge University Press, 1997. HERNÁNDEZ, R.; FERNÁNDEZ, C.; BAPTISTA, M. Metodología de la investigación (Quinta edición). México, D.F., McGraw-Hill, 2020. LANNIN, J.; ELLIS, A. B.; ELLIOTT, R. Developing essential understanding of mathematical reasoning. Pre-K - Grade 8. Reston, VA, NCTM, 2011. LESH, R. A.; BEHR, M; POST, T. Rational numbers relations and proportions. In: C. JANVIER (Ed.), Problems of representation in the teaching and learning of mathematics Hillsdale, NJ, Lawrence Erlbaum Associates. 1987. p. 41-58. MASON, J. Expressing generality and roots of algebra. In: BERNARZ, N.; KIERAN, C.; LEE, L. (Eds.), Approaches to Algebra: Perspectives for Research and Teaching. Dordrecht, Springer Netherlands, 1996. p. 65–86. MORALES, R.; CAÑADAS. M. C.; BRIZUELA, B.; GÓMEZ, P. Relaciones funcionales y estrategias de alumnos de primero de Educación Primaria en un contexto funcional. Enseñanza de las Ciencias, Barcelona, v. 36, n. 3, p. 59–78, 2018. PIAGET, J.; INHELDER, B. The child’s conception of space. Nueva York, NY, Routledge, 1967. PINTO, E. Generalización de estudiantes de 3o a 6o de Educación Primaria en un contexto funcional del álgebr escolar. 2019. 341 f. Universidad de Granada, 2019. RAMIREZ, R.; BRIZUELA, B.; BLANTON, M. L. Kindergarten and First-Grade Students’ Understandings and Representations of Arithmetic Properties. Early Childhood Education Journal, v. first online, 2020. RUSSELL, S.; SCHIFTER, D., BASTABLE, V. Connecting arithmetic to algebra. Portsmouth, NH, Heinamnn, 2011. SARAMA, J.; CLEMENTS, D. H. Early childhood mathematics education research. Learning trajectories for young children. Nueva York, NY, Routledge, 2009. SMITH, E. Stasis and change: Integrating patterns, functions, and algebra throughout the K-12 curriculum. In: KILPATRICK, J.; MARTIN, W. G.; SCHIFTER, D. (Eds.), A research companion to Principles and Standards for School Mathematics. Reston, VA, NCTM, 2003. p. 136–150. STEPHENS, A.; ELLIS, A. B.; BLANTON, M. L.; BRIZUELA, B. Algebraic thinking in the elementary and middle grades. CAI, J. (Ed.), Compendium for research in Mathematics Education. Reston, VA, NCTM, 2017. p. 386–420. SUBSECRETARÍA DE EDUCACIÓN PARVULARIA. Bases Curriculares Educación Parvularia. Santiago, Chile, Ministerio de Educación, 2018. TORRES, M. D., CAÑADAS, M. C.; MORENO, A.; GÓMEZ. P. Estructuras en las formas directa e inversa de una función por estudiantes de 7-8 años. Uniciencia, San José, v. 35, n. 2, p. 1–19, 2021. WARREN, Elizabeth. Young children’s ability to generalise the pattern rule for growing patterns. Proceedings of the 29th Conference of the International group for the Psychology of Mathematics Education, v. 4, p. 305–312, 2005