... reach their goals and repeated failure may result in loss of confidence and self-esteem. Teachers must provide the opportunity for the child to attain their targets. Once the teacher realises the necessity to identify the misconstrued knowledge/concepts, they must discover underlying problems in the most accurate way. To simply study the child's work shows a self-important belief that the teacher can understand what the child is thinking. It is only by discussing with the child their ideas and perceptions that the true reasons for the misconceptions become evident. Alice states that multiplication makes numbers larger and division makes numbers smaller. Alice's statements will be accurate when applied to the contexts of multiplication and division that she is most likely to be familiar with, for example positive integers. When children are first introduced to multiplication in school, they become familiar with the terms 'lots of' and 'sets of', this then leads to an ...

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