Practising algebra, avoiding magic triangles

Practise is really important for learning. I’m currently taking the MOOC “Learning How to Learn” which I highly recommend by the way. One of the points it makes is that practise is important especially when learning abstract concepts like algebra. The research is telling us that students will need a lot of practise to get good at algebra. Pretty uncontroversial right? I bet most maths teachers would agree that their students should practise algebra.

However there is a teaching technique I’ve seen recently in schools which is depriving children of opportunities to practise basic algebra.  I’m talking about the “magic triangle” approach where students write a formula like F=ma into a triangle. By covering up the variable they need to find they can read off the form of the equation that they will need to find their variable. All without rearranging the equation. As far as I can see the logic behind it is “my students find algebra hard, let’s help them by showing them how to get some answers without using algebra”.

The problem of course is that if students never practise algebra on these simple problems they will always find it hard and will have no chance with the more complicated problems that can’t be solved by the triangle method. And by giving students a different method teachers are unwittingly passing on the message “algebra is hard, you can’t do it, don’t bother trying”. I’m sure that’s  not what the teacher intends but I’m pretty sure that is what the student is picking up. This is the very opposite of the growth mindset that gives our kids the best chance of success.

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