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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
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
Mathematical Power: Exploring Critical Pedagogy
 in Mathematics and Statistics,” in Reinventing Critical Pedagogy: Widening the Circle of AntiOppression
, 2006
"... "It no longer suffices to know how things are constituted: we need to seek how things should be constituted so that this world of ours may present less suffering and destitution. " 19thcentury French statistician Eugene Burét Though traditionally viewed as valuefree, mathematics is act ..."
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"It no longer suffices to know how things are constituted: we need to seek how things should be constituted so that this world of ours may present less suffering and destitution. " 19thcentury French statistician Eugene Burét Though traditionally viewed as valuefree, mathematics is actually one of the most powerful, yet underutilized, venues for working towards the goals of critical pedagogy—social, political and economic justice for all. This emerging awareness is due to how critical mathematics educators such as Frankenstein, Skovsmose and Gutstein have applied the work of Freire. Freire’s argument that critical education involves problem posing that challenges all to reconsider and recreate prior knowledge reads like a progressive definition of mathematical thinking. Frankenstein (1990) supports the idea that critical mathematics should involve the ability to ask basic statistical questions in order to deepen one’s appreciation of particular issues and should not be taught as isolated formulas with little relevance to individual experiences. At first, mathematics seems an unlikely vehicle for liberation. As Anderson (1997, p.
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.
197 The Effects of Learners ’ Aptitude and Transformation of Social Web Activity Experiences on Online Learning: An Exploratory Study
"... Abstract: One of the facts of online learning is when learners engage in such learning, the rest of the Web is merely a click away. While many studies have identified an association between learners ’ personal attributes and online learning experiences, few have explored the linkages among learners ..."
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Abstract: One of the facts of online learning is when learners engage in such learning, the rest of the Web is merely a click away. While many studies have identified an association between learners ’ personal attributes and online learning experiences, few have explored the linkages among learners ’ aptitude, experiences of daily social web activities, and perception
MATHEMATICS AND THEIR EPISTEMOLOGIES  AND THE LEARNING OF MATHEMATICS
"... 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 varia ..."
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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.
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