Obstacles en l'aprenentatge matemàtic: la diversitat d'interpretacions de la norma

Student thesis: Doctoral thesis

Abstract

This work reports on some exploratory research with a single class of students. They were given the opportunity to express their views on a variety of teacher strategies used in whole class interactions. The students' responses highlight that developments in the curriculum which support a more problem-based, exploratory approach would be welcomed, particularly if accompanied by opportunities for sharing ideas. This would reduce the shame, public and private, generated by 'getting it wrong'. Gender and class issues are mentioned but not discussed. There is considerable interest currently about the use of whole class teaching in mathematics. This interest has been provoked both by international comparisons (see Jaworski and Phillips 1999) and by government policy (see Brown et al 2000). Previously, there appears to have been an identification of this practice with a traditional, expository approach to learning, with discussion only occurring in the context of small group work (cf Groves and Doig 1998). However, some teachers are re-examining their use of whole class interaction, trying to include in the ensuing talk opportunities both for a more personally dialogic response from students and also for a more equitable one. As a contribution to this debate and concentrating on the affective dimension, we offer the reflections of some school students on their experience of whole class questioning and what they feel would make their mathematics education a more participatory experience for them. Our concern with increased participation stems not simply from a concern with equity but also because of a belief that participation itself is a defining aspect of learning (Lave and Wenger 1991). We note, however, that the value of increasing participation is dependent on just what it is that is being participated in. Research on the different 'classroom traditions' (Cobb et al 1992) or 'social practices' (Boaler 1997) that can be found in mathematics classrooms suggests that interactions are not necessarily mathematical. Such research has tended to focus on paradigmatic cases of different types of classrooms. This approach is valuable in highlighting the importance of differences between such types but it is important to recognise the way in which particular classrooms may share features of the different 'typical cases'. We believe that the evidence presented in this paper tends to support this view. Analysis of the student experiences we report here reflects that their experience of secondary school mathematics has been predominantly that of exposition plus. There is little knowledge about what values teachers are teaching in mathematics classes, about how aware teachers are of their own value positions, about how these affect their teaching, and about how their teaching thereby develops certain values in their students. This work presents parts of the case studies of two Australian mathematics teachers which concern the relationship between their intended and their implemented values. As well as discussing data about these teachers' values, two possible approaches to the analysis of the interview and observational data are also presented. Research Council funded three-year project which included the goals of: (a) investigating and documenting mathematics teachers' understanding of their own intended and implemented values, and (b) investigating the extent to which mathematics teachers can gain control over their own values teaching. Values in mathematics education are the deep affective qualities which education aims to foster through the school subject of mathematics (Bishop, FitzSimons, Seah, & Clarkson, 1999; Bishop, 1996) and are a crucial component of the mathematics classroom affective environment. While accepting that values, beliefs, and attitudes are dialectically related (see Krathwohl, Bloom, & Masia, 1964; McLeod, 1992; Raths, Harmin, & Simon, 1987), our concern is with the values of mathematics, mathematics education, and education in general (see Bishop, 1996), rather than more global values such as social, ecological, moral and so forth - although these are by no means incompatible, and indeed may influence teachers' personal value systems. As Bishop, FitzSimons, Seah, and Clarkson (1999) note, there is little knowledge about what values teachers are teaching in mathematics classes, about how aware teachers are of their own value positions, about how these affect their teaching, and about how their teaching thereby develops certain values in their students. Values are rarely considered in any discussions about mathematics teaching, and a casual question to teachers about the values they are teaching in mathematics lessons often produces an answer to the effect that they don't believe they are teaching any values at all. It is a widespread misunderstanding that mathematics is the most value-free of all school subjects, not just among teachers but also among parents, university mathematicians and employers. Mathematics is just as much human and cultural knowledge as is any other field of knowledge; teachers inevitably teach values, and adults certainly express feelings, beliefs and values about mathematics which clearly relate to the mathematics teaching they experienced at school (FitzSimons, 1994; Karsenty & Vinner, 2000). More fundamentally we believe that the quality of mathematics teaching would be improved if there were more understanding about values and their influences.
Date of Award20 Jul 2001
Original languageCatalan
SupervisorMaria Nuria Gorgorio Sola (Director)

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