Abstract
This special issue discusses various pedagogical innovations and myriad of significant findings. This commentary is not a synthesis of these contributions, but a summary of my own reflections on selected aspects of the nine papers comprising the special issue. Four themes subsume these reflections: (1) Gestural Communication (Alibali, Nathan, Church, Wolfgram, Kim and Knuth 2013); (2) Development of Ways of Thinking (Jahnke and Wambach 2013; Lehrer, Kobiela and Weinberg 2013; Mariotti 2013; Roberts and A. Stylianides 2013; Shilling-Traina and G. Stylianides 2013; Tabach, Hershkowitz and Dreyfus 2013); (3) Learning Mathematics through Representation (Saxe, Diakow and Gearhart 2013); and (4) Challenges in Dialogic Teaching (Ruthven and Hofmann 2013).
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Alibali, M. W., Nathan, M. J., Church, R. B., Wolfgram, M. S., Kim, S., & Knuth, E. J. (2013). Teachers’ gestures and speech in mathematics lessons: Forging common ground by resolving trouble spots. ZDM-The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-012-0476-0.
CCSSM (2012). Common Core State Standards for Mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.
Greeno, G. (1992). Mathematical and scientific thinking in classroom and other situations. In D. Halpern (Ed.), Enhancing Thinking Sills in Sciences and Mathematics (pp. 39–61). Hillsdale: Lawrence Erlbaum Associates.
Harel, G. (1999). Students’ understanding of proofs: a historical analysis and implications for the teaching of geometry and linear algebra. Linear Algebra and its Applications, 302–303, 601–613.
Harel, G. (2008). What is Mathematics? A pedagogical answer to a philosophical question. In R. B. Gold & R. Simons (Eds.), Current Issues in the Philosophy of Mathematics From the Perspective of Mathematicians. USA: Mathematical American Association.
Harel, G., & Sowder, L. (1998). Students’ proof schemes. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research on Collegiate Mathematics Education (Vol. III, pp. 234–283). Providence: AMS.
Jahnke, H. N., & Wambach, R. (2013). Understanding what a proof is: a classroom-based approach. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-013-0502-x.
Kaput, J. (1985). Representation and problem solving: Methodological issues related to modeling. In E. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 381–398). Hillsdale: Lawrence Erlbaum.
Lehrer, R., Kobiela, M., & Weinberg, P. J. (2013). Cultivating inquiry about space in a middle school mathematics classroom. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-012-0479-x.
Lewis, A. (2004). The unity of logic, pedagogy and foundations in Grassmann’s mathematical work. History and Philosophy of Logic, 25, 15–36.
Mancosu, P. (1996). Philosophy of mathematical practice in the 17 th century. New York: Oxford University Press.
Mariotti, M. A. (2013). Introducing students to geometric theorems: How the teacher can exploit the semiotic potential of a DGS. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-013-0495-5.
Palmer, E. (1977). Fundamental aspects of cognitive representation. In E. Rosch & B. Looyd (Eds.), Cognition and categorization. Hillsdale: Lawrence Erlbaum Associates.
Roberts, N., & Stylianides, A. J. (2013). Telling and illustrating stories of parity: A classroom-based design experiment on young children’s use of narrative in mathematics. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-012-0474-2.
Ruthven, K., & Hofmann, R. (2013). Chance by design: Devising an introductory probability module for implementation at scale in English early-secondary education. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-012-0470-6.
Saxe, G. B., Diakow, R., & Gearhart, M. (2013). Towards curricular coherence in integers and fractions: A study of the efficacy of a lesson sequence that uses the number line as the principal representational context. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-012-0466-2.
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.
Shilling-Traina, L. N., & Stylianides, G. J. (2013). Impacting prospective teachers’ beliefs about mathematics. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-012-0461-7.
Stylianides, A. J., & Stylianides, G. J. (2013). Seeking research-grounded solutions to problems of practice: classroom-based interventions in mathematics education. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-013-0501-y.
Tabach, M., Hershkowitz, R., & Dreyfus, T. (2013). Learning beginning algebra in a computer-intensive environment. ZDM—The International Journal on Mathematics Education, 45(3) (this issue). doi:10.1007/s11858-012-0458-2.
Thompson, P. W., & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 95–113). Reston: National Council of Teachers of Mathematics.
Van Hiele, P. M. (1980). Levels of thinking, how to meet them, how to avoid them. Paper Presented at the Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics, Seattle, WA.
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Harel, G. Classroom-based interventions in mathematics education: relevance, significance, and applicability. ZDM Mathematics Education 45, 483–489 (2013). https://doi.org/10.1007/s11858-013-0503-9
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DOI: https://doi.org/10.1007/s11858-013-0503-9