We Can All Do It!

Posted by Havva on Apr 5, 2016

We Can All Do It!

At the moment in my GCSE math class there are 14 people, with an instrumental math problem, 5 people can do them quickly (myself included), 3 cannot grasp and the remainder get it, but it takes a while. However, when the maths problem is relational or based in a real situation, the results are almost reversed, I struggle! This highlights that everyone can do maths as the article states and defines the relational (conceptual) and instrumental (procedural) issue.

Can everyone draw or paint? Most people would answer yes, I am talented or no, I am not talented I cannot draw, but if you ask an art teacher, they would say, everyone who can hold a pencil can draw. Years back I took an evening art class, I was shown how to hold the pencil at eye level and use it to mark the size of the object being drawn, this enabled correct perspective. I didn’t know I could do that until the teacher showed me how, then I had a feeling of satisfaction and felt more confident. I made a big leap from feeling I could not draw to thinking that I could – it now hangs framed on my front room wall.

We all have different learning styles and teaching needs to be done in a way to maximise this – not just procedural, conceptual or factual but a combination of all three, tailored to the individual student within the parameters of the curriculum, to maximise the learning outcome. Imagine you teach maths and you also understand human behaviour, you will know how to adapt your methods to optimise each student’s capacity to learn maths.

So the question is, then not whether anyone can learn maths, but whether we can provide the right stimulus for a student to want to learn it. As the guy in the video from task 2 stated, “I sell a product that nobody wants but is forced by law to have” What I found particularly interesting from the video for the Khan Academy was the teachers’ who had had the insight to flip the classroom lessons. The homework was to listen to the lecture, and the studies done in the classroom was now what would have been the homework – how simple a revolution, how profound the difference – children helping each other learn and the teacher having more time to coach on a more one-to-one basis.

Perhaps maths teachers also need to learn a little bit about human behaviour and expression; learn how to recognise whether the student would benefit best via conceptual or instrumental methodology. This way, I believe the time with each student could be optimised.

In the article it was said there is a math war between traditionalists and progressives, seems this debate has been going on for a long time. I do not agree that students should only be taught procedural, just for the passing of exams, it is just as important to understand the reasoning behind. As with the chicken and egg issue, it doesn’t matter what came first, but that we need both to continue.

Bonus 1

This reminds me of the five stages of learning suggested by practitioners of NLP (neuro-linguistic processing) as follows:

  1. Unconscious incompetence (don’t know whether you can do or can’t do, you haven’t tried)
  2. Conscious incompetence (you now know you cannot do, you have tried)
  3. Conscious competence (you can now do but you really have to think about it)
  4. Unconscious competence (you can do, you don’t have to think about it)
  5. Mastery ( you can simply do)

Most people give at the conscious incompetent stage because they believe they cannot do it, that they are not natural – this is the stage where you learn the most and it is very difficult!


  1. Fintan Donnellan
    9 April 2016

    I also thought the homework/classroom flip could be excellent. I like the idea as a teacher of being able to give some one-to-one time to the students that need it most or students that do understand helping students that do not. I agree that the teacher still has the crucial job of recognising the way students learn and how best for them to understand a concept. I’ve read some of the other ThinkPieces about how Khan Academy would just be a way of making the job easier for the teacher, but I see it as a way of maximizing the learning of a student, in the classroom and at home.

  2. MZwiers
    11 April 2016

    I liked your bit about the 5 stages of learning. Conscious incompetence is exactly where people give up. And if teachers let them, they will be saying they just can’t do maths.

  3. pepsmccrea
    12 April 2016

    Lovely discussion Havva. Some powerful links being make around instrumental/relational, and your ‘art ability’ analogy is spot on! The unconscious competence model is a powerful one. That will keep me thinking for a while!

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