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.
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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.
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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
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