In my last post I argued that we should be teaching the thinking that becomes algebra from as early an age as possible. But what are those skills? What are the Dos and Don'ts? Many of the don'ts stem from the place of arithmetic thinking in our curriculum. Thinking arithmetically is all about getting a right answer, it's not always about being able to use that right answer to get more right answers in the future, and I think this is at the heart of what follows:
To develop algebraic thinking:
- Don't use the equals sign as an operator. Many children see the equals sign and think Do something; Work that out; Add those. The equals sign represents balance, equivalence. Children need to learn that in arithmetic to support their algebraic thinking.
- Don't represent things with the same initial letter as the problem, like 'a' for apples and 'b' for bananas. All it does is reinforce the misconception that the letter stands for an object or a specific number, rather than a variable.
- Don't get tied up in knots about BODMAS (the order that operations are carried out). The context of the given problem will sort that out. It needs to be made explicit when algebraic notation is introduced - you can explain how different calculators work those our sequentially or using an algebraic precedence of operators.
- Don't limit thinking about sequence to the next number. See if the children can see the rule or the pattern.
- Teach patterns from an early an age as possible. Here's Marylin Burns fantastic lesson.
- Do give children plain paper for them to represent their maths graphically.
- Tabulate patterns and sequence so children can move from seeing the 'up-and-down rule' (the sequential generalisation) to the left-to-right rule (the global generalisation).
- Follow the previous step by asking 'what's my rule?'
- Use empty box problems (e.g. 4+□=11)
- Do encourage children to represent the problem, not just solve them. Then the numbers can be changed and children can use the same representation to solve harder problems (perhaps by using a calculator and a spreadsheet).
- Do use a trial and improvement approach. This is especially powerful when it can be done using a spreadsheet.
- Do use the fantastic free materials that exist free all over the internet. Here's some that help children to find rules and describe patterns that the UK government produced a few years back, stored on the website of Dudley LA.
If there are anymore do's and don'ts, or any that you disagree with, please leave a comment.