Abstract
In this commentary we provide an analytical look at the four studies reported within this theme of the volume and we discuss related issues and insights that we obtained from these studies. We offer a focused view of each study in the same order as presented in the four preceding chapters, and we conclude that these studies not only provide new insights into various cognitive and curricular issues in the teaching and learning of proof and proving , but also raise additional issues in relation to curriculum , textbooks and teacher education and professional development. Based on our analysis, we contend that mathematics education research in the area of proof and proving is still at an early stage, given that most studies are relatively small-scale and exploratory in nature. Further theoretical and methodological work, and more in-depth studies, especially larger-scale confirmatory and experimental studies, are needed to move research in this area forward.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Burton, L. (2004). Mathematicians as enquirers: Learning about learning mathematics. Dordrecht, The Netherlands: Kluwer.
Davis, J. D., Smith, D. O., Roy, A. R., & Bilgic, Y. K. (2014). Reasoning-and-proving in algebra: The case of two reform-oriented U.S. textbooks. International Journal of Educational Research, 64, 92–106.
Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks. ZDM-International Journal on Mathematics Education, 45(5), 765–777.
Fan, L. (2014). Investigating the pedagogy of mathematics: How do teachers develop their knowledge? London: Imperial College Press.
Fan, L., Qi, C., Liu, X., Wang, Y., & Lin, M. (2017). Does a transformation approach improve students’ ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms. Educational Studies in Mathematics, 96(2), 229–248.
Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: Development status and directions. ZDM-International Journal on Mathematics Education, 45(5), 633–646.
Fujita, T., & Jones, K. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81–91. https://doi.org/10.1016/j.ijer.2013.09.014.
Giaquinto, M. (2007). Visual thinking in mathematics. Oxford: Oxford University Press.
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31, 396–428.
Jones, K., Bokhove, C., Howson, G., & Fan, L. (Eds.). (2014). Proceedings of the International Conference on Mathematics Textbook Research and Development (ICMT-2014). Southampton: University of Southampton. https://eprints.soton.ac.uk/374809/.
Komatsu, K., Jones, K., Ikeda, T., & Narazaki, A. (2017). Proof validation and modification in secondary school geometry. Journal of Mathematical Behavior, 47, 1–15. https://doi.org/10.1016/j.jmathb.2017.05.002.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
Leong, Y. H., Ho, W. K., & Cheng, L. P. (2015). Concrete-pictorial-abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1–19.
Leung, F. K. S. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47(1), 35–51.
Leung, F. K. S. (2015). What does TIMSS inform us about mathematics (under)achievers in Hong Kong? In K. L. Wong, et al. (Eds.), Proceedings of the Hong Kong Mathematics Education Conference 2015. Hong Kong: Hong Kong Association for Mathematics Education.
Mariotti, M. A. (2006). Proof and proving in mathematics education. In A. Gutierrrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 173–204). Rotterdam, The Netherlands: Sense Publishers.
Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223–239. https://doi.org/10.1007/s10649-016-9720-9.
Otten, S., Gilbertson, N. J., Males, L. M., & Clark, D. L. (2014a). The mathematical nature of reasoning-and-proving opportunities in geometry textbooks. Mathematical Thinking and Learning, 16(1), 51–79.
Otten, S., Males, L. M., & Gilbertson, N. J. (2014b). The introduction of proof in secondary geometry textbooks. International Journal of Educational Research, 64, 107–118.
Senk, S. L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309–321.
Stylianides, G. J. (2008). An analytic framework of reasoning-and-proving. For the Learning of Mathematics, 28(1), 9–16.
Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258–288.
Stylianides, G. J., Stylianides, A. J., & Weber, K. (2017). Research on the teaching and learning of proof: Taking stock and moving forward. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 237–266). Reston, VA: National Council of Teachers of Mathematics.
Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. Chicago, IL: CDASSG Project, University of Chicago. Available online at http://ucsmp.uchicago.edu/resources/van-hiele/. Accessed July 5, 2017.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Fan, L., Jones, K. (2018). About the Teaching and Learning of Proof and Proving: Cognitive Issues, Curricular Issues and Beyond. In: Stylianides, A., Harel, G. (eds) Advances in Mathematics Education Research on Proof and Proving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70996-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-70996-3_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-70995-6
Online ISBN: 978-3-319-70996-3
eBook Packages: EducationEducation (R0)