Students Learning Techniques

Exam practice: a necessary evil; working through loads of past papers. Students need to be familiar with the types of questions and what they mean.

But before this, when students are learning techniques like adding fractions, do they need to do repetitious exercises? Do they need to practice twenty (or more) simple fraction addition questions? In my summer reading book, Developing Thinking in Algebra, the authors argue that students can gain fluency with a technique not by practicing it but by putting it into use. They state that another maths education writer argued that “in order to develop competence and fluency it is necessary to divert your attention away from what you are doing, rather than into it” (a summary of Caleb Gattegno in The Science of Education Part 1: Theoretical Considerations). This reminds me of what my department was trying to do with their year 7 fractions unit. Instead of the repetition of the adding fractions section in the textbooks, I used an nrich activity that investigates a fractions question based on adding fractions. Then the students are drawn into a task about whether all fractions can be written as the sum of unit fractions, and while doing their task they practice adding fractions more than enough.

“Learners do a lot of examples in pursuit of a greater goal,” Watson, Graham, and Johnson-Wilder say: and in doing so they gain the skills that will help them later (for example, to make connections with other areas of maths and also at exam time). They also they see when a technique is needed and how it can be used. And this is more valuable than simple, mindless practice.

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