Melissa Rodd | Institute of Education, University College London (original) (raw)
Papers by Melissa Rodd
This chapter uses psychoanalytical theory to help to understand emotion when a student has diffic... more This chapter uses psychoanalytical theory to help to understand emotion when a student has difficulties in learning mathematics. The centrality of the relationship between student and teacher is theorized and discussed, and issues related to teacher preparation and in-service training are put forward. The notion of a “math-care environment” is developed and ways to help a teacher pause, in order to relate to a learner, are advocated.
This paper uses ideas from the field of neuroscience of attention to investigate emotional (or ot... more This paper uses ideas from the field of neuroscience of attention to investigate emotional (or other affective) responses - ‘points of affect’ - that instigate change in teachers’ or learners’ Space for Geometric Work (‘SWG’). SWG theorises that physical space and tools or artefacts, together with suitable language development, are the components from which a cognitive grasp of geometry is formed. Research from the neuroscience of attention theorises a distinction between ‘top-down’ and ‘bottom-up’ attention. ‘Points of affect’ divert attention and thus can change a person’s SGW. The main body of the paper concerns relationships between deductive and perceptual reasoning in terms of attention processing and points of affect. Application to teaching geometry is discussed.
This description/analysis of a secondary mathematics PGCE session is a case study about mathemati... more This description/analysis of a secondary mathematics PGCE session is a case study about mathematics PGCEteaching practice. The session described and analysed was called 'Preparing for rich mathematical activity' and was taught towards the end of the one-year mathematics PGCE students' course at the University of Leeds in 1999. The aim of the session was to increase the student-teachers' teaching repertoires to include problem-solving activities based on pupils' conceptual problems with National Curriculum (DjEE 1995) topics.
Learning in lectures: multiple representations LEIGH. N. Wood*†, SADHBH. JOYCE†, PETER. PETOCZ† a... more Learning in lectures: multiple representations LEIGH. N. Wood*†, SADHBH. JOYCE†, PETER. PETOCZ† and MELISSA RODD§ † Division of Economic and Financial Studies, Macquarie University, Australia, 2109 § Institute of Education, University of London, UK Correspondence *Corresponding author. Email: leigh.wood@mq.edu.au Lectures remain the lynchpin of mathematics teaching at university even with advances in information technology and access to the internet. This paper examines the requirements for learning mathematics and shows how important it is for lecturers to be aware of the different modes of presentation they are using. We consider ways to assist students to make the connections between different representations with particular reference to students whose first language is not English.
Within a practitioner researcher framework, this paper draws on a particular mathematics educatio... more Within a practitioner researcher framework, this paper draws on a particular mathematics education theory and aspects of neuroscience to show that, from a learner's perspective, moving to a deductive reasoning style appropriate to basic Euclidean geometry, can be facilitated, or impeded, by emotion and/or directed attention. This shows that the issue of a person's deductive reasoning is not a merely cognitive one, but can involve affective aspects related to perception – particularly perception of nearby sense data – and emotion. The mathematics education theory that has been used is that of the Espace de Travail Mathématique, the English translation of which is known as Mathematical Working Spaces (MWS). The aspects of neuroscience that have been used pertain to the distinct processing streams known as top-down and bottom-up attention. The practitioner research perspective is aligned with Mason's teaching-practice-based 'noticing'; qualitative data analysed in t...
In order to address the shortage of mathematics teachers in England, the UK government has funded... more In order to address the shortage of mathematics teachers in England, the UK government has funded various in-service subject knowledge courses for practising teachers, who are not mathematics specialists. These courses aim to develop these teachers’ mathematical subject knowledge (e.g., DfE 2014). In this TAS session we will report on a research project which was set up to investigate how teachers on the in-service programmes offered by our institution developed as teachers of mathematics. We orientated our research around a central research query: How do already qualified, non-specialist mathematics teachers come to see themselves as mathematics teachers? Our previous work (Crisan and Rodd 2011) found that at the end of the course these teachers’ mathematical work showed that they still lacked fluency with mathematics and were far from having secure subject knowledge. However, familiarity with and learning of new maths topics on the course increased their confidence in themselves a...
This paper reports on how choices to study mathematics at university (or not to do so) can be und... more This paper reports on how choices to study mathematics at university (or not to do so) can be understood as being, in part, as a product of defending the self psychoanalytically. As part of a three year multi-methods project Understanding Participation in Mathematics and ...
From several years of teaching an in-service masters course ‘Learning geometry for teaching’, a s... more From several years of teaching an in-service masters course ‘Learning geometry for teaching’, a set of teacher self-report data has been accumulated that records incidences of teachers not being able to ‘see’ a theorem or geometrical relationship that they were in the middle of explaining or discussing. This paper uses neuroscientific understanding of the self-oriented (egocentric) and other-orientated (allocentric) processing pathways in the brain as a theoretical lens to start to understand this phenomenon. It will be argued that ‘visualisation loss mid explanation’ needs not be due to lack of teacher mathematical knowledge. The related issue of teacher defence against the discomfort of loss of geometrical insight is also raised and the question of whether a consequence of this defence might be avoiding geometrical practice in the classroom is discussed.
To address the shortage of mathematics teachers in England, serving teachers, who are not mathema... more To address the shortage of mathematics teachers in England, serving teachers, who are not mathematics specialists, have participated in various government-supported in-service courses on teaching secondary mathematics (DfE 2012). This research concerns the mathematics teacher development of participants of several such secondary mathematics in-service programmes. The topic of issue is: how do such teachers contribute to the teaching of secondary mathematics? A research project was set up to investigate how teachers on our in-service programmes developed as teachers of mathematics. We orientated our research around a central research query: How do already qualified, non-specialist mathematics teachers come to see themselves as mathematics teachers? This query concerns itself with mathematics teacher identity, and our beliefs are consonant with Grootenboer and Zvenberger: “it is essential that teachers of mathematics (at all levels) have well-developed personal mathematical identities...
Mathematics teaching, 2012
ABSTRACT e teach a masters' module called 'learning Geometry for teaching'... more ABSTRACT e teach a masters' module called 'learning Geometry for teaching' which we designed for the institute of education Ma in mathematics education. Students on the course are all teachers of mathematics – some primary, most secondary; some from overseas, most from the london area; usually about a dozen students are enrolled. Having taught this course for four years, we would like to share some of the key features of this course, and some of the things we have found out about learning geometry -by the teachers and ourselves. one of the reasons that a course specifically on geometry was considered worth doing was that many of those currently teaching mathematics in school had little geometrical education. Since the Royal Society review of geometry in the curriculum (Royal Society 2001) there has been a greater awareness that learning geometry is important for someone's mathematics education. Hence, we wanted to provide a course for teachers that focussed on this area of mathematics which they might not have studied explicitly when at school, for rarely is school-style geometry – which is based on euclidean geometry and transformations – encountered within university studies. the design of the course recognised this gap in educational experience, but as we had international students on the course, it would not have been appropriate to start from the beginning and present material in a rather linear manner. Furthermore, in designing the course, we took the view that reasoning geometrically, even in the context of trying to solve a school geometry problem, is not routine in the way, arguably, school algebra or arithmetic can become routine. to address this, the course includes features such as: play time with materials that can represent geometrical concepts, simple starting points and discussions of problems' different solutions. these are exemplified on page 14. the course also includes analysis of pupils' reasoning, axiomatic geometry, technologies for learning and teaching geometry, history of geometry and its teaching and discussion of, and practice in, visualisation. in nearly every session, both of us are present and together we model working on a given geometrical problem by pointing out what is known, querying
Nowadays, at many research intensive UK universities, post-graduates in mathematics departments a... more Nowadays, at many research intensive UK universities, post-graduates in mathematics departments are ‘graduate teaching assistants’ (GTAs), contributing to the teaching of their departments’ undergraduates; this has long been the standard situation in universities in North America (Park, 2004). The UK Higher Education Academy has in the past run workshops for maths GTAs but cuts in public expenditure led to the demise of this specialist mathematics provision. However, a local initiative, ‘the IOEUCL strategic partnership’, in 2014-15, supported designing and running a mathematics-specific teaching course for postgraduate research students which was to take approximately ten hours of their time. This course provided a mathematics practitioner researcher context on which this paper reports. Outline of the paper: The first part is an introduction to the context; firstly some background is given to post-graduate student preparation for university teaching, then a description of the cours...
This paper discusses how a ‘latency’ state of mind might serve to attract a young person towards ... more This paper discusses how a ‘latency’ state of mind might serve to attract a young person towards studying mathematics at university. The psychoanalytic notion of latency, understood here as characterising a typical affect-state of a primary school aged child, is explained following Kleinian object-relations theory, particularly as interpreted by Margot Waddell (1998). Through analysis of narrative style interviews, a case is made that latency attitudes may position a young person favourably for mathematical participation at times of choices and decision-making.
Making the transition from school to university mathematics is a major identity investment for al... more Making the transition from school to university mathematics is a major identity investment for all students and, although there have been significant increases in the proportion of female students studying mathematics at university in recent years, yet in some institutions, university mathematics still exudes an aura of male culture. This chapter is written for university mathematics teachers who want to encourage both female and male undergraduates. It argues that gender is a central aspect of a person’s identity, yet gender does not automatically impact on participating in learning mathematics in a stereotyped way. The notion of ‘pedagogical voice’ is introduced as a way of thinking about establishing learning environments which attend to relational aspects of teaching. Relational aspects of teaching develop through personal connections with students and their mathematics and empowers learners from a range of identities. Quotations from mathematics undergraduates’ mathematical bio...
Canadian Journal of Science, Mathematics and Technology Education, 2014
This paper offers explanations as to why good candidates for mathematics or physics degrees might... more This paper offers explanations as to why good candidates for mathematics or physics degrees might opt to study subjects other than STEM (science, technology, engineering, mathematics) subjects at university. Results come from analysis, informed by psychoanalytic theory and practice, of narrative-style interviews conducted with first-year undergraduates and from survey data. It is argued that psychoanalytic interpretations have a role in educational research. Also, it is shown that unconscious forces influenced young peoples' decision making. Implications for policy are discussed, in particular, the issues of (1) the role of commitment and (2) of being good enough to study a STEM discipline.
The 'mathematics mentor ' is the school teacher tutor for student teachers within schoo... more The 'mathematics mentor ' is the school teacher tutor for student teachers within school-based Initial Teacher Education (ITE). My anecdotal and recorded observations of mentor-student interaction indicated that discussing points of mathematics and mathematical pedagogy were rare, (whereas discussion of general issues, like classroom management, were frequent). Student teachers need to learn strategies for teaching mathematics in particular, as well as children in general. As the students are based in school, the mentors have a key role in developing this learning; what then, is the nature of the mentors ' knowledge and how might they express this knowledge? While I do not attempt an exhaustive analysis of the reasons for why the mentors do not prioritise the teaching of mathematical pedagogy, I suggest there are at least the following considerations: (i) The experience of many of us who have worked with novice teachers is that they have a urgent concern with getting ...
Abstract: This paper reports on some of the social and emotional complexities young people negoti... more Abstract: This paper reports on some of the social and emotional complexities young people negotiate, consciously or otherwise, when applying to study at university and presents reasons for why good candidates for mathematics degrees may not opt to study mathematics. The research comes from one strand of the UPMAP project which is seeking to understand profiles of participation in mathematics and physics. Data analysed come from narrative-style interviews which were conducted with first-year undergraduates who had A level mathematics and who were studying a range of subjects at university.
When animals look around in their environment, their vision enables them to learn about that envi... more When animals look around in their environment, their vision enables them to learn about that environment, what features may be useful and how reliably those features exist. Predicting how those features relate to each other and to the animal itself is a survival mechanism and to prime such a mechanism, emotions are engaged. As human animals, we too stravaig a feature-filled environment. Our senses draw (us to) objects, things and the relationships between them and our sense of sight plays a dominant role. [1] As Dick Tahta stated, “we cannot not do geometry”. Yet how does this lived geometry of sight relate to mathematical knowledge of theorems? In this essay, my aim is to explain how, in the context of elementary Euclidean geometry [2], visualisation is related to the visualiser’s affective state and can be epistemic: knowledge-granting. For example, figure 1 shows a Euclidean geometry stimulus (parallel lines and right angles enclose a rectangle). You may be able to see at-a-glanc...
Undergraduate mathematics students’ affective responses to their studies have been collected from... more Undergraduate mathematics students’ affective responses to their studies have been collected from interviews, questionnaires and observations as part of a three-year longitudinal study of a cohort of mathematics students at two UK universities and from other opportunities from working with undergraduates and post-graduates. The central point of this report is that emotion has a significant part to play in learning mathematics at this level. Far from mathematics being cold and abstract it is hot and abstract! Affect has been classified into the three subdomains of belief, attitude and emotion (McLeod 1992). Attention here is on emotion, the least researched of these subdomains in undergraduate mathematics education. Reasons for the lack of attention in this area are attributed to the elusive task of tracking others’ emotions as well as the abstract nature of mathematics with its concomitant ‘cold’ image. This image belies the strong feelings expressed by or observed among mathematics...
Mathematics in School, 1998
In the summer of 1996 about 3000 people met in Seville, Spain, for the 8th International Congress... more In the summer of 1996 about 3000 people met in Seville, Spain, for the 8th International Congress for Mathematics Education--ICME 8. The majority of those attending were researchers in mathematics education, many of whom also teach mathematics or 'train teachers' as well. What ...
This chapter uses psychoanalytical theory to help to understand emotion when a student has diffic... more This chapter uses psychoanalytical theory to help to understand emotion when a student has difficulties in learning mathematics. The centrality of the relationship between student and teacher is theorized and discussed, and issues related to teacher preparation and in-service training are put forward. The notion of a “math-care environment” is developed and ways to help a teacher pause, in order to relate to a learner, are advocated.
This paper uses ideas from the field of neuroscience of attention to investigate emotional (or ot... more This paper uses ideas from the field of neuroscience of attention to investigate emotional (or other affective) responses - ‘points of affect’ - that instigate change in teachers’ or learners’ Space for Geometric Work (‘SWG’). SWG theorises that physical space and tools or artefacts, together with suitable language development, are the components from which a cognitive grasp of geometry is formed. Research from the neuroscience of attention theorises a distinction between ‘top-down’ and ‘bottom-up’ attention. ‘Points of affect’ divert attention and thus can change a person’s SGW. The main body of the paper concerns relationships between deductive and perceptual reasoning in terms of attention processing and points of affect. Application to teaching geometry is discussed.
This description/analysis of a secondary mathematics PGCE session is a case study about mathemati... more This description/analysis of a secondary mathematics PGCE session is a case study about mathematics PGCEteaching practice. The session described and analysed was called 'Preparing for rich mathematical activity' and was taught towards the end of the one-year mathematics PGCE students' course at the University of Leeds in 1999. The aim of the session was to increase the student-teachers' teaching repertoires to include problem-solving activities based on pupils' conceptual problems with National Curriculum (DjEE 1995) topics.
Learning in lectures: multiple representations LEIGH. N. Wood*†, SADHBH. JOYCE†, PETER. PETOCZ† a... more Learning in lectures: multiple representations LEIGH. N. Wood*†, SADHBH. JOYCE†, PETER. PETOCZ† and MELISSA RODD§ † Division of Economic and Financial Studies, Macquarie University, Australia, 2109 § Institute of Education, University of London, UK Correspondence *Corresponding author. Email: leigh.wood@mq.edu.au Lectures remain the lynchpin of mathematics teaching at university even with advances in information technology and access to the internet. This paper examines the requirements for learning mathematics and shows how important it is for lecturers to be aware of the different modes of presentation they are using. We consider ways to assist students to make the connections between different representations with particular reference to students whose first language is not English.
Within a practitioner researcher framework, this paper draws on a particular mathematics educatio... more Within a practitioner researcher framework, this paper draws on a particular mathematics education theory and aspects of neuroscience to show that, from a learner's perspective, moving to a deductive reasoning style appropriate to basic Euclidean geometry, can be facilitated, or impeded, by emotion and/or directed attention. This shows that the issue of a person's deductive reasoning is not a merely cognitive one, but can involve affective aspects related to perception – particularly perception of nearby sense data – and emotion. The mathematics education theory that has been used is that of the Espace de Travail Mathématique, the English translation of which is known as Mathematical Working Spaces (MWS). The aspects of neuroscience that have been used pertain to the distinct processing streams known as top-down and bottom-up attention. The practitioner research perspective is aligned with Mason's teaching-practice-based 'noticing'; qualitative data analysed in t...
In order to address the shortage of mathematics teachers in England, the UK government has funded... more In order to address the shortage of mathematics teachers in England, the UK government has funded various in-service subject knowledge courses for practising teachers, who are not mathematics specialists. These courses aim to develop these teachers’ mathematical subject knowledge (e.g., DfE 2014). In this TAS session we will report on a research project which was set up to investigate how teachers on the in-service programmes offered by our institution developed as teachers of mathematics. We orientated our research around a central research query: How do already qualified, non-specialist mathematics teachers come to see themselves as mathematics teachers? Our previous work (Crisan and Rodd 2011) found that at the end of the course these teachers’ mathematical work showed that they still lacked fluency with mathematics and were far from having secure subject knowledge. However, familiarity with and learning of new maths topics on the course increased their confidence in themselves a...
This paper reports on how choices to study mathematics at university (or not to do so) can be und... more This paper reports on how choices to study mathematics at university (or not to do so) can be understood as being, in part, as a product of defending the self psychoanalytically. As part of a three year multi-methods project Understanding Participation in Mathematics and ...
From several years of teaching an in-service masters course ‘Learning geometry for teaching’, a s... more From several years of teaching an in-service masters course ‘Learning geometry for teaching’, a set of teacher self-report data has been accumulated that records incidences of teachers not being able to ‘see’ a theorem or geometrical relationship that they were in the middle of explaining or discussing. This paper uses neuroscientific understanding of the self-oriented (egocentric) and other-orientated (allocentric) processing pathways in the brain as a theoretical lens to start to understand this phenomenon. It will be argued that ‘visualisation loss mid explanation’ needs not be due to lack of teacher mathematical knowledge. The related issue of teacher defence against the discomfort of loss of geometrical insight is also raised and the question of whether a consequence of this defence might be avoiding geometrical practice in the classroom is discussed.
To address the shortage of mathematics teachers in England, serving teachers, who are not mathema... more To address the shortage of mathematics teachers in England, serving teachers, who are not mathematics specialists, have participated in various government-supported in-service courses on teaching secondary mathematics (DfE 2012). This research concerns the mathematics teacher development of participants of several such secondary mathematics in-service programmes. The topic of issue is: how do such teachers contribute to the teaching of secondary mathematics? A research project was set up to investigate how teachers on our in-service programmes developed as teachers of mathematics. We orientated our research around a central research query: How do already qualified, non-specialist mathematics teachers come to see themselves as mathematics teachers? This query concerns itself with mathematics teacher identity, and our beliefs are consonant with Grootenboer and Zvenberger: “it is essential that teachers of mathematics (at all levels) have well-developed personal mathematical identities...
Mathematics teaching, 2012
ABSTRACT e teach a masters' module called 'learning Geometry for teaching'... more ABSTRACT e teach a masters' module called 'learning Geometry for teaching' which we designed for the institute of education Ma in mathematics education. Students on the course are all teachers of mathematics – some primary, most secondary; some from overseas, most from the london area; usually about a dozen students are enrolled. Having taught this course for four years, we would like to share some of the key features of this course, and some of the things we have found out about learning geometry -by the teachers and ourselves. one of the reasons that a course specifically on geometry was considered worth doing was that many of those currently teaching mathematics in school had little geometrical education. Since the Royal Society review of geometry in the curriculum (Royal Society 2001) there has been a greater awareness that learning geometry is important for someone's mathematics education. Hence, we wanted to provide a course for teachers that focussed on this area of mathematics which they might not have studied explicitly when at school, for rarely is school-style geometry – which is based on euclidean geometry and transformations – encountered within university studies. the design of the course recognised this gap in educational experience, but as we had international students on the course, it would not have been appropriate to start from the beginning and present material in a rather linear manner. Furthermore, in designing the course, we took the view that reasoning geometrically, even in the context of trying to solve a school geometry problem, is not routine in the way, arguably, school algebra or arithmetic can become routine. to address this, the course includes features such as: play time with materials that can represent geometrical concepts, simple starting points and discussions of problems' different solutions. these are exemplified on page 14. the course also includes analysis of pupils' reasoning, axiomatic geometry, technologies for learning and teaching geometry, history of geometry and its teaching and discussion of, and practice in, visualisation. in nearly every session, both of us are present and together we model working on a given geometrical problem by pointing out what is known, querying
Nowadays, at many research intensive UK universities, post-graduates in mathematics departments a... more Nowadays, at many research intensive UK universities, post-graduates in mathematics departments are ‘graduate teaching assistants’ (GTAs), contributing to the teaching of their departments’ undergraduates; this has long been the standard situation in universities in North America (Park, 2004). The UK Higher Education Academy has in the past run workshops for maths GTAs but cuts in public expenditure led to the demise of this specialist mathematics provision. However, a local initiative, ‘the IOEUCL strategic partnership’, in 2014-15, supported designing and running a mathematics-specific teaching course for postgraduate research students which was to take approximately ten hours of their time. This course provided a mathematics practitioner researcher context on which this paper reports. Outline of the paper: The first part is an introduction to the context; firstly some background is given to post-graduate student preparation for university teaching, then a description of the cours...
This paper discusses how a ‘latency’ state of mind might serve to attract a young person towards ... more This paper discusses how a ‘latency’ state of mind might serve to attract a young person towards studying mathematics at university. The psychoanalytic notion of latency, understood here as characterising a typical affect-state of a primary school aged child, is explained following Kleinian object-relations theory, particularly as interpreted by Margot Waddell (1998). Through analysis of narrative style interviews, a case is made that latency attitudes may position a young person favourably for mathematical participation at times of choices and decision-making.
Making the transition from school to university mathematics is a major identity investment for al... more Making the transition from school to university mathematics is a major identity investment for all students and, although there have been significant increases in the proportion of female students studying mathematics at university in recent years, yet in some institutions, university mathematics still exudes an aura of male culture. This chapter is written for university mathematics teachers who want to encourage both female and male undergraduates. It argues that gender is a central aspect of a person’s identity, yet gender does not automatically impact on participating in learning mathematics in a stereotyped way. The notion of ‘pedagogical voice’ is introduced as a way of thinking about establishing learning environments which attend to relational aspects of teaching. Relational aspects of teaching develop through personal connections with students and their mathematics and empowers learners from a range of identities. Quotations from mathematics undergraduates’ mathematical bio...
Canadian Journal of Science, Mathematics and Technology Education, 2014
This paper offers explanations as to why good candidates for mathematics or physics degrees might... more This paper offers explanations as to why good candidates for mathematics or physics degrees might opt to study subjects other than STEM (science, technology, engineering, mathematics) subjects at university. Results come from analysis, informed by psychoanalytic theory and practice, of narrative-style interviews conducted with first-year undergraduates and from survey data. It is argued that psychoanalytic interpretations have a role in educational research. Also, it is shown that unconscious forces influenced young peoples' decision making. Implications for policy are discussed, in particular, the issues of (1) the role of commitment and (2) of being good enough to study a STEM discipline.
The 'mathematics mentor ' is the school teacher tutor for student teachers within schoo... more The 'mathematics mentor ' is the school teacher tutor for student teachers within school-based Initial Teacher Education (ITE). My anecdotal and recorded observations of mentor-student interaction indicated that discussing points of mathematics and mathematical pedagogy were rare, (whereas discussion of general issues, like classroom management, were frequent). Student teachers need to learn strategies for teaching mathematics in particular, as well as children in general. As the students are based in school, the mentors have a key role in developing this learning; what then, is the nature of the mentors ' knowledge and how might they express this knowledge? While I do not attempt an exhaustive analysis of the reasons for why the mentors do not prioritise the teaching of mathematical pedagogy, I suggest there are at least the following considerations: (i) The experience of many of us who have worked with novice teachers is that they have a urgent concern with getting ...
Abstract: This paper reports on some of the social and emotional complexities young people negoti... more Abstract: This paper reports on some of the social and emotional complexities young people negotiate, consciously or otherwise, when applying to study at university and presents reasons for why good candidates for mathematics degrees may not opt to study mathematics. The research comes from one strand of the UPMAP project which is seeking to understand profiles of participation in mathematics and physics. Data analysed come from narrative-style interviews which were conducted with first-year undergraduates who had A level mathematics and who were studying a range of subjects at university.
When animals look around in their environment, their vision enables them to learn about that envi... more When animals look around in their environment, their vision enables them to learn about that environment, what features may be useful and how reliably those features exist. Predicting how those features relate to each other and to the animal itself is a survival mechanism and to prime such a mechanism, emotions are engaged. As human animals, we too stravaig a feature-filled environment. Our senses draw (us to) objects, things and the relationships between them and our sense of sight plays a dominant role. [1] As Dick Tahta stated, “we cannot not do geometry”. Yet how does this lived geometry of sight relate to mathematical knowledge of theorems? In this essay, my aim is to explain how, in the context of elementary Euclidean geometry [2], visualisation is related to the visualiser’s affective state and can be epistemic: knowledge-granting. For example, figure 1 shows a Euclidean geometry stimulus (parallel lines and right angles enclose a rectangle). You may be able to see at-a-glanc...
Undergraduate mathematics students’ affective responses to their studies have been collected from... more Undergraduate mathematics students’ affective responses to their studies have been collected from interviews, questionnaires and observations as part of a three-year longitudinal study of a cohort of mathematics students at two UK universities and from other opportunities from working with undergraduates and post-graduates. The central point of this report is that emotion has a significant part to play in learning mathematics at this level. Far from mathematics being cold and abstract it is hot and abstract! Affect has been classified into the three subdomains of belief, attitude and emotion (McLeod 1992). Attention here is on emotion, the least researched of these subdomains in undergraduate mathematics education. Reasons for the lack of attention in this area are attributed to the elusive task of tracking others’ emotions as well as the abstract nature of mathematics with its concomitant ‘cold’ image. This image belies the strong feelings expressed by or observed among mathematics...
Mathematics in School, 1998
In the summer of 1996 about 3000 people met in Seville, Spain, for the 8th International Congress... more In the summer of 1996 about 3000 people met in Seville, Spain, for the 8th International Congress for Mathematics Education--ICME 8. The majority of those attending were researchers in mathematics education, many of whom also teach mathematics or 'train teachers' as well. What ...
In this chapter we make sense of our personal mathematical journeys as accounts of defended subje... more In this chapter we make sense of our personal mathematical journeys as accounts of defended subjects, while also exploring the role of discourses in our defences. Following Wendy Hollway and Tony Jefferson (2000, p.21), we argue that “subjects invest in discourses when these offer positions which provide protections against anxiety and therefore supports to identity”. Thus, we aim to understand our accounts as both psychic and social, without reducing one to the other. We begin by outlining the idea of the defended subject before turning to Jacques Nimier’s application of this to mathematics. Next we use these ideas to analyse the extracts above. We argue that a psychoanalytic approach can give us new understandings of the pain, power and pleasure of selection and assessment that provide a critique of current practices.
Reference: Black, L., Mendick, Rodd, M. and Solomon, Y. with Brown, M. (2009) Pain, pleasure and power: selecting and assessing defended subjects. In: L. Black, H. Mendick and Y. Solomon (eds), Mathematical Relationships in Education: Identities and Participation.