A reply to Chris Lehmann
We don’t know how to teach maths nor why we teach it, says Chris. Worse still, the way maths is currently taught derails progressive education because it brings back coercion into the classroom. Chris claims that maths has suffered more than any other subject from ‘siloing’ or isolating disciplines in the school curriculum, and he asks why we teach maths as a separate subject. A debate around maths is much needed and long overdue for progressive educationalists. Chris’s blog is to be welcomed as a starting point for a re-think of maths pedagogy.
Chris characterises maths as “the language of the physical world” and, soon after, states that it is “problem-finding and problem-solving.” It is precisely in these two definitions that the difficulty lies for progressive maths teachers. In maths we set and solve problems, but the efficiency and effectiveness of our solutions depend on our command of the language.
Crucially, these two aspects of maths developed together historically. Solving problems led to the development of a language, which in turn encouraged the expression of more sophisticated problems, followed by a further deepening of the language. This dialectical relationship is the key for teaching maths. (By the way, the maths language in its highest form is algebra – so it is inadmissible and irresponsible for progressive educationalists to simply suggest that we do not teach algebra.)
How then do we stimulate students to set and solve problems and also ensure they learn the language with which to solve them? Chris mentions one model in which students learn in a formal way (or, as in Chris’s example, by using computer software) and then apply thenew knowledge in inter-disciplinary projects. This seems to combine the worst of two worlds: de-contextualised instruction followed by ‘de-instructionalised’ context.
Chris’s own solution is to explore the maths component of ‘real-life’ situations, such as the flight of a Frisbee, a game of poker, or programming a computer. There are two general problems with ‘real life’ in maths teaching: it might not actually be the real life of the student and it might restrict students’ access to the higher forms of the language. So, for one student a card game could be as irrelevant as a traditional maths lesson; for another, a project that requires simply costing an event might hold back progress. While Chris’s suggestion could address the problem-solving side, it says nothing about how students learn the language.
The most important issue for progressive maths teaching is the stimulus to learning. It must be set just above the current level of the students’ knowledge to pique curiosity and encourage questioning, but it must also promote the learning of the language.
Inquiry Maths has attempted to resolve this dichotomy by starting inquiries with prompts that have a curriculum focus, rather than a ‘real-life’ context. Such prompts have led to inquiry classrooms full of inquisitiveness and enthusiasm, and also to students motivated to ask for instruction when it becomes clear that new knowledge is required to develop the inquiry. Students are problem setters and solvers and simultaneously learners of the language through which they can become better setters and solvers.
Andrew Blair, March 2013