Magazine article Mathematics Teaching

Mathematics Education in a Time of Crisis

Magazine article Mathematics Teaching

Mathematics Education in a Time of Crisis

Article excerpt

Time for you and time for me,

And time yet for a hundred indecisions,

And for a hundred visions and revisions,

Before the taking of a toast and tea.

from T.S. Eliot's The love song of J. Alfred Prufrock.

The title of this article is not intended to suggest that mathematics teaching is in crisis, but rather that we are engaging in the project of mathematics education in a time of myriad crises in the world, when there is surely no longer time for indecisions and revisions. A question that is being asked by a small but growing number of mathematics educators is whether, or perhaps when, the global context within which we work will make a significant difference to what we do in our classrooms, this was a theme of the last issue of MT.

In this article, I aim to continue the thread of conversations, and offer some ideas arising from the work of a group of teachers and University staff who contributed to a special issue of the Philosophy of Mathematics Education journal (POME) under the theme of Mathematics and the living world (Ernest, 2017). The title of that collection is taken from a suggestion by George Monbiot (2017) to And more emotive words with which to describe concerns with sustainability or the environment.

In that special issue, Mark Boylan (2018) invited us to consider how mathematics classrooms could become sites for students to develop "ecological selves" and for students to come to know mathematics in a "relational" manner, seeing themselves as actors and active in the process of learning, compared to, say, experiencing mathematics as a fixed body of knowledge to be assimilated in a passive manner. Boylan proposed five aspects that could support the development of ecological selves in a mathematics classroom, which are: enchantment; embodiment; emotionality; ensemble; expansiveness (ibid, p.9). I will take the five aspects in turn and explore them briefly, before offering a classroom example to raise further questions. There seem to me no easy answers as to how mathematics classrooms might be sites of engagement with global and societal challenges, yet perhaps no more pressing question.

Enchantment

Linking mathematics teaching to the living world does not have to mean working with real-world contexts. As Boylan (2018) suggests:

Experiencing astonishment, wonder and enchantment in mathematics practises the capacity to experience these emotions in other relationships. Moreover, mathematics analysis can be a means to understand the animate and non-animate world as wonderful. (p.10)

Another word I find helpful here, alongside astonishment, wonder and enchantment, is "awe". How might mathematics teaching help engender in students a sense of awe and wonder? There are no shortage of surprising results in mathematics. But simply showing a result that is surprising to us as teachers, or mathematicians, may occasion bewilderment as much as astonishment. There is a need, perhaps, for some preparation, or to generate some sense of expectation, before something is surprising. Surprise can be generated by something being "different" when we expected a sameness, or being "the same" when we expected a difference. For example, the two different open cylinders you can make by rolling an A4 sheet of paper might raise an initial expectation of having the same volume.

Embodiment

Again, without necessarily needing to consider real world contexts, Boylan invites us to consider ways that the body might be mobilised in the classroom.

Embracing embodiment as a pedagogical principle [...] suggests the need for enlivening classrooms as places of movement [...]. Thus, gesture and the use of materialities and physical representations would be positively encouraged. (p.12)

I am reminded here both of projects such as People Maths (see, for example, http://www.transum.org/ software/Fun Maths/People Maths.asp) and also Peter Liljedahl's work on building thinking classrooms, in which a key element is getting students into small groups, working on vertical, non-permanent surfaces. …

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