Developing Mathematical Thinking

By Graham Jones 

As a parent who has a keen interest in mathematics, I am always eager to assist my children or nieces and nephews with their maths homework. A few years ago it occurred to me that, in some cases, I was actually doing their homework for them and consequently being inadvertently detrimental to their learning. So I asked myself the following questions, ‘how can I motivate learners to enjoy mathematics so that they willingly solve problems for themselves?' and ‘how do I know what level of assistance actually maximises the learners development?'

An important point to remember in a helping role is ‘telling learners the right answer might get the homework done; however, a tutor helps them to learn for themselves and understand new ways of working'. This can only benefit mathematical thinking in the long run

How can parents help children with maths?

Usually children will only ask for assistance when they are stuck. I appreciate it's the easy way out to just do the problem for them, but this certainly doesn't maximise their learning.  Next time you have a plea for help, try asking a question such as, ‘What do you know?' or ‘What are you trying to find out?' and ‘What have you done so far?' Quite often actually talking through the problem will provide a prompt for moving forward.

Motivating children

Motivating learners is not an easy task. We all know as parents that there are many other more enjoyable pastimes for our children that prove an easy distraction. From an early age it is a good idea to involve children in as many family activities as possible that promote number skills and, most importantly, are enjoyable too. Easily available ones are - dominoes (especially the 5's & 3's version) and numerous family card games that involve scoring points in different ways. Both of these enhance children's learning in basic arithmetic and develop important aspects of mathematical thinking such as working out strategies and improving reasoning.

Maths help for parents

There are numerous books that have exercises you and your child can do. But in my experience, kids are not too keen working from books as it is very similar to what they have done for most of the week at school, they are far more likely to be interested in a web based approach. An excellent web site for maths exercises, is nrich.maths.org, which covers all key stages from 1 to 6 with interactive problems, games and articles on all subjects with different degrees of difficulty.  Just to ease your frustrations (should there be any!) the answers are included as well as hints.  Also, there are activities involving geometric software, so for the learners it's not all pencil & paper!

If you become interested in assisting your children with their homework, as it really is interesting and rewarding, there is a very useful course offered by the OU, which is a Graduate Diploma in Mathematical Education.  It is this course that I'm working through, and it is partly aimed at parents such as me. It has been extremely beneficial to me, my children.  Another source of information and tips about helping children is the Association of Teachers of Mathematics, atm.org.uk.