ABSTRACT

I know that you believe you understand what you think I said, but I’m not sure you realise that what you heard is not what I mean.

(Robert McCloskey)

What does the above quotation mean to you? It reminds me of the frequently heard question in the classroom ‘do you understand?’. Whilst looking rather innocent, this can be a problematic question – for instance, how valid is the answer? If you ask this to a student and they answer ‘yes’, what have you learnt? That they are compliant? That they have heard you? Or that they think they understand you? Perhaps the question you are really asking is ‘do you understand in the manner that I understand?’ or ‘do you understand in the manner that I want you to understand?’ but of course the student may not always know if they do. Even if you can establish that they have understood in the way you intended, what do you mean by understanding? Do you mean that you want them to understand how to do the work or are you hoping for something else mathematically; a spark that suggests something ‘deeper’?