The three bears
Teacher: The biggest bear... is he bigger than mummy bear?
Children: (They shake their heads.) Noo!
Teacher: Is daddy bear bigger than mummy bear? (Points from largest to middle bear.)
Teacher: I think he is, isn't he?
All teachers have experienced this moment: you ask what appears to be a very simple question, to be faced with a seemingly inexplicable response. What might be the reason for this response? One might assume that the students did not understand the relation bigger.
To test this hypothesis, Walkerdine conducted an experiment in which she asked the question, 'Is the daddy bear bigger than the mummy bear?' followed by the reverse question 'Is the mummy bear bigger than the daddy bear?'
Nearly all of the children got the answer to the first question correct - suggesting that the majority of these students do understand size relations - but only half of the students got the second question correct, answering yes to both questions.
If size relations were not the problem, what could explain this confusion?
Initially, I thought that the problem in the children’s response was produced by the confusion over the mummy-daddy relation as signifiers of power or authority over children, and therefore the problem of the relation between differential authority and differential size. This turned out to be over-simplistic.
This paragraph resonates with my experience of teaching. We are often very quick to jump to conclusions to describe/explain what might be happening, but what is actually happening may well be more more complex than we first thought.
This brings to mind the work of Lacan; he believed that psycho-analysts should not leap to ready-made conclusions to answer for for people's behaviour, but rather that they should ask questions, then listen very carefully in order to to find other questions that should be asked. In this way, no two analyses will be the same; any understanding will be found between both parties through dialogue.
The three rectangles
So what would explain the responses to the rectangle questions? Walkerdine offers some suggestions as to why children might have given this incorrect response:
- It is clear that the questioner knows the answer to the questions (called pseudo-questions), so why is the questioner asking the question again (in reverse order)? Does this suggest to the students that they got it wrong the first time? There is research that suggests that people change answers if they are asked a question twice (double-questioning).
- Perhaps some students do not see the difference between the questions; one student answered 'Yes, I said!' to the second question.
- People are more liable to answer in the affirmative if they have not really listened to a question (as most questions require a positive response), or if questions are asked in a certain way.
Perhaps all we can say is that we can't ever really be sure what the underlying reasons are for the children's mistakes, we can only listen to their responses carefully and ask more questions in the attempt to gain understanding of their understanding.
… mummy is a term which is often used as a synonym for big (mummy is big like daddy). This provides an example of the circulation of meanings within certain practices in which the family is inscribed.
This again comes back the theme of the first post - signifiers have different meanings in different practices, and sometimes these meanings create confusion:
The same signifiers may exist across different practices, but this does not mean the same signs are created. In addition, I have tried to suggest that the multiple signification of many signs within particular practices demonstrates the way in which the participants are positioned and regulated, and how emotionality and desire are carried within these relations themselves.
The words emotionality and desire are significant here, and will be explored as themes in subsequent posts.
Walkerdine then goes on to suggest that not only do signifiers have different meanings in different practices, but that the practices themselves lead to different interactions:
At home… there are many activities which are carried out jointly by adult and child... [but] in the nursery, however, the pattern is different. Adults… very rarely act as equal participants in a game or activity: such positions are left to other children. It is not clear to me precisely what effect such differences in adult positions have, but it certainly does produce significant differences in interactions.’
This brings to mind Lave and Wenger's work on situated cognition, and the effectiveness of apprenticeship as a pedagogical approach. Perhaps we should seek to move towards a pedagogy of 'joint activity' in the classroom, similar to that provided at home?
Whatever the reasons for confusion, it is clear that learning in the maths classroom is rarely as simple as it might seem, or as we might want it to be; perhaps the first step is in realising that this is the case:
The teacher… simply does not realize the massive entanglement of differential relations with which the children are having to cope.