I’d like to thank the Academy

Posted by Sergio on Nov 14, 2015

This week I’ll be exploring the ideas presented in an article by Daniel Willingham about mathematical ability and a video by Salman Khan about his website ‘Khan Academy’.

Willingham suggested that human beings find it very easy to relate the concepts of space and Mathematics together and that we have an inbuilt ability to estimate quantities. This made me wonder that this could be related in some way to people being visual learners. This might be why Dan Mayer has had so much success with his methods because he has given the Maths a place in a world with dimensions and quantities where our natural ability to combine Mathematics and space comes into practice. With that said it is also true that some people are happy working with numbers in a textbook and will learn fine never seeing a visual proof. I wonder, in these cases are they relating mathematics to something other than space?

Willingham says it is fundamentally important to learning that we can recall information effectively from our memory banks to simplify complicated problems. It makes sense that students who aren’t comfortable with concepts would be juggling too many things at the same time and consequently find it harder to focus through the problem. I think as educators we need to work patiently in early years to make sure the mental workspace is as uncluttered as possible and take time to reinforce the mathematics behind every step when solving a problem.

Khan talks about this in his video when he says that classrooms will test you at the end of a topic and whether you get 70% or 95% the class will move onto the next topic and those gaps will not be addressed. The benefit of his website is that there are no time constraints and students have the opportunity to repeat exercises and look at lectures or steps until they understand how the problem is solved.

Willingham makes references to the ongoing debate surrounding relational and instrumental approach to understanding. He says a relational understanding seems to be better but that the most commonly accepted view is that we should make use of both styles. However Willingham quotes a study that says American students on average have a poor conceptual knowledge and great procedural knowledge. It is interesting then that we still concede the gauntlet to relational understanding if the instrumental understanding appears more prominent.

In 2011 my friend linked me to Khan Academy and said we could use it to practice for our A level tests. During lessons our teacher would attempt to explain everything relationally and would become frustrated when we didn’t understand the proofs. It turned out that most of us had gaps from GCSE and thus preferred instrumental learning. By using Khan Academy we were able to analyse the steps in how problems were solved. It was only then that we could follow what our teacher was telling us in class and over the two years our gaps were filled. This is precisely what Khan stresses in his video. Khan Academy frees up time for the teachers and allows students to have the full teaching experience from both an instrumental and relational approach.


  1. Sergio
    14 November 2015

    I wish I had 2000 words for this topic I had to cut out so much :(.

  2. Glen
    22 November 2015

    Lovely article Sergio, I like the link to your own experiences, do you believe the Khan academy is useful to you because of your desire to pursue mathematics? what if it was with students who didn’t want to pursue maths post GCSE? Do you feel that it would be as effective to them?

  3. pepsmccrea
    23 November 2015

    Great analysis Sergio. Lots of connections being made here as well as some interesting hypotheses being made RE visual learning. Keep it up!

  4. pepsmccrea
    23 November 2015

    And well done for squeezing it into 500 words 😉

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