Over the past few years, whilst working with trainee teachers, I’ve been exploring the difference between subject knowledge and subject knowledge for teaching (SKfT).
A student of mine shared this great analogy about his initial experience as a ski instructor:
I can ski and I know how to do parallel turns. But when a client asked me how do you do a parallel turn my instinctive answer was to say ‘you just do it’.
Clearly his subject knowledge is good, he has mastered the art of parallel turns and is competent enough at this to have qualified as a ski instructor. But just because you can do a parallel turn doesn’t mean you are able to teach how to parallel turn without further reflection, support and learning.
Specifically I’ve been investigating two things. Firstly what differences there are between subject knowledge and subject knowledge for teaching and secondly how might we create a framework in which to support trainee teachers with their development of not only their subject knowledge, but their subject knowledge for teaching.
What is clear is that having good subject knowledge for teaching is above and beyond having good subject knowledge. Below is an attempt to codify the additional knowledge for any given topic in maths:
1. Exam & curriculum context how the subject knowledge is presented in exam and curriculum contexts
2. Progression an understanding of the progression across topics so that prior knowledge can be checked, built upon and the next steps prepared for
3. Multiple methods and representations what different methods are available for tackling this topic and how it can be represented in different ways. For example, the strategy for solving quadratic equations called completing the square can be represented through shape:
4. Misconceptions consideration of where students might falter in their understanding and the implied impact upon planning
5. Probing questions how we can test understanding and find misconceptions through insightful questioning and purposeful task design
We use these five features as a framework to support trainee teachers in the development of their subject knowledge for teaching. For each topic studied, we can explore these features to better preapre them to teach the topic successfully.
Here is an example, by one of my trainees, of how the framework is used to develop their subject knowledge for teaching: