Why Pick One?

Posted by Laura on Nov 16, 2015

I was interested to read the article by Willingham on whether or not some people are genetically predisposed to difficulty with mathematics. I found many of the concepts within the article similar to those we have previously looked at such as different teaching and learning styles that lend themselves to different styles of understanding. Willingham speaks of conceptual knowledge, being similar to the relational understanding as Skemp explains it, and procedural knowledge taking a form similar to instrumental knowledge. An interesting point made in this article was that unlike previous literature where I felt that conceptual or relational understanding was seen to be superior and a more idealistic way of teaching, in this piece a link is made more between the need for both types of understanding and that rather than contradicting each other, they can compliment each other to give a more holistic learning experience. I think this is really important for us to consider in our classrooms as one of the points brought up was that to teach entirely relationally could have a massive impact on the amount of material that could be covered in the short time span available in an academic year. To teach conceptual and procedural methods side by side could enable educators to enhance current methods without sacrificing time schedules imposed by the curriculum.

Thinking of ways to supplement current teaching methods made me consider how tools such as Khan academy can fit into modern teaching. There’s no doubt in my mind that students are more excited by the thought of using IT in their learning than pen and paper however, the resources we are using need to maintain that engagement over a prolonged time. Over use of a particular resource can often lead to student becoming bored of it and just as switched off as with repetitive textbook methods. The key, I think, is to incorporate these methods within our teaching so that we are presenting as varied selection of appropriate and functional teaching styles as possible.

Thinking about this further I was very interested in the idea mentioned in the video that one teacher sets her classes Khan academy as homework to introduce a topic and uses lesson time to work on consolidation of the knowledge. I think this idea is fantastic in theory, but I wonder if there are downsides to it as well. Having watched several instructional videos online about various mathematical topics and from a variety of sources I agree that they are a fantastic resource for learning at your own pace and being able to rewind and re-watch sections however, how useful is it to watch and re-watch something you don’t understand over and over again? Often instructional videos of this type use one method or representation to solve the problem. In the classroom if a student isn’t understanding a certain way of explaining something, there is the opportunity to try a different method or representation. I wonder if the videos represented here can offer this to students.


  1. Stephen
    17 November 2015

    Really like the way you have linked back to Skemp and that you find that relational and instrumental should go hand in hand. The point about boredom due to overuse of materials of materials is valid. I wondered what you thought about Wilinghams suggestion for reusing analogies to aid in the conceptual understanding. Do you think if analogies are overused that they will also lead to boredom?

  2. pepsmccrea
    23 November 2015

    Great analysis here. You are really thinking about both sides of the story (the pros and the cons) in an effort to reach a deeper understanding of the ideas explored. Lots of good links back to previous ideas too, and building on them in a helpful way. Keep up the good work!

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