Saturday, 25 June 2011

The yin and yang of maths education - Part 1.

File:Yin and Yang.svg
Many authors have written about the need to move from a curriculum which teaches an established curriculum to one which encourges students to mathematise their experiences of the world for themselves.

I see things a little differently.

I believe that both forms of mathematics education are justified and of great importance.

Modern technology offers students a wide variety of ways by which they can efficiently and effecitvely acquire orthodox knowledge.  Teachers who utilise this technology can create more time in the classrooms on the types of tasks which effectively develop students' abilities to interpret real life situations, struggle with connected and extended task and to learn to express and develop their own thinking. 

Modern technology can also enhance the quality and relevance of the experience a students has when they explore mathematics for themselves because they can rapidly interact with established thinking, notation and invididuals who are interested in their area of enquiry.

So it is natural both that more constructivist teaching can and will occur and also that such teaching will lead to a greater coverage of core concepts.  But I prefer not to think of the outcome as being a shade of grey although that's how my lessons might appear to others. I prefer the visualise black and white, yin and yang.

Here is an analogy.
Which is better - pop music?  classical music?  something which is halfway between the two?  or something which is unashamedly both, black and white, yin and yang with no compromise to either?  Here's a video to illustrate my preference.

More orthodox justifications for and desriptions of this perspective will follow as and when I have time.


  1. Regarding the "ying and yang of maths education," you initiated an exchange between the two of us on that subject on my blog "Hake'sEdStuff" at .

    Therein I wrote:

    "It's possible that it might eventually be shown that, unlike for introductory physics, both "Interactive Engagement" (IE) and "Traditional" (T) methods are required for effective introductory math instruction.

    But unfortunately [except for Epstein's (2007) work] there's been little, if any, pre/post testing in math courses with mathematics Concept Inventories."

    Richard Hake
    Emeritus Professor of Physics, Indiana University

    P.S. I'm an HTML dummy so you'll have to copy and paste the URL's above and below into your browser window.

    Epstein, J. 2007. "Development and Validation of the Calculus Concept Inventory," in "Proceedings of the Ninth International Conference on Mathematics Education in a Global Community," 7-12 September, edited by Pugalee, Rogerson, & Schinck; online as a 48 kB pdf at

  2. (fuller reply sent privately)

    Hello Richard,

    Thank you so much for getting in touch, it would be lovely to correspond with you directly. I've been contemplating revisiting this topic for a while and indeed you have prompted me to get going.

    The challenges of synthesising curriculum based and constructivist approaches to mathematics teaching has been discussed extensively in UK maths education over the years. By the time I became a head of department I had already clearly developed my thinking on synthesising paradims. I will write about the development of my thinking and the practicalities of implementing it in the next sections of this blog. I hope you stay along for the ride and would greatly value your comments.

    Could you explain in more detail what you mean by 'mathematical concept inventories?' Testing and individualised tracking and intervention was fundamental to my approach so I may have the kind of data you are looking for.

    Best regards,


  3. Paradigms not paradims. I wish I could edit comments!