The Art of Maths
TASK 2: RESILIENCE AND UNDERSTANDING
I really enjoyed looking into both Dan Meyer’s talk and Richard Skemp’s article, both touched upon how there are multiple ways to go about teaching mathematics, how students are currently being told step by step how to best answer mathematical problems rather than being allowed to explore and understand these problems themselves while creating discussions amongst their peers.
Richard Skemp goes as far to say that there are two different subjects being taught and that unless all students, teachers and teaching materials (textbooks) are aligned to teach the same maths (one based on instrumental understanding and the other on relational understanding) then it could be a detriment to the learner, I found this especially interesting as I have always leaned towards the idea of relational understanding and never considered that students would be opposed to this way of thinking due to their previous experiences and may act stubborn to change. Richard Skemp cleverly explores the possibilities of why instrumental understanding is focussed on in classrooms and one of his points was that the immediate rewards of instrumental understanding was a prominent factor and I completely agree, working with young people it is evident that if they think they understand something, even if it is just memorising an equation and learning which context to use it in creates a brief confidence boost that may well last the duration of the lesson. However if they run into a situation where that equation does not work then they may lose enthusiasm completely and speaking from past experience if the student is given a task with little direction and can come up with a fitting solution (much like the ones that Dan Meyers presents in his video) through discussion with their peers then there is a much bigger emotional and intellectual investment and will give them a massive boost in confidence that will last not just through their maths lesson but most likely into their other subjects and beyond.
I often thought throughout school I had found a way to get by from doing the minimal amount of work possible and it was through memorising equations, rules, step by step methods, which exam questions where likely to come up, just long enough until I did not need to remember them, I called it surface learning and it worked extremely well for me until University where it was not enough, I had to understand the content not just know how to use it. Unfortunately by this time I was so used to understanding this way that I was almost lazy and was far too behind in my subject knowledge. So I understand the massive disadvantages in instrumental learning and would be wary of relying too heavily on this approach.
Dan Meyer’s video and diagnosis of the ski lift problem was fascinating and I will now critically look at any mathematic problems and think about how to strip it down to create discussion amongst students without compromising the mathematical content of the questions, after watching the video I was eager to have a look at the activities on Desmos.com, I was left disappointed as I thought the car parking activity was just step by step, not much discussion required questions (though seeing younger students tackle these activities may prove me wrong) I started thinking about other approaches to the same problem and thought a much more exciting task to start students on is a far more simple one:
How many cars can fit in a car park?