A few things have caught my attention in the last couple of weeks.
Firstly, I had the pleasure of recently attending a session on assessment in the Understanding by Design curriculum framework led by Jay McTighe. It was a great day – this framework continues to inspire, redirect and focus my thinking about teaching and learning…especially how best to plan, implement and assess learning for understanding by deliberately focusing on documenting curriculum in ways that compel us to think about these things. At one point during the day, Jay asked us to divide up into discipline groups: the humanities and the ‘inhumanities’. Although it was said with tongue very firmly in cheek, it did give me pause. Many adults (and students) DO see the learning of mathematics as an inhumane activity; a form of suffering brought on by acute and chronic torture of their psyches and how they see themselves. I think that mathematics, more than any other discipline, presents students with the stark alternatives of ‘success’ and ‘failure’.
Appearing in the March 2008 edition of Educational Leadership – the magazine of the Association for Supervision and Curriculum Development – was an article by Kieran Egan and Gillian Judson in which is the following paragraph:
To engage students in learning, we must begin by bringing out the imaginative and emotional features of the content, whether in mathematics, science, or any other curriculum area. Everything in the curriculum is human knowledge – a product of human hopes, fears and passions. If we want to make that knowledge engaging to students, we have to show it in the context of the hopes, fears and passions from which it has grown and in which it finds a living meaning. By shaping curriculum content around the cognitive tools that students have available, we can make it more imaginatively engaging and more human.
Couldn’t agree more. Many believe that mathematics is purely abstract, encapsulating a ‘separateness’ from humanity. It was born, however, from human concerns and a desire to symbolise, explore, and use the patterns of the world in which we live. It is as instrinsically linked to the human condition as any other discipline. It has aesthetic qualities. As Bob Kaplan is quoted as saying in today’s Education Age:
Mathematics is so beautiful, it’s like music.
I have only recently heard of Bob and Ellen Kaplan. I attended a Summer School participant catch-up meeting a few weeks ago and one of the teachers at this meeting mentioned them. They are also highlighted in the Education Age. Bob Kaplan is also reported to have said that our mathematical ability lies in the way we develop when given the encouragement, the time to speak, think, explore and to make mistakes. These are all aspects of mathematical learning on which I have ‘soap-boxed’ for some years now. The Kaplans operate a website called themathcircle (well worth a look) and their philosophy can be summarised in the following quote:
“What you have been obliged to discover
by yourself leaves a path in your mind
which you can use again when the need
arises.” –G. C. Lichtenberg
They, like me and many others, believe that students learn best when constructing their own knowledge. This is not, however, to imply teachers are ‘merely’ guides on the side or ‘facilitators’ (horrible word). Teachers do important work. To ensure that we teach for understanding, teachers need to deliberately plan for learning to occur, for meaning to be made and for transferral across contexts to be engendered. This requires hard, reflective effort. Curricula need to target the understandings we want to elicit and focus our activities in class on developing those understandings in ways that compel students to form the cogntive structures and pathways that will lead to mathematical learning. Ideally, these activities would be done in such a way that reveals the humanity behind the discipline. THIS would be my humane curriculum.