What do mathematicians do?

We ask children what mathematicians do, and the answers include, “they do mathematics”, “they get things right”, and “they answer questions.” Hmm.
Recently in guest workshops I asked about 120 pre-service primary/elementary teachers how many see themselves as mathematicians. Each time, there were about 10% who identified as mathematicians. I then asked them, how many would like the children they teach to think of themselves as mathematicians. It was almost 100% to the affirmative. And then I ask, “Do we have a problem?”

We do have a problem.

I also introduced the idea of maths trauma, that I wrote about in a previous post, and explained that preservice elementary school teachers have been found to have the highest rate of self-identified maths trauma among undergraduate students. The heads were nodding, so I asked who would say they had maths trauma. Nearly one-third of the teachers said they felt traumatised by maths. Some came and talked to me individually after our session, and told me how their fear of maths was restricting the age group they felt they would be comfortable teaching. My message to them, is the very important message I learned from the webinar – “It is not your fault.” They have been taught maths in a way that was not suitable to them, or they many have had one terrible experience that put them off permanently. It is not their fault. And we and they need to do something about this.
Now there is quite a gap between being traumatised by maths, and perceiving oneself as a mathematician. I have, before my mathematical renaissance, been known to say that I was not a mathematician, as I saw myself as an operations researcher or statistician, rather than the abstract-focused (I believed) mathematician. I tend to think concretely, and had perceived that that excluded me from the ranks of true mathematicians. I have also written posts outlining the difference between mathematicians and statisticians (and operations researchers).
But these days, I have become a maths activist. Or maybe a maths whisperer? My mission, for the rest of my life, is to help people, and in particular, teachers, overcome their fear or dislike of mathematics and perceive themselves as mathematicians.

Education is a political act, and knowledge of maths and statistics empowers people, allows greater career choice and enables informed citizenship. (Nic Petty)

I have learned a great deal from the MTBOS or Maths Twitter Blogosphere. I hope one day to attend a Twitter Math Camp (#tmc17), but I fear I am destined always for #tmcjealousycamp where all the wannabetheres lurk. One of the best things was to find out about “Becoming the Math Teacher you wish you’d had” by Tracey Zager. The book is organised in chapters focused on what mathematicians do. We found this inspiring and have spent some more time grouping together our own, Zager’s and others’ ideas of what mathematicians do into the following structure:

I put my initial ideas out into the Twitterverse, where they were retweeted and endorsed. I have done some more refining to come up with these.

Mathematicians work in different ways

Mathematicians work together and alone. Too often classroom teaching has focussed on individual endeavour, whereas many people prefer to work in groups, where we can bounce ideas around.
Mathematicians work at different paces. I recently saw a Tweet quoting Jo Boaler who said “There is a common and damaging misconception in mathematics- the idea that strong math students are fast math students.” The person tweeting added, “ It’s not always about speed.” I replied, “Actually, it is never about speed.”
Mathematicians work intuitively and methodically. Sometimes we get a hunch and it turns out to be correct, or useful. Other times we just have to grunt through some ideas and processes to find things out.
Mathematicians estimate and calculate. Sometimes we just need an answer near enough. Often we need to have an idea of the near enough answer so we can check our calculations. Sometimes we need to calculate carefully and with precision.

Mathematicians Strive

This set of ideas would apply to many subjects, but I have found them really useful to encourage bravery in mathematics.
Mathematicians rise to a challenge. When we visit schools with our Rich Maths events, we tell students how mathematicians rise to a challenge. Then when we outline the different activities the can choose from, we tell them that one in particular is very challenging. We have seen many children take great delight in taking on the challenge. You can see it here: Challenging activity
Mathematicians take risks. Too often students are so focussed on getting things correct that it seems too risky to try new things and push boundaries.
Mathematicians persevere. When we see students struggling with a challenging problem, it is really important as teachers to reinforce the characteristic of persevering, and not to “rescue” them. It can be very difficult to hold back, when you are bursting to help them, but short term help is no help. Encouraging them to keep persevering, and recognising what they have already done is far more beneficial.
Mathematicians make mistakes and learn. This is one of the key ideas we emphasise in our visits. It is one of the key principles in the Growth Mindset way of thinking. When we get things right all the time, there is less learning than when we make mistakes.  Sometimes really interesting discoveries come from mistakes. I’d like to add a little aside here that maths teachers ALSO make mistakes and learn. If you have never had a lesson fail miserably, you are not taking enough risks!
I will address the remainder of our characteristics and behaviours of mathematicians in a later post.
Here are the five in summary form:

I would love to hear your opinion – is this what your students think mathematicians do? Is it what you think mathematicians do? Do you make enough mistakes?