Archives for November 2015

TEDx Johannesburg : 19 Nov 2015

I have been asked to talk at TEDx Johannesburg which will take place on 19 November 2015. This is my first time talking at TEDx and it is great to have the opportunity to talk about your passions, but the challenge is how to put a life’s work and visions into 15 minutes!

I have entitled my talk “BRAIN SURGERY ON YOUNG MATHEMATICAL MINDS” and the message is that mathematics is important and relevant, and that there are ways to improve mathematics learning which are like brain surgery, in changing the brain, but are not invasive. Rather these methods use the power of human learning, to move towards a balance with the environment, in order to enhance the speed and effectiveness of learning.

Within this talk I present the following mathematical question, which is at around the Grade 9 level, which is to find the value of the following expression:


This question is not difficult, and is worth around 3 marks out of a possible 100 marks for in a 2 hour Grade 9 examination. This means that you would have around 3 minutes to answer the question and to write your answer, and you should write three elements to your workings towards the answer to indicate that you have mastered the method and have applied it to this question. It is not sufficient to only provide the final answer, since it is the workings which reveal how this problem has been solved, and this is considered evidence of your proficiency.

I will provide the answer to this question at a later time….for now just examine the question, try to read it and to break it into parts, and try to make sense of it. Specifically, try to find in your brain what mathematics you may need to solve this. This question is actually easier than it seems, and it is common that much of what appears to be “hard” in mathematics just means that you cannot see which of your current knowledge to apply. It is not that you do not know the subject, it is rather that you do not know how to use the knowledge which you have.

In this sense, our mathematical knowledge is like a set of tools, which we have in our mental toolbox. And there is no sense having a great tool if we do not know how to use it. In a school environment these mathematical tools are often taught in isolation from each other, and when a tool is required in a new context it is not considered because it does not seem to fit.

Mathematics knowledge is viewed as a set of tools which we call “SCHEMAs” and which reside in our brains, or in our minds, or somewhere else – but in reality we do not actually know WHERE mathematical knowledge is stored, except that it seems to be available when we need it. These SCHEMAs are built in response to our experiences, and to help us make sense of the world. Thus if the world presented to us is wrong, then we may developed the wrong SCHEMAs. Given the right environment, and in particular the right questions and the right feedback to our attempts, we can learn rapidly.

My contribution to mathematics education is three-fold:

  • exploring the automation of various teacher functions: such as understanding the learner, posing the right question, and providing the right feedback – which I am planning to make available as online mathematics intelligent tutoring facilities based on AI methods
  • exploring how parents can help their children in developing mathematics knowledge and proficiency, which is a topic I will draw on later in other posts
  • building up a base of knowledge about mathematics for future generations in the Museum of Mathematics, which is a project which has commenced recently and is being structured at present.

I hope that the TEDx talk will appear on YouTube and on the TED web site shortly, and I will provide a link here.