How we learn = how to teach?

Posted by Marjan, Uncategorized on Apr 5, 2016

“I’m no good at maths !” How often do we hear this, not only in the US and UK but also in the Netherlands and even said with pride, no embarrassment whatsoever. I do think everyone can learn maths and it’s one of reasons for me to become a teacher. This task’s article and videos reinforce this idea and have given me a lot to think about how we learn and how I can use that in teaching.

The article describes how we are born with the ability to learn maths, although developing further ability does require time and hard work. Yes, we can learn maths but no, it does not come easily to most of us. The author states three types of knowledge: factual, procedural and conceptual. Thinking back: factual and procedural sound like instrumental, conceptual like relational thinking. I was interested in the idea that factual learning frees up working memory to use for more complex problems. The author is in favor of memorizing times tables but with widespread use of calculators, how important is this?  I agree with the article that factual, procedural and conceptual should be taught together linking the conceptual ‘Why’ with procedural ‘How’. Just as was said about relational learning, conceptual knowledge is often weak and more difficult to learn so ideas on how to teach conceptual knowledge are discussed. Concepts build on knowledge of previous concepts so what to do if previous knowledge is poor? Explain previous concepts from scratch or press on which will lead to instrumental teaching? Here time constraints will also make it difficult to teach new concepts if previous ones are not fully understood. I agree with explaining concepts by using examples and analogies but new for me was looking at why this worked and considering familiarity and concreteness of examples. I will try to remember to tell students to look for commonalities, see what is important to the concept and what is incidental. And find an analogy that can be used across topics. Choosing a limited number of concepts per year and in a certain order is also worth remembering.

Technology and the internet have led to an abundance of free videos and courses available online and the Khan Academy looks like a great one. I have used several of the videos to refresh A-level content for a different module. Nowadays any self-motivated student can watch these videos and try to learn something new. But there’s my reservation: what about students who are not motivated. Flipped classroom sounds great for groups who will happily watch the video as homework, but what if they never do homework? Or do not pause and rewind and keep trying until they get it? If they haven’t watched the video, they won’t be able to do any work in class. And the class with all pupils behind a screen working at their own pace also sounds great but is this  ‘humanizing’ the classroom when everyone is looking at a screen? It doesn’t feel that way to me. I would rather see pupils working together on problems and class discussions. And does everyone learn as well from watching a video? Mr Khan mentions that a video is not the same as a one size fits all lecture, but only because it can be watched at your own pace. The way a problem is explained is still the same and some pupils may learn differently and need a different type of explanation. The tracking of individual students and the motivational input such as badges (inspired by gaming) were interesting.

Finally, I also enjoyed the video on learning and finding out more about our brain, especially the advice to ignore our brain’s careful warnings when something is hard: do the opposite!

Little fascinating detail: that in tests with number lines and small versus large numbers, Iranians had reversed results because they read from right to left. I wonder if this affects learning about number lines in general?


  1. aw677
    5 April 2016

    I think that you bring up some really interesting points, particularly about those children who don’t do their home work and the impact that would have on the Khan Academy classroom. There will always be students who don’t do their homework, for a variety of reasons but in this case doesn’t it have more impact on the individual than the whole class? There doesn’t seem to be an easy answer to this! But I also find myself agreeing with you about students working together in groups to solve problems and discussing the many merits of mathematics. Maybe we need to find a balance, find our own way and do what’s best for the individuals we will teach, I think experience will be our greatest teacher.

  2. Martha
    12 April 2016

    I agree Marjan – wouldn’t it be great if we as teachers could change the minds of those who ‘just can’t do maths’?!

  3. pepsmccrea
    12 April 2016

    Great balanced discussion here. Good to see you making important connections between conceptual/procedural/instrumental/relational etc. And some really important questions posed in the latter paragraph.

    Interesting about the Iranian research. Wonder if Chinese (reading differently again) learners would have different results too?

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