Preparing to Teach a Topic also known as Structure of a Topic
What do I need to remind myself about when preparing to teach a topic?
A topic can be taken to be as specific as ‘what is a triangle?’ or ‘what is a fraction?’ and as broad as Circle theorems or adding fractions, or even triangles as shapes or fractions in all their manifestations and uses. To prepare to teach a topic (even if it has been taught many times before) it is useful to bring to mind a number of different features which contribute to understanding and appreciating the whole
Main Section
The proposal here is that there are three strands to
understanding or
appreciating any mathematical topic: cognitive, affective and enactive components (see
psyche) also known as awareness, emotion and behaviour.
Cognitive (awareness): What images and associations are part of this topic? What connections with other topics? [see also
concept images] What other topics are needed in this topic? What are the obstacles that learners often encounter? What misconceptions often appear? What previous
awarenesses can be made use of?
Affective (emotion): what were the root problems which turned into this topic, which this topic resolves? Historically, where did this topic come from? Why is it in the curriculum? In what other contexts might this topic be encountered or be relevant?
Enactive (behaviour): what patterns of language are used in this topic? What technical terms are used? How are they related to everyday usage of the same or similar words and phrases? What techniques are part of this topic. What sorts of tasks are used to assess learner competence? What problems might really probe understanding?
Probes & Prompts
What comes to my mind when I am reminded of the topic? What would I like to come to learners’ minds after they have studied the topic?
How can I prompt learners to experience all the elements that comprise the topic?
What other topics are needed or are involved in this topic?
Additional questions:
How might learners be called upon to experience, make use of, and develop their natural powers and mathematical Habits of Mind?
How might learners be encouraged to make significant mathematical choices while working on this topic?
What tasks might prompt significant discussion between learners about aspects of this topic? Taking Action
Begin a notebook for this topic in which you list responses to the three types of questions, using a double spread page for each.
Make a note of unusual examples which learners produce, interesting things they say, and obstacles to understanding that they encounter.
Case Studies
Research Sources
Griffin, P. & Gates, P. (1989). Project Mathematics UPDATE: PM753A,B,C,D, Preparing To Teach Angle, Equations, Ratio and Probability, Open University, Milton Keynes.
Mason, J. & Johnston-Wilder, S. (2006). Designing and Using Mathematical Tasks. St. Albans: Tarquin.
Cuoco, A. Goldenberg, P. & Mark, J. 1996, Habits of Mind: an organizing principle for mathematics curricula, Journal of Mathematical Behaviour 15 p375-402.
See Also
Categories
Constructs