Introduction

 

 

 

This blog is aimed at people (be they parents, tutors or teachers) working with children in late-primary, early-secondary school. It contains tasks to help children develop a better sense of number and other aspects of mathematics.

The blog is aimed particularly at those children who have developed the view that mathematics is essentially about procedures and who have got out of the habit of making sense of the mathematical elements (eg numbers) that they are working with. For example, I have in mind a Year 7 child who, when asked to find 20+20, instead of coming up with 40 in their head, felt compelled to write the numbers in a column: "0 plus 0 is 0, 2 plus 2 is 4, the answer is 40".

This is not an argument against procedures, but I do wonder whether we give them too much emphasis, and at too early a stage. Schools, teachers and pupils are put under considerable pressure these days by the high-stakes tests that pupils are required to take. In the UK, this applies especially to the Key stage 2 national curriculum tests (SATs or Standardised Assessment Tests) that pupils take towards the end of Year 6 (age 10-11 years). In maths, pupils take three such tests, one on 'arithmetic', two on 'reasoning', and there is a strong focus on procedures in each of them.

Some of the tasks in this blog will use items from these tests to throw light on these procedures and to explore other ways in which the items can be solved. The blog will also contain non-standard tasks so that children who would normally reach for a procedure are given the opportunity to use their 'natural' intelligence and some of the many skills that they have developed as they grow up.

For convenience, I am arranging the blog into sets of 'weekly' tasks, usually with 5 tasks per week. However, this format should not be taken too literally. For example, it doesn't mean that you should use one task every day, and only one task, though I would urge that when you use a task, allow plenty of time; don't rush through it and on to the next. It also doesn't mean that the weekly sets, or the tasks within them, have to be used in order. The order is up to you.

My hope is that the tasks in this blog will help children get a better feel for what mathematics and mathematical thinking is primarily about and that the children will become more confident about maths and get more joy from doing it.

Dietmar Küchemann