Anyone with an interest in both mathematics and linguistics must grin with rueful fascination as ... more Anyone with an interest in both mathematics and linguistics must grin with rueful fascination as they watch the way that the term 'ethnomathematics' is thrown about both in the public media and in the mathematics education literature. It is a versatile toy, fulfilling several functions in an on-going game of catch. Since the 1984 ICME address by Ubiratan D'Ambrosio (1985) which is widely regarded as establishing the field in its contemporary form this word has been used in the political games of curriculum development in many countries. It has also:
The Holy Grail of educational research is to link student learning to pedagogical interventions. ... more The Holy Grail of educational research is to link student learning to pedagogical interventions. It is an impossible quest because the goal is never clearly defined, and the myriad of variables and external influences mean causal links are obscured. Nevertheless, Sir Galahad pursued the chalice relentlessly, and so must we. We are a group of eager knights who join the quest, learn as we traverse the path, and return with a few treasures, if not the chalice itself. Undergraduate mathematics pedagogy has evolved through tradition adapted by necessity-for example lecture theatres have become media centres, but not sites of interaction; examinations have been augmented by coursework, but remain the prime criterion for the award of grades. The result is a discontinuity between student outputs sought by lecturers (and, indeed, by employers and the students themselves), and the outputs that we conventionally measure in undergraduate learning (Speer, Smith, & Horvath, 2010). New Zealand research has explored the edges of this question. In specific contexts for specific subjects questions have been asked about, for example,-soft skills‖ required in vocational activity (Ferguson, 2010); affective factors (Shepard, 2008); and self-efficacy (Dalgety & Cole, 2006). The problem in undergraduate mathematics is that we do not have comprehensive tools with which to evaluate student learning against espoused desired outcomes. Learning is assessed in assignments and examinations, where knowledge of content is the main focus. However, students' mathematical thinking, their mathematical processes, their understanding of the field in broad terms, their ability to work together and communicate mathematically, and their attitudes towards the subject, are also regarded as important attributes by lecturers and employers. We do not evaluate the impact of their undergraduate experience on these characteristics, and hence we are in no position to evaluate the impact of course design on students' learning. We need to create a framework in which the learning goals of undergraduate mathematics courses can be comprehensively specified, and then produce a practical scheme by which we can observe, analyse, and effectively report student learning for a particular course. Such a framework and scheme (which together we call a Course Learning Profile (CLP)) needs to be trialled in a variety of contexts where different outcomes are anticipated, so that it can be tested for robustness, and build its credibility amongst those who design and deliver these courses, and those who receive the graduates. Only then can we claim to have practical research-based evidence for comparing one type of course design against another. There is some evidence that existing, traditional course delivery approaches need to be modified to achieve some of the learning outcomes desired by employers and graduate courses (Ferguson, 2010; Hart Research, 2010). This is particularly in the case of engineering and mathematical sciences education. Innovations need to be proposed and trialled, and some NZ work has been done, for example, Klymchuk, Zverkova, Gruenwald, and Sauerbier (2008) and Sneddon (2006). But we also need a basis on which to judge the result and adopt, modify or abandon these approaches.
Ce travail examine les connaissances mathematiques utilisees dans la vie courante et enseignees a... more Ce travail examine les connaissances mathematiques utilisees dans la vie courante et enseignees a l'ecole en Nouvelle-Zelande et en France en particulier concernant les fractions. Dans les pays anglo-saxons, les fractions sont abondamment utilisees, et les nombres mixtes du type 3 ½ pour 3,5 sont encore manipules. Alors qu'en France, pionniere en matiere de decimalisation, les ecritures decimales sont utilisees beaucoup plus volontiers. Ceci revele une culture mathematique differente qui aboutit a l'utilisation de notations mathematiques differentes, aussi bien dans la vie quotidienne que dans les programmes scolaires. Afin de situer notre propos, nous developpons tout d'abord certains aspects historiques concernant les fractions et les nombres decimaux. Nous examinons ensuite les differences entre la culture anglo-saxonne et francaise : d'une part en etudiant les aspects culturels et langagiers des fractions puis d'autre part en considerant les aspects didac...
Mathematics Teacher Education and Development, 1999
As part of a larger research project, seven trainee mathematics teachers completing a one year po... more As part of a larger research project, seven trainee mathematics teachers completing a one year post-graduate secondary teaching diploma were observed teaching two lessons each. The researchers, who were experienced mathematics teachers, ranked the pre-service teachers in terms of their future effectiveness using two methods of ranking. One involved an observation schedule derived from behaviours associated with effective teacher research. The other required the two researchers to make a 'gut feeling' ranking of the pre-service teachers. An investigation of the 'gut feeling' ranking showed that it could be explained using standard teacher effectiveness models. The correlations between the two rankings were high, raising some interesting questions to be investigated using larger samples.
How does a resource become “lived”? If we may play on the etymology for a moment, becoming “lived... more How does a resource become “lived”? If we may play on the etymology for a moment, becoming “lived” means enlivened, to get full of life, to become, to be born. The four chapters of this part tell us how a resource enters the world “mewling and puking in the nurse’s arms” (Shakespeare, As You Like It, Act II, Scene 7). The bard gets it right, again. The carer of the resource is responsible for nurturing and shaping its potential, helping it to grow, ignoring the unseemly squeaking, and clearing up the spilt milk. On the one hand, Adler shows us how the nurse invests herself into the new life: how does teacher knowledge emerge during events in the classroom? Gueudet and Trouche want us to focus on the nurse’s actions in caring for the baby: how do resources become transformed in a particular teacher’s hands? Sensevy, on the other hand, wants us to look at the nurse’s aims: how are the teacher’s actions driven by developing intentions? Mariotti and Maracci ask us to watch the baby itse...
How did you solve this problem? “Assuming everyone selects a number at random,” you think, “the a... more How did you solve this problem? “Assuming everyone selects a number at random,” you think, “the average would be 50. Two-thirds of 50 is about 33. I should select that!” But your other mental voice interjects, “Ah! But everyone else is thinking the same! Therefore, they all select 33. Two-thirds of 33 is 22. That’s the number...” “Wait!” Back and forth your mind lobs. “I can see this continuing...I’ll select 0.” Phrased in mathematical jargon, the above problem is asking you to find the Nash Equilibrium of the given situation. If we had written the problem in such terms, some of you would not have made any progress while others would perhaps have selected 33 or one of the numbers along the sequence. Still others would have seen that the answer is 0 and engaged in the type of iterative thinking caricatured above. The present article expands on this last type of experience, of solving a mathematical problem by first seeing a resolution and a path leading to that resolution unfold into...
Background: This paper reports on a professional development workshop in University level mathema... more Background: This paper reports on a professional development workshop in University level mathematics. The workshop was grounded in Schoenfeld's (How we think. A theory of goal-oriented decision-making and its educational applications, 2010) theoretical approach, emphasizing the roles of Resources (primarily, knowledge), Orientations (primarily, beliefs), and Goals (R/O/Gs) as factors in teachers' "in the moment" decision-making. Participants characterized their R/O/Gs prior to instruction, bringing for discussion videotapes of their instruction that raised issues for them about their R/O/Gs or the choices they made during teaching. Results: For a surprisingly large percentage of these university mathematicians, the "mathematical correctness" of what they presented was a dominant consideration, to the point where it overshadowed other considerations. Conclusion: This gives rise to a conjectural characterization of three somewhat overlapping classes of teachers (university mathematicians, expert teachers, and proficient teachers), with the suggestion that professional development might profitably differ in the ways that it is targeted to these three groups.
Hacettepe Journal of Mathematics and Statistics, 2017
This note highlights an often overlooked aspect of Michael Brown s scholarship: his interest in l... more This note highlights an often overlooked aspect of Michael Brown s scholarship: his interest in language, especially as it relates to mathematics.
This is a report of the establishment and first stage of a 5-year project working with senior sec... more This is a report of the establishment and first stage of a 5-year project working with senior secondary students in eight schools in a low socio-economic area in Auckland, New Zealand. The students are predominantly from Maori, Pacific Island or new immigrant families. The aim is to enhance the achievement and participation in mathematics of students in their final two years at secondary school, and to promote their transition into mathematical programmes in tertiary education. Methodological principles are outlined, and the Pilot Programme undertaken during 2001 is described1. Background In 1999 the Mathematics Education Unit of The University of Auckland and the Woolf Fisher Research Centre investigated the possibility of promoting mathematics education in a low socio-economic region of Auckland. This region has a high Pacific Island and indigenous Maori population. The Scoping Study involved a needs analysis, a review of research, base-line data-gathering, and a proposal for a ma...
The Proceedings of the 12th International Congress on Mathematical Education, 2015
Honourable Mr Lee, Minister of Education Professor Sung Je Cho, Convenor of this wonderful confer... more Honourable Mr Lee, Minister of Education Professor Sung Je Cho, Convenor of this wonderful conference ICMI Colleagues and friends Our moment has arrived. Isn't this wonderful! I am delighted to be here, to open the 12th International Congress of Mathematics Education-to be honest, it is a moment I have been looking forward to for more than 4 years. Our community is very fortunate to have attracted a conference bid from Korea, and our Korean friends are already proving to us that we made a very good decision to accept their bid. These few minutes are my opportunity to address the wider ICMI community about the things that I believe are important about mathematics education on the international stage. I cannot detail all the many, many activities of ICMI as an organisation: ICMI Studies, Regional conferences, Affiliated organisations, and on and on. I urge everyone in this room to find out who their ICMI country representative is, and ensure that they become part of their national network. You should also subscribe to the ICMI Newsletter (on line) or become a Facebook Friend. We survive as an organisation through your participation. I wish to mention three topics: our major development project; the Klein Project; and finally some comments on how our community communicates. Since the last ICME in Mexico, ICMI as an organisation has changed dramatically. We have extended our development activities significantly. It is no longer true that we are primarily an organisation of professionals in mathematics education. Now we spend at least half our efforts and resources on worldwide development activities. A major part of this effort is the Capacity and Networking Project, that we call CANP.
Discussion, theorising and research in the area of mathematical knowledge for teaching began by a... more Discussion, theorising and research in the area of mathematical knowledge for teaching began by asking what level of mathematical qualification teachers need. We have moved on considerably since then, using concepts such as pedagogical content knowledge, and frameworks such as those from Deborah Ball in Michigan or, more recently, Tim Rowlands in Cambridge or Alan Schoenfeld in Berkeley. Some lovely
Topology has its own specialised language. Where did this come from? What are the differences in ... more Topology has its own specialised language. Where did this come from? What are the differences in the language of topology when it is expressed in English, Spanish, Mandarin, Czech or Turkish? Does topology itself change when expressed in different languages? What effect has language had on the development of topology? Does the language of the topologist make a difference to the mathematics? A research programme aimed at answering these questions has begun. This paper is the first in a series that provides a background to the research. Topological discourse in various languages is being examined for its particular features, and possible influences on the concepts developed through these languages. Data from Turkish topologists and topological terminology are examined. They show why there is reason to suspect that language influences mathematical concept development. The data are also used to explore methodological issues for the research project.
The example set by Klein was not to proscribe any "best" approach nor define an ideal curriculum.... more The example set by Klein was not to proscribe any "best" approach nor define an ideal curriculum. His intention was to awaken, to broaden, and to provide background
... Thanks to the many who read ommented on my writing: in particular Ivan Reilly, Marcelo ,Trish... more ... Thanks to the many who read ommented on my writing: in particular Ivan Reilly, Marcelo ,Trish Gribben, John Gribben, Emily Perkins, Karl Maughan, ave Ritchie. ... They are trying to explain the difference between continuous iscrete data to a Maori elder. ...
International Journal of Mathematical Education in Science and Technology, 2011
I lay a new theoretical framework across my own lecturing in order to understand what is happenin... more I lay a new theoretical framework across my own lecturing in order to understand what is happening. On the one hand, this is a test of the framework. On the other, I gain insights into both better practices and better course design. The framework constructs undergraduate teaching as the interaction between the discipline and the university pedagogical context. Overlaying this
An early abbreviated draft of Chapters 1 and 4 are to appear in a special edition of Educational ... more An early abbreviated draft of Chapters 1 and 4 are to appear in a special edition of Educational Studies in Mathematics (ed Steven Lerman), and Sections 2.1 and 2.2 are to appear in an International Handbook on Mathematics Education (ed Alan Bishop) to be released at ICME-8. vii Contents 0 Introduction...
In 2008 the New Zealand Institute of Mathematics and Its Applications (NZIMA) funded a project to... more In 2008 the New Zealand Institute of Mathematics and Its Applications (NZIMA) funded a project to take a hard look at mathematics education in the four years from the last two years of secondary education to the first two years of undergraduate university education. The structure, pedagogy and content of mathematics in this period have been largely driven by tradition and particular interest groups. However not only has mathematics changed, but also the student body has changed, the teaching and lecturing body has changed, the reasons people study the mathematical sciences have changed, and the mathematical preliminaries have changed. The prime aim of the project was to get mathematical science senior secondary teachers and undergraduate lecturers to talk to each other. Such communication has not happened before in New Zealand on a large scale, and the ongoing discourse is couched in terms of blame and complaint. We explain how the project overcame these obstacles, and describe the emerging vision.
Anyone with an interest in both mathematics and linguistics must grin with rueful fascination as ... more Anyone with an interest in both mathematics and linguistics must grin with rueful fascination as they watch the way that the term 'ethnomathematics' is thrown about both in the public media and in the mathematics education literature. It is a versatile toy, fulfilling several functions in an on-going game of catch. Since the 1984 ICME address by Ubiratan D'Ambrosio (1985) which is widely regarded as establishing the field in its contemporary form this word has been used in the political games of curriculum development in many countries. It has also:
The Holy Grail of educational research is to link student learning to pedagogical interventions. ... more The Holy Grail of educational research is to link student learning to pedagogical interventions. It is an impossible quest because the goal is never clearly defined, and the myriad of variables and external influences mean causal links are obscured. Nevertheless, Sir Galahad pursued the chalice relentlessly, and so must we. We are a group of eager knights who join the quest, learn as we traverse the path, and return with a few treasures, if not the chalice itself. Undergraduate mathematics pedagogy has evolved through tradition adapted by necessity-for example lecture theatres have become media centres, but not sites of interaction; examinations have been augmented by coursework, but remain the prime criterion for the award of grades. The result is a discontinuity between student outputs sought by lecturers (and, indeed, by employers and the students themselves), and the outputs that we conventionally measure in undergraduate learning (Speer, Smith, & Horvath, 2010). New Zealand research has explored the edges of this question. In specific contexts for specific subjects questions have been asked about, for example,-soft skills‖ required in vocational activity (Ferguson, 2010); affective factors (Shepard, 2008); and self-efficacy (Dalgety & Cole, 2006). The problem in undergraduate mathematics is that we do not have comprehensive tools with which to evaluate student learning against espoused desired outcomes. Learning is assessed in assignments and examinations, where knowledge of content is the main focus. However, students' mathematical thinking, their mathematical processes, their understanding of the field in broad terms, their ability to work together and communicate mathematically, and their attitudes towards the subject, are also regarded as important attributes by lecturers and employers. We do not evaluate the impact of their undergraduate experience on these characteristics, and hence we are in no position to evaluate the impact of course design on students' learning. We need to create a framework in which the learning goals of undergraduate mathematics courses can be comprehensively specified, and then produce a practical scheme by which we can observe, analyse, and effectively report student learning for a particular course. Such a framework and scheme (which together we call a Course Learning Profile (CLP)) needs to be trialled in a variety of contexts where different outcomes are anticipated, so that it can be tested for robustness, and build its credibility amongst those who design and deliver these courses, and those who receive the graduates. Only then can we claim to have practical research-based evidence for comparing one type of course design against another. There is some evidence that existing, traditional course delivery approaches need to be modified to achieve some of the learning outcomes desired by employers and graduate courses (Ferguson, 2010; Hart Research, 2010). This is particularly in the case of engineering and mathematical sciences education. Innovations need to be proposed and trialled, and some NZ work has been done, for example, Klymchuk, Zverkova, Gruenwald, and Sauerbier (2008) and Sneddon (2006). But we also need a basis on which to judge the result and adopt, modify or abandon these approaches.
Ce travail examine les connaissances mathematiques utilisees dans la vie courante et enseignees a... more Ce travail examine les connaissances mathematiques utilisees dans la vie courante et enseignees a l'ecole en Nouvelle-Zelande et en France en particulier concernant les fractions. Dans les pays anglo-saxons, les fractions sont abondamment utilisees, et les nombres mixtes du type 3 ½ pour 3,5 sont encore manipules. Alors qu'en France, pionniere en matiere de decimalisation, les ecritures decimales sont utilisees beaucoup plus volontiers. Ceci revele une culture mathematique differente qui aboutit a l'utilisation de notations mathematiques differentes, aussi bien dans la vie quotidienne que dans les programmes scolaires. Afin de situer notre propos, nous developpons tout d'abord certains aspects historiques concernant les fractions et les nombres decimaux. Nous examinons ensuite les differences entre la culture anglo-saxonne et francaise : d'une part en etudiant les aspects culturels et langagiers des fractions puis d'autre part en considerant les aspects didac...
Mathematics Teacher Education and Development, 1999
As part of a larger research project, seven trainee mathematics teachers completing a one year po... more As part of a larger research project, seven trainee mathematics teachers completing a one year post-graduate secondary teaching diploma were observed teaching two lessons each. The researchers, who were experienced mathematics teachers, ranked the pre-service teachers in terms of their future effectiveness using two methods of ranking. One involved an observation schedule derived from behaviours associated with effective teacher research. The other required the two researchers to make a 'gut feeling' ranking of the pre-service teachers. An investigation of the 'gut feeling' ranking showed that it could be explained using standard teacher effectiveness models. The correlations between the two rankings were high, raising some interesting questions to be investigated using larger samples.
How does a resource become “lived”? If we may play on the etymology for a moment, becoming “lived... more How does a resource become “lived”? If we may play on the etymology for a moment, becoming “lived” means enlivened, to get full of life, to become, to be born. The four chapters of this part tell us how a resource enters the world “mewling and puking in the nurse’s arms” (Shakespeare, As You Like It, Act II, Scene 7). The bard gets it right, again. The carer of the resource is responsible for nurturing and shaping its potential, helping it to grow, ignoring the unseemly squeaking, and clearing up the spilt milk. On the one hand, Adler shows us how the nurse invests herself into the new life: how does teacher knowledge emerge during events in the classroom? Gueudet and Trouche want us to focus on the nurse’s actions in caring for the baby: how do resources become transformed in a particular teacher’s hands? Sensevy, on the other hand, wants us to look at the nurse’s aims: how are the teacher’s actions driven by developing intentions? Mariotti and Maracci ask us to watch the baby itse...
How did you solve this problem? “Assuming everyone selects a number at random,” you think, “the a... more How did you solve this problem? “Assuming everyone selects a number at random,” you think, “the average would be 50. Two-thirds of 50 is about 33. I should select that!” But your other mental voice interjects, “Ah! But everyone else is thinking the same! Therefore, they all select 33. Two-thirds of 33 is 22. That’s the number...” “Wait!” Back and forth your mind lobs. “I can see this continuing...I’ll select 0.” Phrased in mathematical jargon, the above problem is asking you to find the Nash Equilibrium of the given situation. If we had written the problem in such terms, some of you would not have made any progress while others would perhaps have selected 33 or one of the numbers along the sequence. Still others would have seen that the answer is 0 and engaged in the type of iterative thinking caricatured above. The present article expands on this last type of experience, of solving a mathematical problem by first seeing a resolution and a path leading to that resolution unfold into...
Background: This paper reports on a professional development workshop in University level mathema... more Background: This paper reports on a professional development workshop in University level mathematics. The workshop was grounded in Schoenfeld's (How we think. A theory of goal-oriented decision-making and its educational applications, 2010) theoretical approach, emphasizing the roles of Resources (primarily, knowledge), Orientations (primarily, beliefs), and Goals (R/O/Gs) as factors in teachers' "in the moment" decision-making. Participants characterized their R/O/Gs prior to instruction, bringing for discussion videotapes of their instruction that raised issues for them about their R/O/Gs or the choices they made during teaching. Results: For a surprisingly large percentage of these university mathematicians, the "mathematical correctness" of what they presented was a dominant consideration, to the point where it overshadowed other considerations. Conclusion: This gives rise to a conjectural characterization of three somewhat overlapping classes of teachers (university mathematicians, expert teachers, and proficient teachers), with the suggestion that professional development might profitably differ in the ways that it is targeted to these three groups.
Hacettepe Journal of Mathematics and Statistics, 2017
This note highlights an often overlooked aspect of Michael Brown s scholarship: his interest in l... more This note highlights an often overlooked aspect of Michael Brown s scholarship: his interest in language, especially as it relates to mathematics.
This is a report of the establishment and first stage of a 5-year project working with senior sec... more This is a report of the establishment and first stage of a 5-year project working with senior secondary students in eight schools in a low socio-economic area in Auckland, New Zealand. The students are predominantly from Maori, Pacific Island or new immigrant families. The aim is to enhance the achievement and participation in mathematics of students in their final two years at secondary school, and to promote their transition into mathematical programmes in tertiary education. Methodological principles are outlined, and the Pilot Programme undertaken during 2001 is described1. Background In 1999 the Mathematics Education Unit of The University of Auckland and the Woolf Fisher Research Centre investigated the possibility of promoting mathematics education in a low socio-economic region of Auckland. This region has a high Pacific Island and indigenous Maori population. The Scoping Study involved a needs analysis, a review of research, base-line data-gathering, and a proposal for a ma...
The Proceedings of the 12th International Congress on Mathematical Education, 2015
Honourable Mr Lee, Minister of Education Professor Sung Je Cho, Convenor of this wonderful confer... more Honourable Mr Lee, Minister of Education Professor Sung Je Cho, Convenor of this wonderful conference ICMI Colleagues and friends Our moment has arrived. Isn't this wonderful! I am delighted to be here, to open the 12th International Congress of Mathematics Education-to be honest, it is a moment I have been looking forward to for more than 4 years. Our community is very fortunate to have attracted a conference bid from Korea, and our Korean friends are already proving to us that we made a very good decision to accept their bid. These few minutes are my opportunity to address the wider ICMI community about the things that I believe are important about mathematics education on the international stage. I cannot detail all the many, many activities of ICMI as an organisation: ICMI Studies, Regional conferences, Affiliated organisations, and on and on. I urge everyone in this room to find out who their ICMI country representative is, and ensure that they become part of their national network. You should also subscribe to the ICMI Newsletter (on line) or become a Facebook Friend. We survive as an organisation through your participation. I wish to mention three topics: our major development project; the Klein Project; and finally some comments on how our community communicates. Since the last ICME in Mexico, ICMI as an organisation has changed dramatically. We have extended our development activities significantly. It is no longer true that we are primarily an organisation of professionals in mathematics education. Now we spend at least half our efforts and resources on worldwide development activities. A major part of this effort is the Capacity and Networking Project, that we call CANP.
Discussion, theorising and research in the area of mathematical knowledge for teaching began by a... more Discussion, theorising and research in the area of mathematical knowledge for teaching began by asking what level of mathematical qualification teachers need. We have moved on considerably since then, using concepts such as pedagogical content knowledge, and frameworks such as those from Deborah Ball in Michigan or, more recently, Tim Rowlands in Cambridge or Alan Schoenfeld in Berkeley. Some lovely
Topology has its own specialised language. Where did this come from? What are the differences in ... more Topology has its own specialised language. Where did this come from? What are the differences in the language of topology when it is expressed in English, Spanish, Mandarin, Czech or Turkish? Does topology itself change when expressed in different languages? What effect has language had on the development of topology? Does the language of the topologist make a difference to the mathematics? A research programme aimed at answering these questions has begun. This paper is the first in a series that provides a background to the research. Topological discourse in various languages is being examined for its particular features, and possible influences on the concepts developed through these languages. Data from Turkish topologists and topological terminology are examined. They show why there is reason to suspect that language influences mathematical concept development. The data are also used to explore methodological issues for the research project.
The example set by Klein was not to proscribe any "best" approach nor define an ideal curriculum.... more The example set by Klein was not to proscribe any "best" approach nor define an ideal curriculum. His intention was to awaken, to broaden, and to provide background
... Thanks to the many who read ommented on my writing: in particular Ivan Reilly, Marcelo ,Trish... more ... Thanks to the many who read ommented on my writing: in particular Ivan Reilly, Marcelo ,Trish Gribben, John Gribben, Emily Perkins, Karl Maughan, ave Ritchie. ... They are trying to explain the difference between continuous iscrete data to a Maori elder. ...
International Journal of Mathematical Education in Science and Technology, 2011
I lay a new theoretical framework across my own lecturing in order to understand what is happenin... more I lay a new theoretical framework across my own lecturing in order to understand what is happening. On the one hand, this is a test of the framework. On the other, I gain insights into both better practices and better course design. The framework constructs undergraduate teaching as the interaction between the discipline and the university pedagogical context. Overlaying this
An early abbreviated draft of Chapters 1 and 4 are to appear in a special edition of Educational ... more An early abbreviated draft of Chapters 1 and 4 are to appear in a special edition of Educational Studies in Mathematics (ed Steven Lerman), and Sections 2.1 and 2.2 are to appear in an International Handbook on Mathematics Education (ed Alan Bishop) to be released at ICME-8. vii Contents 0 Introduction...
In 2008 the New Zealand Institute of Mathematics and Its Applications (NZIMA) funded a project to... more In 2008 the New Zealand Institute of Mathematics and Its Applications (NZIMA) funded a project to take a hard look at mathematics education in the four years from the last two years of secondary education to the first two years of undergraduate university education. The structure, pedagogy and content of mathematics in this period have been largely driven by tradition and particular interest groups. However not only has mathematics changed, but also the student body has changed, the teaching and lecturing body has changed, the reasons people study the mathematical sciences have changed, and the mathematical preliminaries have changed. The prime aim of the project was to get mathematical science senior secondary teachers and undergraduate lecturers to talk to each other. Such communication has not happened before in New Zealand on a large scale, and the ongoing discourse is couched in terms of blame and complaint. We explain how the project overcame these obstacles, and describe the emerging vision.
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Papers by Bill Barton