Abstract
Many articles and papers over the past 100 years have suggested that mathematics education has lost its way in a number of critical respects. One indication of this is certainly the hugely destructive debate between discovery and drill, a consequence of which is an emphasis, throughout the school curriculum, on technical routines.
For me, mathematics is the abstract study of structure. The structures that mathematicians choose to work with have sophistication and beauty, and it is remarkable that these same structures arise in art, in nature, and in the physical and even social sciences. So often, it is by following the beauty that we are led to the truth, and mathematics is a powerful showcase for this delightful principle. But in spite of a century-long call that school math attend to this vital aspect of mathematics, an emphasis on structure and beauty, for example, in the choice of material, is notably absent from realized curricula.
My view is that such a curriculum change cannot happen without a change in the very structure of the curriculum. Quite simply, we must put aside our technical wish list and select for our students activities and problems that give them a true mathematical experience, and then build the curriculum from there. Thus this article is about structure at two different levels: The first is the structural richness of the mathematical activities I want to see in the classroom, and the second is a new structure for the curriculum itself.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Change history
01 February 2020
The published version of this book included multiple errors in code listings throughout the book. These code listings have now been corrected and text has been updated.
References
Barabe, G., & Proulx, J. (2017). Revolutionner l’enseignment des mathematiques: Le projet visionnaire de Seymour Papert. Learning of Mathematics, 37(2), 25–29.
Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass.
Commission on Standards for School Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Available at the web site: http://www.enc.org/reform/index.htm
Dewey, J. (1934). Art as experience. New York, NY: Putnam.
Dewey, J. (1938). Experience and education. New York, NY: Collier Books. Retrieved from http://ruby.fgcu.edu/courses/ndemers/colloquium/experienceducationdewey.pdf
Gadanidis, G., Borba, M., Hughes, J., & Lacerda, H. (2016). Designing aesthetic experiences for young mathematicians: A model for mathematics education reform. International Journal for Research in Mathematics Education, 6, 225–244.
Kilpatrick, J. (1997). Confronting reform. American Mathematical Monthly, 104, 955–962.
Kline, M. (1973). Why Johnny Can’t add: The failure of the new math. New York, NY: St. Martin’s Press.
Liljedahl, P. (2017). Card tricks, discovery learning, and flow in mathematics teacher education. In J. Cummings & M. Blatherwick (Eds.), Creative dimensions of teaching and learning in the 21stcentury (pp. 175–179). Rotterdam, NL: Sense Publishers.
Papert, S. (1972). Teaching children to be mathematicians versus teaching about mathematics. International Journal of Mathematical Education in Science and Technology, 3, 249–262.
Raymond, K. (2018). M is not just for STEM: How myths about the purposes of mathematics education have narrowed mathematics curricula in the United States. Education in Science, 8, 47. https://doi.org/10.3390/educsci8020047
Sinclair, N. (2006). Mathematics and beauty. New York, NY: Teacher’s College Press.
Sinclair, N., & Watson, A. (2001). Wonder, the rainbow and the aesthetics of rare experiences. For the Learning of Mathematics, 21(No1), 39–42.
Strand, T. (2011). Moving Beyond Conventional Notions of Educational Processes: The Contribution from Charles S. Peirce. Paper presented at a seminar sponsored by Faculty of Education, 18 may 2011, PLACE academic group & PESGB, Cambridge: University of Cambridge.
Taylor, P. (2016). www.math9-12.ca
Taylor, P. (2018). Teach the mathematics of mathematicians. Education in Science, 8(2), 56. https://doi.org/10.3390/educsci8020056
The National Committee on Mathematical Requirements. (1923). The Reorganization of Mathematics in Secondary Education. Washington, DC: Mathematical Association of America, Inc..
Whitehead, A. N. (1929). Aims of education. New York, NY: The Free Press.
Wu, H. (1997). The mathematics education reform: Why you should be concerned and what you can do. American Mathematical Monthly, 104, 946–954.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Taylor, P. (2019). Reforming School Mathematics: Two Levels of Structure. In: Felmer, P., Liljedahl, P., Koichu, B. (eds) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-29215-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-29215-7_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29214-0
Online ISBN: 978-3-030-29215-7
eBook Packages: EducationEducation (R0)