Sunday, 29 November 2015

Mathematics and Moral Courage

I have been preparing a paper for a conference in Hamburg Germany with the support of my supervisors - Professor Diana Coben and Assoc Professor Jenny Young-Loveridge.  The paper is pulled from data I collected as part of the PhD but has not made it into the thesis.  The data set is a full audio recording of a vocational mathematics class which included Youth Guarantee learners and older adult learners.  

The paper contrasts three engagement patterns found within the class.  There are actually as many engagement patterns as there are learners but when limited to 8 pages it is not possible to include more.  I called the three: resistant, defensive and engaged. 

What I found is that some learners are very hesitant, or resistant to engage with mathematics because it presents danger to their social-selves.  They are even more resistant to engaging in a discussion because of the social aspect. Some are defensive, in fact they are aggressive about their non-engagement.  Obviously, this is going to have an impact on the class dynamic, and it certainly has a constraining effect on the others.

Finally, there are those that engage fully, and make new understandings.  Quite amazing to watch.   In summary, in a class of 15 learners, five engaged at a meaningful level, and of these five, two made new meanings out of the content presented.

Many mathematics researchers insist that discussing mathematics is the only way to learn.  Some even suggest that you are only doing mathematics when you are arguing about it (Lakatos for example).  Polya argues that doing mathematics requires moral courage above all else.  You must be able to generate an idea that might be wrong, share it with others, and then work toward a better idea. Your idea will likely be wrong, but you have to be brave enough to do it anyway - that's the courage part.  You have to accept that it might be wrong, and be graceful when others point that out, and then move forward - that is the moral part.

This raises real challenges for the Tertiary sector.  How do we better engage and support learners who have had poor school experiences?  Or those who begin to feel small when they make mistakes with maths? Or those who are terrified their friends will think they are dumb? How do we get learners to take risks and engage - how do we cultivate moral courage?

I'll be very interested to see what the international community makes of it all.  Not sure whether the paper has been accepted but will find out over Christmas.


  1. One thought is that the teacher or tutor model the 'okness' of making errors along the way. Creating a culture starts with the leader so perhaps we need to rethink how we train our teachers in order to work with our youth?

    1. Totally agree that the tutor plays a huge role in cultivating the values of the class, and the discourse practices. In my observations I noticed that the tone of voice the tutor used when responding to a learner's incorrect answer had an effect (usually negative) on the class. Sometimes shutting a learner down for about 10 minutes! A challenge for tutors in adult classes is that the tutors ability to cultivate that type of culture is diminished relative to the learners own beliefs, expectaions and interpretations. I have a great example of this that I'll post about. A key finding was the difficulty a tutor has in undoing negative beliefs that continue to harm the learner - largely because the beliefs appear shared across the learners - it is socially reinforced. Thus it becomes the tutor versus a collective that seeks to reinforce its beliefs - given that the natural authority of a tutor is very limited in an adult class (unlike school - adult and child) this adds to the difficulty. I'm still struggling with the exact mechanisms by which a tutor might effect change. But I'm totally with you that part of the solution lies in training tutors and rethinking exactly what they need to do to support learners to feel okay about making errors.