Usar a linguagem algébrica com compreensão: o papel das conjeturas, generalizações e justificações

Referencias

Arcavi, A., Drijvers, P., & Stacey, K. (2017). The learning and teaching of algebra: Ideas, insights and activities. Routledge. https://doi.org/10.4324/9781315545189 Bogdan, R., & Biklen, S. (1994). Investigação qualitativa em educação. Porto Editora. Carraher, D., Martinez, M., & Schliemann, A. (2008). Early algebra and mathematical generalization. ZDM-Mathematics Education, 40(1), 3–20. https://doi.org/10.1007/s11858-007-0067-7 Cobb, P., Jackson, K., & Dunlap, C. (2016). Design research: An analysis and critique. Em L. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3ª ed., pp. 481–503). Routledge. Friedlander, A., & Arcavi, A. (2017). Tasks and competencies in the teaching and learning of algebra. NCTM. Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. Em F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805–842). NCTM. Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P. (2000). Making sense: Teaching and learning mathematics with understanding. Heinemann. Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96, 1–16. https://doi.org/10.1007/s10649-017-9761-8 Lannin, J., Austin, C., & Geary, D. (2023). Developing meaning for mathematical expressions. Mathematics Teacher: Learning and Teaching PK-12, 116(8), 598–603. https://doi.org/10.5951/MTLT.2022.0234 Lannin, J., Ellis, A., & Elliot, R. (2011). Developing essential understanding of mathematics reasoning: Pre-K-Grade 8. NCTM. Ministério da Educação. (2021). Aprendizagens essenciais: Matemática. DGE. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM. National Council of Teachers of Mathematics. (2009). Focus in high school mathematics: Reasoning and sense making. NCTM. Ponte, J. P. (2005). Gestão curricular em matemática. Em GTI (Ed.), O professor e o desenvolvimento curricular (pp. 11–34). APM. Ponte, J. P., Branco, N., & Matos, A. (2009). Álgebra no ensino básico. ME, DGIDC. Ponte, J. P., Quaresma, M., & Mata-Pereira, J. (2020). Como desenvolver o raciocínio matemático na sala de aula? Educação e Matemática, 7–11. Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization. Mathematical Thinking and Learning, 5(1), 37–70. https://doi.org/10.1207/S15327833MTL0501_02 Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191–228. https://doi.org/10.1007/BF01273663 Stylianides, G., Stylianides, A., & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. Em J. Cai (Ed.), Compendium for research in mathematics education (pp. 237–266). NCTM. White, I., Foster, M., & Lobato, J. (2023). Making sense of algebraic expressions in context. Mathematics Teacher: Learning and Teaching PK-12, 116(8), 604–612. https://doi.org/10.5951/MTLT.2022.0196