Break the rules!! (by letting students find them for themselves)

Posted by Charlotte on Mar 1, 2016

I want to start by saying that, if I’m honest, I got completely lost with the various analogies in Skemp’s lengthy article and enjoyed watching Meyer’s video (including the unrelated animation at the end).

I do think that, although really interesting points were raised, the main points of the article could have been made in a much more succinct way. This being said,  I did learn a lot about relational and instrumental understanding, two terms which were completely new to me. I could see the benefits of teaching a relational understanding of mathematics rather than just an instrumental understanding. I can see the benefits of teaching instrumentally, Skemp acknowledges the short term benefits (much like the impatient problem solvers in Meyer’s talk) and how it enables students and teacher to work towards the exams- a practice which I wish we had moved away from by now. The thing is, unfortunately, teachers are now facing a bombardment of pressure to get the results needed both in terms of targets and results based raises on the pay scale. When teachers have so little time to prepare lessons, isn’t it tempting to teach in the way that gets the quickest results? I also feel that instrumental and relational understanding do not have to stand alone and think a mixture of a little instrumental understanding built upon relational ideas wouldn’t hurt anyone.

This is where Meyer’s patient problem solving theories come in. It was refreshing to see his approach to teaching his classes. The use of multi-media videos and images to bring the 2D, unrealistic and frankly quite boring questions that can be found in text books. Meyer furthers the ideas found in Skemp’s article and brings them into the 21st century (in Skemp’s defense his article was written in 1976). From experience, I agree that teachers (and teaching assistance for that matter) can often be seen to help students too much- which can not only make students lazy, but also doesn’t prepare them for the exam, let alone real life situations when the mathematics may be needed.

I was very interested in Meyer’s (stolen from Einstein) idea that student should be involved in the formulation of the problem itself. Stripping back the questions and allowing the students to build them up themselves seems like a very good practice- one I would like to try and incorporate in my own teaching next year. I do wonder how much time he actually spends on this though. I also wonder how long the multi-media parts of the lessons take to create- I’m definitely not as tech savvy as I would like to be (or as people assume I am with my age) and I would question the ability of some of the more experienced teachers I know to be able to create the stimuli. I think that it’s a good idea, but I go back to my view from last week on practicalities.

In conclusion, I feel that both stimulus this week present interesting and useful techniques in tackling the issue of teaching for the exam. I feel that students will increase their long-term understanding with patient problem solving and relational teaching (with a sprinkling of instrumental teaching thrown in near exams so they can prove their understanding to the ‘evil’ examiners).


  1. Ray
    6 March 2016

    I liked your points about having an intelligent mix of instrumental and relational teaching and for using media/technology to make problems more interesting to students.

  2. fbontemps
    6 March 2016

    Hi Charlotte, thank you for sharing your thoughts, it’s the first time that I’ve kind of hearing instrumental and relational understanding too. Unconsciously it seems that instrumental understanding was universally accepted until skemp and perhaps others before him, realised that new measures needed to be taken. Is it the period of awakening for mathematics? Exciting time!!!!

  3. Havva
    7 March 2016

    Hi Charlie,
    You have certain interesting points that is highlighted in your piece, as you have been and still are a teaching assistant, I can see that you had plenty of observations of mathematics teaching in school. You raise an interesting point concerning the multimedia capabilities of maths teachers!

  4. pepsmccrea
    8 March 2016

    Good to see you taking on board these ideas so openly (even though Skemp’s paper is a bit hard going!). Also good to see you begin to explore the reasons why relational teaching is not more widespread. Keep up the strong thinking!

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