Struggling at mathematics 

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It was a Saturday morning and I was stood in a field in the North of England, holding a shotgun. I had just missed five clay pigeons in a row while being gently mocked by the instructor. It was my friend’s stag weekend. The night before had been a late one and I was feeling a little depleted.

I gestured to a grassy bank and said that I was going to sit down. “I’ll just watch from now on,” I explained. The instructor, feeling a little guilty, tried to talk me around; he wanted me to get my money’s worth. But I was having none of it. Clay pigeon shooting and me were over.

This is how maths must feel to many students, except that we rarely let them sit it out – perhaps with the exception of some kinds of group work. Instead, we keep throwing them into the struggle and making them confront their own shortcomings. It can’t feel good. Maths is unforgiving in this regard. You can write a sentence full of spelling mistakes but, at the end of it, you’ve still written a sentence. If you’ve failed to solve a maths problem then you’ve achieved nothing.

Progressive maths educators recognise this issue. For them, it is even more prominent because of their view that learning maths should be mainly about problem solving. They valorise open-ended problems. They think these are motivating. But the motivation is fragile. It can be easily shot down. 

So their solution is to change the personalities of maths students. Instead of being bummed-out by failure, students should see this as a good thing. I don’t think it’s true to claim that every time you make a mistake, your brain grows, but this kind of statement might serve a useful purpose in shaping mindsets. We should teach students to value struggle

Such a strategy might even work for a short period of time. We might be able to psych our students up for the struggle so that they feel positive about it. But learning maths is a long term process. It will include times when our students are feeling depleted. It seems a stretch to think that we can change their attitudes in such a radical and persistent way.

There is an alternative, of course. Progressive educators want to take traditional maths teaching and revolutionise it. Explicit instruction, on the other hand, enhances traditional maths teaching with research-based practices. It works with the grain of how teachers naturally teach maths. 

One such enhancement is to tailor the teaching to obtain a high success rate of around 80% or more. This forms a key part of the gradual release of responsibility that starts with the teacher fully explaining and demonstrating and that ends with students independently solving complex problems. One tactic that I use to obtain success early in this process is the use of example-problem pairs: a fully worked example placed next to an almost identical problem for the students to solve.

This builds motivation because success builds motivation. Hitting four out of five clay pigeons is far more motivating than hitting none.

So you have a choice. Which option seems the best bet to you? Should you seek to cause a long-term change to your students’ personalities or should you enhance your teaching to ensure a higher success rate?

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4 Comments on “Struggling at mathematics ”

  1. Ben says:

    Do I have to make the choice? Isn’t it possible to use traditional methods, like explicit instruction, to instill long-term personality changes surrounding perseverance?

    • Greg Ashman says:

      Maybe. However, my primary focus is on teaching maths.

    • For most students I imagine perseverance comes with experience that SOMETIMES success comes with persistence. This is premised upon the existence of successful experiences, and will be maximized by learning environments which maximize opportunities for success. Progressive methods have a tendency to attempt this by redefining success, a transparent subterfuge that quickly wears off. Students, even very young ones, aren’t consistently fooled. Explicit & direct instruction tends to maximize opportunities for success by leveraging the Worked Example Effect, breaking learning into more easily masterable quanta and providing less ambiguous expectations for students.


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