More on simple arithmetic skills that people don’t always understand as well as they think they do, leading to difficulties at a later stage.
In the OU Science Faculty we use the mnemonic BEDMAS (others use BODMAS or BIDMAS) to remind students of the rules governing the order of precedence for arithmetic operations:
Brackets take precedence over
Exponents. Then
Division and
Multiplication must be done before
Addition and
Subtraction.
When analysing student responses to iCMA questions, lack of understanding of the rules of precedence and related issues, whilst not contributing to as many errors as do problems with fractions and/or units, it’s still up there as a common difficulty. Sometimes the problem can be attributed to poor calculator use e.g. a lot of students interpret 3 6/3 as meaning (3 6)/3, perhaps because they don’t stop and think before using their calculator. This misunderstanding (seen in lots of variants of a question in summative use) led to a talk I used to give: ‘Why is the answer always 243?’. But it goes deeper than that! For example, even after teaching students how to multiply out brackets etc., many think that (x + y) 2 is the same as x2+ y2. Mistakes of this ilk are completely understandable, but it is nevertheless something to watch out for.