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Less is more: Improving by removing

journal contribution
posted on 2023-04-12, 14:00 authored by Colin FosterColin Foster

The pressures currently on teachers of mathematics at every level seem greater than ever, whether that is university mathematics lecturers, school teachers or those who work with very young learners. So, I began my Presidential Address with the hope that no one would leave the Joint Conference of Mathematics Subject Associations 2023 feeling as though they were not good enough and must do more. I did not want anyone to go home with a lengthy to-do guilt list of additional things they must try to incorporate into their practice. Instead, I advocated giving attention to the ancient proverb "less is more", versions of which are found within many cultures; e.g., "brevity is the soul of wit" (Hamlet), “Sometimes diminishing a thing adds to it; Sometimes adding to a thing diminishes it” (Tao Te Ching). I offered five aspects of mathematics teaching and learning that might benefit from ‘less of’ something, in each case trying to see how this might create space for more of something else. In this article, I present these five suggestions for improving by removing.

According to a recent paper in Nature, when asked to solve a variety of kinds of problems, people tend to default to proposing additive transformations, and they systematically overlook possible subtractive changes that could be made.1 Just as a doctor may be inclined to prescribe supplementary pills to deal with the side-effects arising from previous ones, rather than discontinuing one of those previous pills, teachers may find it harder to notice places where subtracting something from our practice may be more beneficial than adding anything new.

However, it is well worth spending the time needed to find these opportunities for removal. A first draft of a piece of writing can often be improved by deleting unnecessary words, making it more concise and easier on the reader. As Mark Twain is supposed to have written, “I didn't have time to write you a short letter, so I wrote you a long one instead.” It does indeed take effort to remove things, but investing in subtractive solutions seems potentially valuable. So, here are five suggestions for doing less but doing it better.



  • Science


  • Mathematics Education Centre

Published in

Mathematical Gazette


Cambridge University Press


  • AM (Accepted Manuscript)

Publisher statement

This article has been published in a revised form in Mathematical Gazette [http://doi.org/XXX]. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © copyright holder.

Acceptance date







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Dr Colin Foster. Deposit date: 7 April 2023

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