We are all on this course because we want to become good maths teachers. My initial reaction to both the article and the video was: “Yes, that’s how I think I should teach maths!” But of course, reading and watching again made me wonder if it would be so simple. Below are some ideas I want to explore about what kind of teacher I want to become:
I was always under the impression that my understanding of maths WAS relational. Some parts of the course have reinforced this such as our discussion about shapes and this morning the investigation into trigonometry using a unit circle. But on the other hand, I immediately recognise the examples Richard Skemp notes at the beginning of his article as instrumental about ‘borrowing’ and ‘turn upside down and multiply’. I do that. And I struggle to explain what these rules actually mean. So part of my maths knowledge is instrumental and part is relational. Maybe once we really understand when and how to use a method, we all use the method instrumentally. And we usually get it right because we’ve learnt when it’s appropriate? Even though I think I should teach relationally, would I forget to explain clearly a method that has become instrumental for me? Would I assume they should have been taught something in primary school and then struggle to explain this relationally?
One of the disadvantages of relational teaching was that it might take longer. When the short-term goal is to pass your GCSE, it may be easier to just learn the rule and become proficient using it. I wonder if one of the reasons I feel I was taught differently, is that we did not do exams until we were 18 (if we were going on to university). This allowed us to gradually explore topics up to A-level instead of this need to be able to grasp the basics in time for the GCSE. How to teach the expected curriculum relationally in the time given?
Dan gave examples of how text-book questions guide you through the problem and give exactly all the information you need. This is something I also realized after working as an engineer for several years. In real life I found one of the major difficulties was to figure out what values to use. If e.g. a calculation for a foundation is based on a constant that depends on the soil composition, you never ever have a clearcut knowledge of what to use. The soil is never homogenous or easy to classify. So you need to estimate or guess or use a range of values.
In Jo Boaler’s book (from task 1) she discusses that she has found that often girls ask why a method works and want to understand the reasoning. When this is not addressed they tend to switch off and disengage. Boys often seem quite happy to just get the right answers to a list of questions. Should we especially teach relationally for girls? Would the methods Dan uses with ‘conversations’ appeal more to girls?
PS I really liked the description of relational schemas as organic, having a sense of growth, like a tree.