In the comments of Dan Meyer's response to my post about making mathematics 'meaningful', John Mason wrote this:

I am rather taken by the passionate expression of doubt about forcing people to study mathematics. I am not in favour of forcing people at all, but it then behoves us to attract people to work on things that they might not otherwise encounter. This is the Vygotskian stance: schools as institutions are responsible for bringing students into contact with ideas, ways of thinking, perceiving etc. that they might not encounter if left to their own devices.

Once forced to do something, I am with you on asking why it should be this or that and not something else. However, it is also the case that applications or uses of mathematics in socially relevant contexts tends to dwell in arithmetic, and not to encounter mathematics.

So the weakness in your stance is, I think, that while promoting social awareness of inequality etc., that your language can be taken to mean ‘relevance’ is what people already do day by day, and that, I think, will condemn people to not discovering ways of thinking that open up possibilities for them...

I agree with John. School mathematics provides students with opportunities to think critically, to experience shifts in awareness between the particular and the general, to consider alternative ways of thinking and working (individually

*and*collaboratively). Studying maths is valuable in educating awareness, as well as being applicable to the world we live in.

Students should have opportunities to solve problems

*and*explore models. They should experience mathematics as an end in itself

*and*as a means for exploring social or political issues. The what and how of school mathematics should not be either/or, but rather

*both/and*.

Do our students hold these beliefs about the nature of mathematical activity? Do they view it as a human endeavour, or as a solely abstract discipline, separate in some way from humanity? I would suggest that many students view it as the latter.

My underlying point in the discussion with Dan Meyer (and this post) is that mathematics education may benefit from a shift towards towards the social and political - the human - without losing the mathematical.

This is not a new call. In MT71, written in the year I was born, David Wheeler wrote an article called Humanising Mathematical Education, in which he describes a key purpose of teaching mathematics to be to educate children's awareness:

The education of awareness may appear to be an oversimple answer to the huge problem of humanising mathematical education, yet it is indeed the only answer that is capable of handling the complex challenge of providing an education that knows where it is, and shows the children where they are, and yet respects everyone's right to be educated independently of theories, ideologies and fashions and the inhuman demand that one should be content to be subservient and conformist.

The call to humanise mathematics education is taken further by Rochelle Gutierrez in her paper The Sociopolitical Turn in Mathematics Education:

[One] way in which a sociopolitical turn can help mathematics education is that it opens the door for mathematics itself to be deconstructed and examined so that we are more conscious of the discourses and practices that we reinforce and/ or challenge. If mathematics is not something out there (rational, universal, innately useful), separate from humans, then researchers and practitioners can learn from students and communities (both inside and outside of school) the various meanings that can be ascribed to doing/creating mathematics. Some research suggests that, in fact, holding a view of mathematics where truth is historically located, connected to the knower, and mutable may be an important component of being a critical mathematics educator.

This process of learning from students and communities does not mean a kind of appropriation or exploitation of meanings or practices separate from that which is negotiated by and with individuals. That is, we would not expect to import tasks that involve basketball or dominoes into the classroom merely because they have meaning for some African American students outside of school. The meaning of a mathematical concept (e.g. What is slope?) cannot be extracted from the meaning of the mathematical task that is presented to and interpreted by students. However, being open to the multiple meanings that students place on mathematical practices and offering an educational setting where those meanings can be valued and built upon is a step in the right direction.

It is important to pay attention to the views of subordinated peoples, as they offer a critique of what has been normalized in school. In this way, we open the possibility not just for teaching mathematics in more equitable ways (as it relates to oppressed peoples), but also for a radical revolution in mathematics. This move to challenge what counts as mathematics is driven not from a perspective that assumes certain students cannot be motivated by abstract versions of mathematics, or that all mathematical practices should relate to the “real world” in a concrete sense, but rather from a perspective that assumes that mathematics as a human practice can become more just.

So: Is there a need to humanise mathematics education? What exactly might this mean?

If so, how can we make these things happen? Are they possible, or even desirable?