In Section 3 the articles are about pupils' and teachers' perceptions. Over recent years there has been a shift in focus of research from considering the single perspective of the teacher towards listening to the learners. Much of the research with teachers looked at possible changes in classroom practice while the learner's perspective shows how the creation of a collaborative community of practice can impact on the development of mathematical thinking. Although much research has looked at pupils' learning and their opinions (for example, Rudduck, 1996) the focus of this research was not mathematics and the research had a tendency to look at the whole school issues rather than those which pertain specifically to teaching and learning mathematics.
In Chapter 11, Alba Thompson is concerned with the possible link between teachers' views of mathematics and their pedagogic practice. Although this research dates back to the early 1980s it is still relevant today because it shows how a teacher's perception of the nature of mathematics may affect their practice. Thompson presents her research in the form of case studies showing how three teachers behave in different ways depending on their perception of mathematics. She is quick to point out that the way teachers view mathematics and their subsequent classroom practice is not simply down to cause and effect. Not only did she find differences in the classroom practices of the three teachers but also in their view of what evidence of mathematical understanding looked like. There were also differences in the way that teachers planned lessons and this had an impact on the flexibility they displayed in their teaching.
Jo Boaler's research (Chapter 12) was set in two schools that used different approaches to teaching. One school was traditional in its style with pupils in sets while the other was progressive with pupils in mixed ability groups. Boaler found that setting had an impact on pupils' ideas about, and responses to, mathematics as well as their eventual achievement. She found that pupils had four main complaints about setting: the pace of lessons; pressure and anxiety; restricted opportunities; and setting decisions. Boaler also found that a disproportionate number of working-class pupils were placed in the lower sets, which may indicate inequity within the setting system. Some of the students became disillusioned with mathematics due to the pace of lessons and the expectation on them that resulted from their positioning in a particular set. Boaler's findings are significant at a time when setting is becoming increasingly prevalent in UK schools. If the impact of setting is to cause learners to become disillusioned then it may be time to reconsider its use.