Uma caracterização do conhecimento especializado do professor de matemática da educação infantil e anos iniciais em tópicos de medida

Referencias

Ainswor th, S. (2006). A concept ual f ramework for consider ing lear ning with multiple representations. Learning and Instruction, 16, 183–198. https://doi.org/10.1016/j.learninstruc.2006.03.001Barrett, J. E., Cullen, C., Sarama, J., Clements, D. H., Klanderman, D., Miller, A. L., & Rumsey, C. (2011). Children’s unit concepts in measurement: A teaching experiment spanning grades 2 through 5. ZDM, 43(5), 637-650. https://doi.org/10.1007/s11858-011-0368-8Bar rett, J. E., Sarama, J., Clements, D. H., Cullen, C., McCool, J., Witkowski-Rumsey, C., & Klander man, D. (2012). Evaluating and improving a lear ning t rajector y for linear measurement in elementary grades 2 and 3: A longitudinal study. Mathematical Thinking and Learning, 14, 28–54. https://doi.org/10.1080/10986065.2012.625075Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235–268. https://doi.org/10.1007/BF00376322Berka , K. (1983). Mea surement: its concepts, theorie s a nd problem s ( Vol. 72). Spr i nger Netherlands. https://doi.org/10.1007/978-94-009-7828-7 umacaracterizaçãodoconhecimentoespecializadodoprofessor133Relime26 (1), Marzo 2023Boyd, D. J., Grossman, P. L., Lankford, H., Loeb, S., & Wyckoff, J. (2009). Teacher preparation and student achievement. Educational Evaluation and Policy Analysis, 31(4), 416 – 440. https://doi.org/10.3102/0162373709353129Bragg, P., & Outhred, L. (2004). A measure of r ulers—The importance of units in a measure. Inter national Group for the Ps ycholog y of Mathematics Ed ucation, 2, 159 –166. https://files.eric.ed.gov/fulltext/ED489702.pdfCald at to, M. E., Fiorent i n i, D. & Pavanello, R. M. (2018). Uma análise do Projeto de formação profissional de professores privilegiada pelo PROFMAT. Zetetiké, 26, 260–281. https://doi.org/10.20396/zet.v26i2.8651034Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, Á., Ribeiro, M., & Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236–256. https://doi.org/10.1080/14794802.2018.1479981Charalambous, C. Y. (2015). Working at the intersection of teacher knowledge, teacher beliefs, and teaching practice: A multiple-case study. Journal of Mathematics Teacher Education, 18, 427–445. https://doi.org/10.1007/s10857-015-9318-7Charles, R. I. (2005). Big ideas and understandings as the foundation for elementary and middle school Mathematics. Journal of Mathematics Education Leadership, 7(3), 9–24. https://jaymctighe.com/wp-content/uploads/2011/04/MATH-Big-Ideas_NCSM_Spr05v73p9-24.pdfClements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. Em F. K. Lester (Org.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 461–555). Information Age Publishing.Clements, D. H., & Sarama, J. (2009). Learning and teaching early Math: The learning trajectory approach. Routledge.Clements, D., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. Em D. Clements, J. Sarama & A.-M. DiBiase (Orgs.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 299–317).Di Ber nardo, R., Policastro, M., Almeida, A. R. de, Ribeiro, M., Melo, J. M. de, & Aiub, M. (2018). Conhecimento matemático especializado de professores da educação infantil e anos iniciais: Conexões em medidas. Cadernos Cenpec, 8(1), 98–124. http://dx.doi.org/10.18676/cadernoscenpec.v8i1.391Gamboa, G., Badillo, E., Ribeiro, M., Montes, M., & Sanchéz-Matamoros, G. (2020). The role of teachers’ knowledge in the use of learning opportunities triggered by mathematical connections. In S. Zehetmeier, D. Potari, & M. Ribeiro, Professional development and knowledge of Mathematics teachers (1ª ed., pp. 24–43). Routledge.Godino, J. D., Batanero, C., & Roa, R. (2002). Magnitudes y medida. Em Medida de magnitudes y su didáctica para maestros. (p. 611–654). Universidad de Granada, Proyecto de Investigación y Desarrollo del Ministerio de Ciencia y Tecnología.Gómez, P., & Cañadas, M. C. (2016). Dificultades de los profesores de matemáticas en formación en el aprendizaje del análisis fenomenológico. Revista Latinoamericana de Investigación en Matemática Educativa, 19(3), 311–334. https://doi.org/10.12802/relime.13.1933Hiebert, J. (1984). Why do some children have trouble learning measurement concepts? The Arithmetic Teacher, 31(7), 19–24. http://www.jstor.org/stable/41192320Hill, H. C., & Chin, M. (2018). Connections between teachers’ knowledge of students, instruction, and achievement outcomes. American Educational Research Journal, 55(5), 1076 –1112. https://doi.org/10.3102/000283121876961 m. policastro, m. ribeiro134Relime26 (1), Marzo 2023Ho, A., & McMaster, H. (2019). Is’ capacity’volume? Understandings of 11 to 12-year-old children. Em G. Hine, S. Blackley & A. Cooke (eds.), Mathematics Education research: Impacting practice (Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia) (pp. 356–363). MERGA. https://files.eric.ed.gov/fulltext/ED604312.pdfIrwin, K. C., Ell, F. R., & Vistro-Yu, C. P. (2004). Understanding linear measurement: A comparison of Filipino and New Zealand child ren. Mathematics Education Research Journal, 16(2), 3–24. https://doi.org/10.1007/BF03217393Klein, F. (1932). Elementary mathematics from an andvanced standpoint: Arithmetic, algebra, analysis (3a ed., Vol. 1). Macmillan.Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of measurement in the elementary grades. Learning and Teaching Measurement, 1, 100–121.Ma, L. (1999). Knowing and teaching elementary Mathematics: Teacher’s understanding of fundamental Mathematics in China and the United States. Lawrence Erlbaum Associates.Mariotti, M. A., & Fischbein, E. (1997). Defining in classroom activities. Educational Studies in Mathematics, 34(3), 219–248. http://www.jstor.org/stable/3482837Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical str ucture for all. Mathematics Education Research Journal, 21(2), 10–32. https://doi.org/10.1007/BF03217543Ministério da Educação (2018). Base Nacional Comum Curricular. http://basenacionalcomum.mec.gov.br/National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics—National Council of Teacher of Mathematics. Reston, VA.Norton, A., & Boyce, S. (2015). Provoking the construction of a structure for coordinating n+1 levels of units. The Journal of Mathematical Behavior, 40, 211–232. https://doi.org/10.1016/j.jmathb.2015.10.006Organisation for Economic Co-operation and Development (2010). PISA 2009 results: What studentsknow and can do. Student performance in reading, mathematics, and science (Vol. 1). OECD.Pape, S., & Tchoshanov, M. A. (2001). The role of representation(s) in developing mathematical understanding. Theory into Practice, 40(2), 118–127. https://doi.org/10.1207/s15430421tip4002_6Panorkou, N. (2020). Dynamic measurement reasoning for area and volume. For the Learning of Mathematics, 40(3), 9–13. https://www.jstor.org/stable/27091164Panorkou, N. (2021). Exploring students’ dynamic measurement reasoning about right prisms and cylinders. Cognition and Instruction, 1–35. https://doi.org/10.1080/07370008.2021.1958218Passalaigue, D., & Munier, V. (2015). Schoolteacher trainees’ difficulties about the concepts of attribute and mesaurement. Educational Studies in Mathematics, 89, 307–336. https://doi.org/10.1007/s10649-015-9610-6Policastro, M. S., Almeida, A. R., & Ribeiro, M. (2017). Conhecimento especializado revelado por professores da educação infantil e dos anos iniciais no tema de medida de comprimento e sua estimativa. Revista Espaço Plural, 36(1), 123–154. https://e-revista.unioeste.br/index.php/espacoplural/article/view/19714Policastro, M. S., Almeida, A. R., Ribeiro, M., & Jakobsen, A. (2020). Kindergarten teacher’s knowledge to support a mathematical discussion with pupils on measurement strategies and procedures. In M. Carlsen, I. Erfjord, & P. S. Hundeland. Mathematics education in early years (pp. 263–279). Springer.Policastro, M. S., & Ribeiro, M. (2021). Conhecimento especializado do professor que ensina matemática relativo ao tópico de divisão. Zetetiké, 29, 1–24. https://doi.org/10.20396/zet.v29i00.8661906Ribeiro, M., Almeida, A. R. de, & Mellone, M. (2021). Conceitualizando tarefas formativas para desenvolver as especificidades do conhecimento interpretativo e especializado do professor. Perspectivas da Educação Matemática, 14(35), 1–32. https://doi.org/1046312/pem.v14i35.13263 umacaracterizaçãodoconhecimentoespecializadodoprofessor135Relime26 (1), Marzo 2023Ribeiro, M., Carrillo, J., & Monteiro, R. (2012). Cognições e tipo de comunicação do professor de matemática. Exemplificação de um modelo de análise num episódio dividido. Revista latinoamericana de investigación en matemática educativa, 15(1), 93–121. https://www.redalyc.org/journal/335/33523151005/html/Ribeiro, M., Gibim, G., & Alves, C. (2021). A necessária mudança de foco na formação de professores de e que ensinam matemática: Discussão de tarefas para a for mação e o desenvolvimento do conhecimento interpretativo. Perspectivas da Educação Matemática, 14(34), 1–24. https://doi.org/10.46312/pem.v14i34.12686Ribeiro, M., Jakobsen, A., & Mellone, M. (2018). Secondary prospective teachers’ interpretative knowledge in a measurement situation. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter, Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, p. 35–42). PME.Ribeiro, M., & Policastro, M. (2021). As medidas e as especif icidades do conhecimento do professor para que os alunos aprendam Matemática com significado (1.ª ed., vol. 2). CRV.Sarama, J., Clements, D. H., Barret, J., Van Dine, D. W., & MacDonel, J. S. (2011). Evaluation of a learning trajectory for length in the early years. ZDM Mathematics Education, 43, 667–680. https://doi.org/10.1007/s11858-011-0326-5Scheiner, T., Montes, M. A., Godino, J. D., Carrillo, J., & Pino-Fan, L. R. (2017). What makes Mathematics teacher knowledge specialized? Offering alternative views. International Journalof Science and Mathematics Education, 1–20. https://doi.org/10.1007/s10763-017-9859-6Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum. American Educator, Summer, 1–18. https://www.math.mun.ca/~hsgaskill/refs/curriculum.pdfSmith, J. P., Van den Heuvel-Panhuizen, M., & Teppo, A. R. (2011). Learning, teaching, and using measurement: Introduction to the issue. ZDMMathematics Education, 43(5), 617–620. https://doi.org/10.1007/s11858-011-0369-7Stake, R. E. (1995). The art of case study research. (1.ª ed.). Sage Publications.Steffe, L. P. (2003). Fractional commensurate, composition, and adding schemes: Lear ning trajectories of Jason and Laura: Grade 5. The Journal of Mathematical Behavior, 22(3), 237–295. https://doi.org/10.1016/S0732-3123(03)00022-1Stephan, M., & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. Em D. H. Clements & G. Bright (eds.), Learning and teaching measurement: 2003 yearbook (pp. 3–16). National Council of Teachers of Mathematics.Strauss, A., & Corbin, J. (1994). Grounded theory methodology: An overview. Sage Publications.Subramaniam, K. (2014). Prospective secondary mathematics teachers’ pedagogical knowledge for teaching the estimation of length measurements. Journal of Mathematics Teacher Education, 17, 177–198. https://doi.org/10.1007/s10857-013-9255-2Szilagyi, J., Clements, D. H., & Sarama, J. (2013). young children’s understandings of length measurement: Evaluating a lear ning t rajector y. Journal for Research in Mathematics Education., 44(3), 581–620. https://doi.org/10.5951/jresematheduc.44.3.0581Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics wiht particular reference to limits and continuity. Educational Studes in Mathematics, 12, 151–169. https://doi.org/10.1007/BF00305619Vale, C., McAndrew, A., & Krishnan, S. (2010). Connecting with the horizon: Developing teachers’appreciation of mathematical structure. Journal of Mathematics Teacher Education, 14, 193–212. https://doi.org/10.1007/s10857-010-9162-8Van den Heuvel-Pan huizen, M., & Elia, I. (2011). Kindergar t ners’ perfor mance in length measurement and the effect of picture book reading. ZDM Mathematics Education, 43(5), 621–635. https://doi.org/10.1007/s11858-011-0331-8 m. policastro, m. ribeiro136Relime26 (1), Marzo 2023Venturi, G. (2014). Foundation of Mathematics between theory and practice. Philosophia Scientiæ, 18(1), 45–80. https://doi.org/10.4000/philosophiascientiae.912Vinner, S. (2002). The role of definitions in the teaching and learning of mathematics. Em D. Tall (ed.), Advanced mathematical thinking (pp. 65–81). Springer.Vysotskaya, E., Lobanova, A., Rekhtman, I., & Yanishevskaya, M. (2020). The challenge of proportion: Does it require rethinking of the measurement paradigm? Educational Studies in Mathematics, 106, 429-446. https://doi.org/10.1007/s10649-020-09987-8Weber, K. (2002). Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique. For the Learning of Mathematics, 22(3), 14–17. https://www.jstor.org/stable/40248396Zakaryan, D., & Ribeiro, M. (2018). Mathematics teachers’ specialized knowledge: A secondary teacher’s knowledge of rational numbers. Research in Mathematics Education, 21(3), 1–19. https://doi.org/10.1080/14794802.2018.1525422Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education, 36(4), 317–346. https://www.jstor.org/stable/30035043Zazkis, R., & Leikin, R. (2008). Exemplifying definitions: A case of a square. Educational Studies in Mathematics, 69(2), 131–148. https://doi.org/10.1007/s10649-008-9131-7