Mathematics teachers’ specialized knowledge: a secondary teacher's knowledge of rational numbers

References

• Askew, M., Brown, M., Rhodes, V., Johnson, D., & Wiliam, D. (1997). Effective teachers of numeracy. London: King’s College.
   Google Scholar
• Ball, D. L. (1993). Halves, pieces, and twoths: Constructing representational contexts in teaching fractions. In T. Carpenter, E. Fennema, & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 157–196). Hillsdale, NJ: Erlbaum.
   Google Scholar
• Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. doi: 10.1177/0022487108324554
   Web of Science ®Google Scholar
• Bardelle, C. (2010). Interpreting monotonicity of functions: a semiotic perspective. In M. F. Pinto & T. F. Kawasaky (Eds.), Proceedings of PME 34 (Vol. 2, pp. 177–184). Belo Horizonte, Brazil: PME.
   Google Scholar
• Behr, M. J., Harel, G., Post, T., & Lesh, R. (1993). Rational numbers: Toward a semantic analysis-emphasis on the operator construct. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 13–47). New York, NY: Erlbaum.
   Google Scholar
• Carreño, E., Rojas, N., Montes, MÁ, & Flores, P. (2013). Mathematics teacher’s specialized knowledge. Reflections based on specific descriptors of knowledge. Proceedings of CERME 8 (pp. 2976–2984). Antalya, Turkey: METH.
   Google Scholar
• Carrillo, J., Climent, N., Contreras, L. C., & Muñoz-Catalán, M. C. (2013). Determining specialized knowledge for mathematics teaching. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of CERME 8 (pp. 2985–2994). Antalya, Turkey: METH.
   Google Scholar
• Carrillo, J., Climent, N., Montes, M., Contreras, L., Flores-Medrano, E., Escudero-Ávila, D., … & Muñoz-Catalán, M. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education. Advance online publication. doi:10.1080/14794802.2018.1479981.
   Web of Science ®Google Scholar
• Delors, J. (1994). Informe a la UNESCO de la Comisión internacional sobre la educación para el siglo XXI. La educación encierra un tesoro. Santiago de Chile: Santillana.
   Google Scholar
• Domoney, B. (2002). Student teachers’ understanding of rational number: Part-whole and numerical constructs. Research in Mathematics Education, 4(1), 53–67. doi: 10.1080/14794800008520102
   Google Scholar
• Duval, R. (1993). Semiosis y noesis. In E. Sánchez & G. Zubieta (Eds.), Lecturas en didáctica de la matemática: Escuela Francesa (pp. 118–144). México: CINVESTAV-IPN.
   Google Scholar
• Fischbein, E., Jehiam, R., & Cohen, C. (1995). The concept of irrational number in high-school students and prospective teachers. Educational Studies in Mathematics, 29, 29–44. doi: 10.1007/BF01273899
   Google Scholar
• Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel.
   Google Scholar
• 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. doi: 10.12802/relime.13.1933
   Google Scholar
• Jakobsen, A., Ribeiro, C. M., & Mellone, M. (2014). Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, 19(3–4), 135–150.
   Google Scholar
• Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101–144). Columbus, OH: ERIC/SMEAC.
   Google Scholar
• Kuntze, S. (2012). Pedagogical content beliefs: Global, content domain-related and situation-specific components. Educational Studies in Mathematics, 79(2), 273–292. doi: 10.1007/s10649-011-9347-9
   Web of Science ®Google Scholar
• Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–668). Charlotte, NC: Information Age Publishing.
   Google Scholar
• Li, Y., Huang, R., & Yang, Y. (2011). Characterizing expert teaching in school mathematics in China – A prototype of expertise in teaching mathematics. In Y. Li & G. Kaiser (Eds.), Expertise in mathematics instruction (pp. 167–195). New York: Springer.
   Google Scholar
• Li, Y., & Kaiser, G. (Eds.). (2011). Expertise in mathematics instruction. An International Perspective. New York: Springer.
   Google Scholar
• Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
   Google Scholar
• Magiera, M., van den Kieboom, L., & Moyer, J. (2011). Relationships among features of pre-service teachers’ algebraic thinking. In B. Ubuz (Ed.), Proceedings of the 35th PME (Vol. 3, pp. 169–176). Ankara, Turkey.
   Google Scholar
• Mahir, N. (2009). Conceptual and procedural performance of undergraduate students in integration. International Journal of Mathematical Education in Science and Technology, 40(2), 201–211. doi: 10.1080/00207390802213591
   Google Scholar
• Mason, J. (2015). Responding in-the-moment: Learning to prepare for the unexpected. Research in Mathematics Education, 17(2), 110–127. doi: 10.1080/14794802.2015.1031272
   Web of Science ®Google Scholar
• Muñoz-Catalán, M. C., Contreras, L. C., Carrillo, J., Rojas, N., Montes, M. A., & Climent, N. (2015). Conocimiento especializado del profesor de matemáticas (MTSK): un modelo analítico para el estudio del conocimiento del profesor de matemáticas. La Gaceta de la Real Sociedad Matemática Española, 18(3), 589–605.
   Google Scholar
• Nye, B., Konstantopoulos, S., & Hedges, L. V. (2004). How large are teacher effects? Educational Evaluation and Policy Analysis, 26(3), 237–257. doi: 10.3102/01623737026003237
   Web of Science ®Google Scholar
• Pagni, D. (2004). Fractions and decimals. The Australian Mathematics Teacher, 60(4), 28–30.
   Google Scholar
• Pinto, H., & Ribeiro, C. M. (2013). Conhecimento e formação de futuros professores dos primeiros anos - o sentido de número racional. Da Investigação às Práticas, 3(1), 85–105.
   Google Scholar
• Potari, D., Berg, C., Charalambous, C., Figueiras, L., Hošpesová, A., Ribeiro, C. M.,  …  Zehetmeier, S. (2013). Group 17 – From a study of teaching practices to issues in teacher education: Introduction. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), Proceedings of CERME 8 (pp. 2896-2907). Antalya: ERME.
   Google Scholar
• Ribeiro, C. M., & Amaral, R. (2015). Early year’s prospective teachers’ specialized knowledge on problem posing. In K. Beswick, T. Muir, & J. Wells (Eds.), Proceedings of PME 39 (Vol. 4, pp. 81–88). Hobart, Australia.
   Google Scholar
• Ribeiro, C. M., & Carrillo, J. (2011). Discussing a teacher MKT and its role on teacher practice when exploring data analysis. In B. Ubuz (Ed.), Proceedings of PME 35 (Vol. 4, pp. 41–48). Ankara, Turkey: PME.
   Google Scholar
• Ribeiro, C. 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(2), 277–310.
   Google Scholar
• Rico, L., Castro, E., & Romero, I. (1996). The role of representation systems in the learning of numerical structures. In A. Gutiérrez & L. Puig (Eds.), Proceedings of the 20th Conference of the International Group of Psychology of Mathematics Education (Vol. 1, pp. 87–102). Valencia: PME.
   Google Scholar
• Rojas, N., Carrillo, J., & Flores, P. (2012). Características para identificar a profesores de matemáticas expertos. In A. Estepa, Á Contreras, J. Deulofeu, M. C. Penalva, F. J. García, & L. Ordóñez (Eds.), Investigación en Educación Matemática XVI (pp. 479–485). Jaén, Spain: SEIEM.
   Google Scholar
• Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8, 255–281. doi: 10.1007/s10857-005-0853-5
   Google Scholar
• Rowland, T., Martyn, S., Barber, P., & Heal, C. (2000). Primary teacher trainees’ mathematics subject knowledge and classroom performance. Research in Mathematics Education, 2(1), 3–18. doi: 10.1080/14794800008520064
   Google Scholar
• Scheiner, T., Montes, M. A., Godino, J. D., Carrillo, J., & Pino-Fan, L. (2017). What makes mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education. doi: 10.1007/s10763-017-9859-6
   PubMed Web of Science ®Google Scholar
• Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. doi: 10.3102/0013189X015002004
   Google Scholar
• Stake, R. E. (1995). The art of case study research. Thousand Oaks, CA: Sage.
   Google Scholar
• Tatto, M. T., Schwille, J., Senk, S. L., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher education and development study in mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.
   Google Scholar
• Teacher Education Studies in Mathematics [TEDS-M]. (2009). Released items. Future teacher mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) –Primary. East Lansing: Michigan State University.
   Google Scholar
• United Nations Educational, Scientific and Cultural Organization (UNESCO). (2015). Resumen ejecutivo. Primer cuestionario sobre el estado de situación de la Educación para la Ciudadanía Mundial en América Latina y el Caribe. Retrieved from http://www.unesco.org/new/en/santiago/education/global-citizenship-education/
   Google Scholar
• Vamvakoussi, X., & Vosniadou, S. (2007). How many numbers are there in a rational numbers interval? Constraints, synthetic models and the effect of the number line. In S. Vosniadou, A. Baltas, & X. Vamvakoussi (Eds.), Reframing the conceptual change approach in learning and instruction (pp. 265–283). Amsterdam, The Netherland: Elsevier.
   Google Scholar
• Zakaryan, D., Ribeiro, C. M., & Valenzuela, P. (2015). Conocimiento matemático especializado de los números racionales-un caso de una profesora chilena. In P. Scott & A. Ruíz (Eds.), Educación Matemática en las Américas: 2015. Vol.2: Formación Inicial para Secundaria (pp. 137–148). Chiapas, México: CIAEM.
   Google Scholar