This is the first of a series of posts explaining my thoughts around some maths education articles. First up is Only Awareness is Educable by John Mason, from MT120.
The article is heavily influenced by Gattegno (the title is a quotation of his), who once said of questioning how children learn:
It's a discipline you have to give to yourself - a spiritual discipline. This is part of the education of teachers.
This article is John Mason at his most spiritual. It contains a verse from the Rg Veda that appears in many of his articles, and appears on the homepage of his website pmtheta.org:
I love this verse. I always chuckle about it with my partner when it re-appears in another of John's papers. I regularly show it in my lessons, and ask the students what they think it means. I know it by heart and repeat it every now and then. They love making hypotheses about it. What does the verse mean to you?
This article, and much of John's work, seems to speak about the bird that looks on without eating.
Much of the writing I enjoy about maths education talks of awareness. To John, the phrase 'only awareness is educable' suggests that we can try to develop and refine our powers to notice, with the hope of effecting transformation. This is the discipline of noticing:
To think of changing others is presumptuous; to work on changing myself may serve as a role model for others. To work on changing myself is essential if I wish to be able to help others to change.
To change how I respond in a given situation, I must notice, in the moment, the possibility of choosing to act differently.
I take so much from these sentences. They have changed my practice, my relationships with children, colleagues, friends, family.
I have the sentence: "I cannot change others, I can only work at changing myself," pinned above my computer screen. I am reminded of a phrase I read somewhere, written by Dick Tahta, about 'taking the wanting out of the waiting'.
These mantras affect my teaching, when I watch others teach, when I talk to others about teaching, when I talk to students. They remind me to move away from evaluation, to support, away from 'teacher lusts'. This is difficult to do, to change the habits of a lifetime, and I often slip.
The idea that we can change the way we respond: by first noticing (awareness), reflecting, then bringing that reflection into the moment, and then acting differently, is I believe fundamental to improving teaching, to improving the way we interact with others. Perhaps we can alter the 'habitus', through cycles of noticing and validation, what Brousseau terms the dialectics of action, formation, and validation.
The choice of word respond was not taken lightly. To respond, rather than react. A desire to change ourselves through personal responsibility, as opposed to attempted enforced change through managerial accountability and measurement. The work of Gert Biesta comes to mind here.
In order to educate awareness, to help teachers and students develop themselves, John suggests we provide:
- support for positive (non-judgemental) reflection;
- support for noticing moments when they could have acted differently, or wished they had acted differently;
- support for preparing themselves to notice similar possibilities in the future.
This has formed the basis of the work we have been doing in our maths department this year.
Individual - particular - universal
Finally, John asks: what are the characteristics of maths education? What are the invariants?
Mathematics education is characterised by the application of psychological and social ways of noticing to inform the action of awakening and evoking of pupils' mathematical awarenesses, and to release their inherent powers...
Mason again draws heavily on Gattegno, who talks of developing children's 'human powers', trying to discover the facts of awareness by studying learning, 'where it takes place: in front of us, in the classroom.'
This is a spiritual education grounded in every day experience. It brings to mind Hegel's individual - particular - universal triad, which he believed defined the human condition. John agrees:
Seeing the general in the particular, and the particular in the general is fundamental to human functioning. It is the means whereby we simplify and structure our experience so as to make sense of it. It is the mechanism of resonance, the educating of awareness.
There is a connection here to JG Bennett's 'present moment', a totality of one's awareness in a moment, an awareness of awareness. Those moments when you perhaps experience things as they really are, or at least at some other level, perhaps feeling a sense of connection with others, with humanity, and the past.