Task 2 – Is there a right or wrong way of learning?

Posted by Fintan on Mar 1, 2016

I enjoyed studying math at school. At times it was frustrating when I came across a problem I had trouble with, but when I finally understood how to do the problem, I felt great satisfaction. So when I listen to Dan Meyer propose a complete makeover of the subject I enjoyed in school, I can’t help but feel a little crestfallen. According to Meyer and Skemp, the subject that I loved as a student was not taught to me correctly. On the one hand, I see the merits in their arguments of how students learn math in a very superficial way. I could recite Pythagoras’ Theorem, but until recently, I had very little understanding as to its applications. On the other hand, I want to defend my education in math. It’s a subject I loved at school and so to have it somewhat devalued by the arguments of Meyer and Skemp is difficult to accept. I do realize that I’m in the minority when it comes to those who liked math at school, but as math does appeal to a small group of us, then surely there are some good points as to how it’s been taught.
I think Meyer’s ski-lift problem and how it was broken up into different components would be an effective way of presenting a problem to students. Rather than immediately presenting students with the exact information that they need, they can be guided on how to tackle the problem. However, his attitude on the current state of math problems is a little dismissive. Meyer makes it seem as if math in school is not challenging at all and reduces it down to “decoding a textbook”. Although the style of math problems in schools currently might not be very engaging for a lot of students, I don’t think they are as easy as he makes out*. This is where Skemp presents a much more balanced argument, as he acknowledges some of the benefits of instrumental learning: It can be a quicker way of ‘learning’ and ‘understanding’ math*; and students can achieve success more readily through instrumental learning. I think these could be some of the reasons why I enjoyed math at school. Are these the wrong reasons for liking math? Perhaps I didn’t develop the correct math skills, but it has at least led me and others to this point in time where we can develop these skills and help other students develop them.
I played with some of the Desmos math games and had great fun with them. I can see how students would be more engaged with math if it was more like this. You can see the math unfold before your eyes as you input different numbers and observe the effects that they have. It’s much more lucid than a textbook problem and would be more likely to engage students by tapping into a person’s desire to complete challenges (much like a computer game). I think I would have loved to learn math this way, but maybe other instrumental learners would not have. Let us not alienate any student by prescribing ‘the correct way’ of learning. We all learn in different ways and as prospective teachers, we need to be aware of that.

*I realise that instrumental understanding is not our ultimate goal as educators. However, do we insist on students learning in a relational way if it is something with which they continue to show frustration ? Or do we accept that instrumental understanding might be the best that we can expect from some students?

3 Comments

  1. aw677
    1 March 2016

    I find I can disagree with very little that you have written Fintan, it is true that most of us are of an age where teaching methods were of a more prescriptive variety and yet we still came to love maths. But does that make it right? The fact that we are in the minority speaks volumes in itself. I agree that a fundamental shake up is neither possible or right, but perhaps it is time to try something new.

  2. jat32
    4 March 2016

    Hi Fintan
    I really enjoyed your defence your maths teaching. I suspect that all of us must have enjoyed maths to a degree at school (and I love a rule that works). But I do wonder if there is more that teachers could do to make the topic more enganging especially as it is a required subject up to GCSE level leaving the pupils and teachers no choice but to grin and bear it for 11 years of a pupil’s(and teacher’s) life. And I do think that the methods that Skemp and Meyer put forward hold some of the solutions for this.
    Jane

  3. pepsmccrea
    8 March 2016

    Lots of interesting points here. It’s good to see you be critical of the ideas presented. We need to be careful not to get swept away by non-rigorous arguments. Your final *note is where things really start to heat up!

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