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Democratic access to powerful mathematical ideas
 In L. D. English (Ed.), Handbook of international research in mathematics education. Directions for the 21st Century
, 2002
"... Abstract. The emergence of the informational society creates the paradoxes of inclusion and citizenship, which call into question any simple interpretation of the meaning of “democratic access to powerful mathematical ideas”. In exploring this thesis we put forward ways of understanding what “powerf ..."
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Abstract. The emergence of the informational society creates the paradoxes of inclusion and citizenship, which call into question any simple interpretation of the meaning of “democratic access to powerful mathematical ideas”. In exploring this thesis we put forward ways of understanding what “powerful mathematical ideas” represent logically, psychologically, culturally and sociologically. As a way of tackling the issues of democratic access to these ideas, we elaborate on three arenas of mathematics education practices where it is possible to build a meaningful participation to committed political action, namely the classroom, school organization, and society both locally and globally. To conclude we explore the potentialities of the space of investigation into democratic access to powerful mathematical ideas defined by the four interpretations of “powerful ” and by the three arenas of democratic access. We point to the necessity of covering this whole space of research in order to give a full picture of the complexity of mathematics education in our current informational society. Carlos had to move out of his home. His mother seems to be worried. She lost her job and the money she made through great effort to pay for the small house is in the hands of the bank. Carlos, a tenth grade student, is one of the many Colombian youngsters who will finish high school at the beginning of the 21 st Century. Many of these students seem to be confused about their future. Teachers insist on the importance of schooling and learning, especially mathematics. Yet how could that help in their actual situation? On the other side of the world, in Denmark, Nicolai got seriously sick after eating a home
Empowerment in Mathematics Education
 Retrieved April 15, 2002, from the World Wide Web: http://www.ex.ac.uk/~PErnest/pome15/empowerment.htm
, 2000
"... this paper I explore the meaning of empowerment in the teaching and learning of mathematics. The main part of the paper is devoted to distinguishing three different but complementary meanings of empowerment concerning mathematics: mathematical, social and epistemological empowerment. Mathematical ..."
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this paper I explore the meaning of empowerment in the teaching and learning of mathematics. The main part of the paper is devoted to distinguishing three different but complementary meanings of empowerment concerning mathematics: mathematical, social and epistemological empowerment. Mathematical empowerment concerns gaining the power to use mathematical knowledge and skills in school mathematics
MATHEMATICS AND THEIR EPISTEMOLOGIES AND THE LEARNING OF MATHEMATICS
"... Abstract: This paper reports on the results of a study of the epistemologies of seventy research mathematicians utilising a model containing five categories, sociocultural relatedness, aesthetics, intuition, thinking style and connectivities. The perspectives of the mathematicians demonstrate extre ..."
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Abstract: This paper reports on the results of a study of the epistemologies of seventy research mathematicians utilising a model containing five categories, sociocultural relatedness, aesthetics, intuition, thinking style and connectivities. The perspectives of the mathematicians demonstrate extreme variability from one to another but certain persistent themes carry important messages for mathematics education. In particular, although mathematicians research very differently, their pervasive absolutist view of mathematical knowledge is not matched by their stories of how they come to know, nor of how they think about mathematics.
A Resource for Teacher Educators
"... With support from the United States Agency for International ..."
WHAT IS THE PHILOSOPHY OF MATHEMATICS EDUCATION?
"... This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one o ..."
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This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one of several such perspectives, practices or areas of study. Use of the definite article ‘the ’ suggests to some the arrogation of definitiveness to the account given. 1 In other words, it is the dominant or otherwise unique account of philosophy of mathematics education. However, an alternative reading is that ‘the ’ refers to a definite area of enquiry, a specific domain, within which one account is offered. So the philosophy of mathematics education need not be a dominant interpretation so much as an area of study, an area of investigation, and hence something with this title can be an exploratory assay into this area. This is what I intend here. Moving beyond the first word, there is the more substantive question of the reference of the term ‘philosophy of mathematics education’. There is a narrow sense that can be applied in interpreting the words ‘philosophy ’ and ‘mathematics education’. The philosophy of some area or activity can be understood as its aims or rationale. Mathematics education understood
Landscapes of Investigation
"... Abstract: According to many observations, traditional mathematics education falls within the exercise paradigm. This paradigm is contrasted with landscapes of investigation serving as invitations for students to be involved in processes of exploration and explanation. The distinction between the exe ..."
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Abstract: According to many observations, traditional mathematics education falls within the exercise paradigm. This paradigm is contrasted with landscapes of investigation serving as invitations for students to be involved in processes of exploration and explanation. The distinction between the exercise paradigm and landscapes of investigation is combined with a distinction between three different types of reference which might provide mathematical concepts and classroom activities with meaning: references to mathematics; references to a semireality; and references to a reallife situation. The six possible learning milieus are illustrated by examples. Moving away from the exercise paradigm and in the direction of landscapes of investigation may help to abandon the authorities of the traditional mathematics classroom and to make students the acting subjects in their learning processes. Moving away from reference to pure mathematics and in the direction of real life references may help to provide resources for reflection on mathematics and its applications. My hope is that finding a route among the different milieus of learning may provide new resources for making the students both acting and reflecting and in this way providing mathematics education with a critical dimension. Kurzreferat: Der traditionelle Mathematikunterricht fällt vielen Beobachtungen nach in das Übungsparadigma. Dieses Paradigma wird den "landscapes of investigation " gegenüber gestellt, einer Einladung an Schüler, sich auf den Prozess des Entdeckens und der Erklärung einzulassen. Übungsparadigma und "landscapes of investigation " werden zusammen mit dem
ICOTS6, 2002: Vithal LEARNING TO TEACH STATISTICS THROUGH PROJECT WORK
"... Whatever the debates about the relation between mathematics and statistics as disciplines, the latter is typically offered within school mathematics curricula. This relatively new inclusion has enhanced the opportunity for learners to experience a greater relevance of mathematics curricula to their ..."
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Whatever the debates about the relation between mathematics and statistics as disciplines, the latter is typically offered within school mathematics curricula. This relatively new inclusion has enhanced the opportunity for learners to experience a greater relevance of mathematics curricula to their own lives, and hence also created the imperative to better understand how best to organise teaching and learning toward such goals. Not surprisingly, teacher education has had to take on such challenges and in so doing brought a focus also on what happens within the halls of tertiary institutions. The question this paper addresses is how best do we prepare teachers to connect mathematics and statistics education to learners ’ own realities. If project work, within a broad social, cultural political approach, is one means for forging such links then there is a need to analyse and better understand the kinds of teacher education pedagogies that may be engaged to build the necessary knowledge, skills, attitudes and values among teachers.
How to Do Educational Research in University Mathematics?
"... Situated as a Ph.D. student in university mathematics education, I present some of my considerations about my identity as a researcher in this field. I discuss the larger global and local societal issues and their connections to educational research in university mathematics. My discussion goes beyo ..."
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Situated as a Ph.D. student in university mathematics education, I present some of my considerations about my identity as a researcher in this field. I discuss the larger global and local societal issues and their connections to educational research in university mathematics. My discussion goes beyond personal considerations and touches upon the structures and ideas that are both internal and external to university mathematics education. I discuss the different political projects that I can identify from my personal experiences across the fields of educational research, practice, and policy in university mathematics. I place myself firmly within the tradition of critical education, but also draw on postmodern theories. The results of the discussion are the identification of challenges for a postmodern critical mathematics education, with a focus on university mathematics.
Persistent Iniquities: A TwentyYear Perspective on “Race, Sex, Socioeconomic Status, and Mathematics”
"... Calls for mathematics for all and the discourse of equity have become normative in the field of mathematics education. The 1988 publication of Reyes and Stanic’s Race, Sex, Socioeconomic Status, and Mathematics could serve as a marker for this new emphasis. This essay reconsiders their model to orie ..."
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Calls for mathematics for all and the discourse of equity have become normative in the field of mathematics education. The 1988 publication of Reyes and Stanic’s Race, Sex, Socioeconomic Status, and Mathematics could serve as a marker for this new emphasis. This essay reconsiders their model to orient research; it is the response of the silenced interviewer in conversation with the model’s authors. It is argued that the enforced passivity of mathematics educators has contributed to the twenty years of persistent iniquities in mathematics classrooms. While the model can still be of use within mathematics education, its users must consider its underexplored assumptions by answering why teach mathematics, questioning the demarcation of difference, and allowing for agency. Bringing equitable notions of these assumptions makes possible an approach to public education in which a mathematics education would emerge. While it seems as though we in mathematics education ride tumultuous waves of reform and rescindication 1, we have in fact changed little during the past two decades (Wiliam, 2002), if not the last century (G. M. A. Stanic, personal communication, May 11, 2005), in the assumed certainty that mathematics should be an important part of the school curriculum and in the persistent iniquities that emerge from our mathematics teaching (e.g., see NAEP results over the past 30 years at