A class of nine- and ten-year-old children was working on fractions of shapes. Two worksheets were given out and the children were asked to look first at the one starting with a rectangle. This caused some confusion as one sheet started with a circle and one with a square. In response to this, the teacher asked, 'Do you know what a rectangle is?' He pointed to the sheet in question and one of the children said, 'But it's a square'. The teacher looked again at the sheet, admitted that it was a square and apologised for calling it a rectangle. As the teacher started to explain the sheet, one of the children sighed slightly and said in a whisper, 'Well, anyway, it is a rectangle'.
The last remark uttered in the above was one of many unsolicited comments heard during a year of participant-observation research in a mathematics classroom with myself in the role of a classroom helper. This article will focus on these remarks and those who made them.
The class in question comprised nine- and ten-year-olds in a British primary school. They were a 'bottom set': in other words, they were all considered to be 'less able' as far as mathematics was concerned. There were four children in the class who regularly made unsolicited comments about the mathematics being considered. I call them 'the whisperers', as many of the comments were made as whispered asides without apparent expectation of a response. Sometimes the contributions were louder and represented a challenge to official classroom discussion.
The whisperers formed an unofficial culture within the classroom, with a discourse which differed from the official classroom one. Comparing the two discourses and the two cultures which they represent shows that the whisperers adopted an inquiry mathematics perspective, whilst their teacher followed a school mathematics tradition. The two cultures failed to interact successfully and the whisperers continued to be considered as relatively unsuccessful at mathematics.
This study contrasts with existing work which suggests that inquiry mathematics is something introduced by teachers and often met with resistance by children. It also highlights the difficulties of categorising children according to 'mathematical ability'.