Task 2 – The rules are confusing
The video and article were very relevant, and well timed, for me because they link directly to my recent experiences in university and in observing lessons in school. We are benefiting from relational* learning at university and are mostly observing instrumental** teaching in school.
Last week, at Hastings Academy, I watched real life examples of problems that can be caused by using an instrumental teaching approach. We observed 2 lessons that used this method, by different teachers, and both of them had issues. I was particularly surprised by a boy in a year 10 algebra class. He quickly progressed, ahead of most of the class, from solving simple problems ( such as a + 4 = 15 ) through a group of slightly harder ones ( such as 4a + 3 = 2a + 9 ) and then onto ones that involved brackets ( such as 3 ( a – 2 ) = a + 4 ). After some independent work time, the class was brought back together to work on the slightly harder category of question. The boy found it impossible to switch back from the “solving equations with brackets mode” and to find the “rule” he had used for the slightly harder questions. This demonstrated, to me, that he didn’t actually understand what he was doing and would struggle to solve this type of problem in the future. In the other example, the teacher gave a formula that she openly copied from a piece of paper and made no attempt to explain where it came from.
The video had some great ideas for a relational teaching approach to maths lessons. Let the class explore ideas of how to solve a real problem, such as steepest part of a ski chair lift or time to fill a water tank, and to identify for themselves the information they would enable them to calculate an answer. It seems so much better than leading the student like sheep through a prescribed step of simple operations that they are less likely to learn from.
The article*** gave a balanced view of the pros and cons of each teaching approach but the author admitted his clear preference for relational teaching. As someone new to the teaching profession, and keen on promoting a proper understanding of maths, it was interesting to hear an opinion that it would be easier for me to embrace a relational approach to teaching than someone with years of experience using an instrumental style. The challenge may be in convincing more senior staff that a potentially “radical” approach is appropriate in their school environment.
The most likely objection to adopting a relational teaching approach is that it initially takes longer to learn a topic and to therefore be assessed on it. The benefits really come in the longer term as it is easy to revise, or re-learn, something that you understood thoroughly before. It would be great, as a secondary maths teacher, if key stages 1 and 2 adopted a relational teaching approach.
* Relational teaching is based on building an understanding of what to do and why.
** Instrumental teaching is based on learning rules without necessarily understanding the reasoning behind the rules.
*** I thought the musical analogy in this article was great and liked the fact that it aligned with the Jo Boaler views from task 1. It also amused me that the relational approach to music teaching used instruments and the instrumental approach didn’t, highlighting another point that was made about how language can be misleading.