Research often focuses on disaffection in the mathematics classroom as evident in disruptive behaviour, absenteeism or special needs: thus, it ignores a group of students whose disaffection is expressed in a tacit, non-disruptive manner, namely as disengagement and invisibility. Ignoring this often large group implies that the mathematical potential of these learners may remain defunct. This article reports on a one-year study of quiet disaffection conducted in three Year 9 mathematics classrooms in Norfolk. Through extensive observation and interviewing of seventy 13/14 year-old pupils, a profile of quiet disaffection from secondary school mathematics was constructed. It is proposed that its characteristics include: Tedium, Isolation, Rote learning (rule-and-cue following), Elitism and Depersonalisation. The proposed characteristics are described and exemplified. Finally, the themes that emerged from the students' statements about their images of effective mathematics teaching (Nature of Classroom Activities - the notion of 'Fun', Teaching Styles; Role of the Teacher; Role of Stratification Structures such as Setting) are outlined
In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of studying Calculus. These shifts concern the lecturers' and students' communicative practices, routines of constructing mathematical objects and ways of resolving commognitive conflicts. We then propose that commognitive constructs such as subjectification can be deployed towards ‘scaling-up’ the hitherto fine-grained focus of commognitive analyses. Finally, we conclude with observing how the commognitive approach relates to constructs from other sociocultural approaches to research in university mathematics education, such as “legitimate peripheral participation” from the theory of Communities of Practice and “didactic contract” from the Theory of Didactic Situations
This report1 from the ICME12 Survey Team 4 examines issues in the transition from secondary school to university mathematics with a particular focus on mathematical concepts and aspects of mathematical thinking. It comprises a survey of the recent research related to: calculus and analysis; the algebra of generalised arithmetic and abstract algebra; linear algebra; reasoning, argumentation and proof; and modelling, applications and applied mathematics. This revealed a multi-faceted web of cognitive, curricular and pedagogical issues both within and across the mathematical topics above. In addition we conducted an international survey of those engaged in teaching in university mathematics departments. Specifically, we aimed to elicit perspectives on: what topics are taught, and how, in the early parts of university-level mathematical studies; whether the transition should be smooth; student preparedness for university mathematics studies; and, what university departments do to assist those with limited preparedness. We present a summary of the survey results from 79 respondents from 21 countries.
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