# Classroom-based interventions in mathematics education: relevance, significance, and applicability

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## 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).

## Keywords

Proof Scheme Instructional Intervention Symbol Manipulation Common Core State Standard Gestural Communication## References

- 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.Google Scholar - 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.CrossRefGoogle Scholar - 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.Google Scholar - 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.Google Scholar - 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.Google Scholar - 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.CrossRefGoogle Scholar - Mancosu, P. (1996).
*Philosophy of mathematical practice in the 17*^{th}*century*. New York: Oxford University Press.Google Scholar - 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.Google Scholar - 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.Google Scholar - 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.Google Scholar - 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.Google Scholar