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4472 WordsJun 5, 201418 Pages
Pupils’ Misconceptions in Mathematics One of the most important findings of mathematics education research carried out in Britain over the last twenty years has been that all pupils constantly ‘invent’ rules to explain the patterns they see around them. (Askew and Wiliam 1995) While many of these invented rules are correct, they may only apply in a limited domain. When pupils systematically use incorrect rules, or use correct rules beyond the their proper domain of application, we have a misconception. For example, many pupils learn early on that a short way to multiply by ten is to ‘add a zero’. But what happens to this rule, and to a child’s understanding, when s/he is required multiply fractions and decimals by ten? Askew…show more content…
The presence of the operator symbol, +, makes the ‘answer’ appear unfinished. In short, pupils see such symbols as +, –, x, and ÷ as invitations to do something, and if something is still to be done, then they ought to do it. If we have to remove the symbol by doing what it tells us to do, in this case adding, it is only natural that 3m + 6 should become 9m. Readers who find it difficult to understand this tendency may like to consider their own response to the following statement 3 ÷ 40 = 3 /40 Most people respond differently to the two sides of this equation. The left-hand-side looks like a question, namely “What is three divided by forty?” The right-hand-side, however, is not a question but simply a fraction: three fortieths. In a sense these are just two different ways of writing the same thing, but this may also be seen as revealing that in both arithmetic and algebra some expressions lead a dual existence as both process and product. 3m + 6 can be seen as a set of instructions for 13 calculating a numerical value, but also as mathematical object in its own right (French 2003). The resistance to accepting 3m + 6 as an answer is easily understood. In ordinary arithmetic it is always possible to remove the operator signs (unless there are infinite in number), and the final answer has not been reached until they are all gone.. Strategies and Remedies For reasons that should already be clear, despite its obvious appeal

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