When students ponder why they consider it relevant to learn math it becomes apparent that their attributions of relevance do not meet what educational policies state as goals. While they generally consider the subject to be important, their explanations why they do so are limited to only elementary mathematical skills needed in everyday life or unspecified skills for later work life, rarely connecting them to broader societal topics. Integrating Critical Mathematics Education (CME) tasks into math lessons might (...) be a chance to let attributions of relevance evolve further. This contribution shows in how far the students’ perspectives on the relevance of math changed after they experienced several CME units. 16 students from three different schools have participated in two rounds of interviews where they have been asked about their image of math and math learning and if and what they consider relevant. Within the second round of interviews, after they experienced several CME units, additional questions about their experiences in these lessons have been added. The analysis shows that students’ general attribution of relevance did not change considerably. However, effects could be identified in their reflections about the CME units. Students talked about how these units let them experience a connection between math and societal topics that leads to a more personal and direct relevance of math for their lives. However, their understanding of what counts as doing math might hinder them to easily transfer their experiences within these units to their general attributions of relevance of math. If teachers regularly include CME tasks into their math lessons and make reflections on what mathematical activities have been applied to make sense of them an integral part of instruction, CME seems to offer the opportunity for students to broaden their conceptions of math and experience connections between math and societal topics more clearly. (shrink)

Theoretically, critical mathematics education (CME) differs markedly from traditional, teacher-centered mathematics teaching approaches. In addition to meeting mathematical goals, a main focus of CME lies on fostering students’ critical consciousness and positioning them as active and informed actors in the classroom and beyond. However, only few empirical studies explicitly focus on how students experience CME instruction and curriculum. In this contribution, we draw on interview data to examine how K-12 students in one Austrian and one (...) American school setting respond to and perceive CME lessons. The analysis revealed that, within both classroom settings, students’ perceptions vary greatly, with some perceiving CME lessons as being completely different from prior experiences in school mathematics to some seeing little-to-no difference. Additionally features of CME instruction that mathematics teachers and researchers might consider to be the most salient are not necessarily the ones that students report attending to. Reasons for that might be manifold, and students might need more time with CME instruction and especially with reflecting on such lessons to identify the rationale behind the instructional approach. Moreover, researchers should be aware that students might not share their understanding of critical instructional reforms and might have diverse or even divergent perceptions. (shrink)

In this article, modern standards of early years mathematics education are criticized and a proposal for change is presented. Today's early years mathematics education standards rest on a view of mathematics that became obsolete already at the end of the 19th century while the spirit of children's mathematics is precisely the spirit of modern mathematics. The proposal for change is not a return to the “new mathematics” movement, but something different.

This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society (...) in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future. (shrink)

This book discusses both the philosophy of mathematics and of mathematics education. The first part is a critique of existing approaches and a new philosophy of mathematics. Chapters include: (1) "A Critique of Absolutist Philosophies of Mathematics," (2) "The Philosophy of Mathematics Reconceptualized," (3) "Social Constructivism as a Philosophy of Mathematics," (4) "Social Constructivism and Subjective Knowledge," and (5) "The Parallels of Social Constructivism." The second part of the book explores the philosophy of (...) mathematics education and shows that many aspects of mathematics education rest on underlying, usually implicit, philosophical assumptions. Making these assumptions explicit puts a critical tool into the hands of teachers and researchers. Chapters in this section are: (6) "Aims and Ideologies of Mathematics Education," (7) "Groups with Utilitarian Ideologies," (8) "Groups with Purist Ideologies," (9) "The Social Change Ideology of the Public Educators," (10) "Critical Review of Cockcroft and the National Curriculum," (11) "Hierarchy in Mathematics, Learning, Ability and Society," (12) "Mathematics, Values and Equal Opportunities," and (13) "Investigation, Problem Solving and Pedagogy." Each chapter contains notes. (Contains 654 references.) (MKR). (shrink)

The field of mathematics education has been fashioned by a diversity of theoretical and philosophical perspectives. The purpose of this study is to add to this field an analysis of the philosophical position of critical realism. To achieve this objective, the study addresses the following questions: what does critical realism have to offer mathematics education? How may critical realism underlabour for this discipline? In addressing these questions, the study provides an overview of the (...) basic theories and the possible weak points of and arguments against critical realism and realism in general. It then draws upon the notion of a dialectical phenomenology to provide a sequence of Achilles' heel critiques of some of the perspectives that constitute broadly the theoretical landscape of mathematics education research. This critique proceeds with an analysis of didactically oriented empiricism, hermeneutics, pragmatism, postmodernism, traditionally recognized forms of constructivism, traditionally recognized theories of activity, and ethnomathematics. The last section summarizes the implications of philosophical underlabouring for a more beneficial science of mathematics education. (shrink)

Research In Mathematics Education In Australasia 2016–2019 (sometimes shortened to RiMEA 2016–2019) is a timely and important edited collection where contributors provide critical reviews on mathem...

This editorial, introducing the Journal for Theoretical & Marginal Mathematics Education, is historically situated in a moment when the field of mathematics education research is on the precipice of acknowledging that the old world is dying. That is to say, the way research has been done before is no longer adequate for operating within the White, Colonial, cis-hetero Patriarchal, Abled Capitalist dystopia we find ourselves. This inadequacy is, however, not a reason for despair but instead for (...) celebration. Instead of directing our resources towards reifying existing norms and structures, towards adopting exhausted methods and theories—as is the way of the old world—we can instead foster a ‘new aesthetics’ of mathematics education research, wherein we remake the very material that constitutes mathematics education research itself. In doing so, we engage with the politics of the margins of mathematics education research. We discuss the critical, philosophical, and psychoanalytic as three potential, but non-exhaustive, departures from mathematics education research as it has been. Each of these marginal approaches, in their own way, points to the ways that presuming a fixed mathematics education research enacts exclusionary politics and precludes change. Let this be our manifesto, written from the margins, for a more root-grasping, more self-reflective, and freer mathematics education research. (shrink)

It is a rather safe statement to claim that the social dimensions of the scientific process are accepted in a fair share of studies in the philosophy of science. It is a somewhat safe statement to claim that the social dimensions are now seen as an essential element in the understanding of what human cognition is and how it functions. But it would be a rather unsafe statement to claim that the social is fully accepted in the philosophy of (...) class='Hi'>mathematics. And we are not quite sure what kind of statement it is to claim that the social dimensions in theories of mathematics education are becoming more prominent, compared to the psychological dimensions. In our contribution we will focus, after a brief presentation of the above claims, on this particular domain to understand the successes and failures of the development of theories of mathematics education that focus on the social and not primarily on the psychological. (shrink)

The purpose of this paper is to critically analyse and discuss the views of constructivism, on the teaching and learning of mathematics. I provide a background to the learning of mathematics as constructing and reconstructing knowledge in the form of new conceptual networks; the nature, role and possibilities of constructivism as a learning theoretical framework in Mathematics Education. I look at the major criticisms and conclude that it passes the test of a learning theoretical framework but (...) there is still a gap between theory and mathematics classroom practice. (shrink)

Tasks in Primary Mathematics Teacher Education is intended to advance relevant research and innovative international practices in the preparation and professional development of mathematics teachers. Emerging from discussion at the ICMI study on teacher professional development, this volume, focused on primary and elementary teachers, culls a richness that can only be found by gathering wisdom from varied experiences around the world. The choice of tasks, and the associated pedagogies, is a key aspect of teaching and learning (...) class='Hi'>mathematics. Arguing that what students learn is largely defined by the tasks they are given, several major themes are presented. One such major strand, the form, function and focus of tasks, is discussed throughout several chapters, offering analysis, discussion of implementation, and exemplars of a broader category of illustrative techniques for developing critical understanding. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 11.2 (2003) 141-156 [Access article in PDF] Music Education as Critical PracticeA Naturalist View Lauri Väkevä University Of Oulu, Finland I This essay defends naturalism as a framework for philosophy of music education. I have three general reasons for supporting naturalism. First, by taking naturalism seriously we can keep our philosophies up-to-date with scientific inquiry. Second, naturalism can emancipate us (...) from transcendental pseudo-questions and instead help us to deal with the empirical problems of everyday life. Third, with naturalism, we can free ourselves from a priori theories of morals and aesthetics and thus view the active part that normative and aesthetic concerns play in human praxis. Even if I endorse naturalism, I do not subscribe to scientism. 1 Rather, I submit to a pragmatist view that stresses the role of philosophy (and science) in dealing with the questions of our life practices. Of the recent perspectives in the philosophy of music education my approach comes closest to the critical praxialism discussed in the MayDay group. 2All in all, I find a lot in common with the praxialist discussion (within or outside the MayDay group) and the kind of pragmatism that follows John Dewey's mature philosophy. 3 However, it seems to me that the naturalist bent of Deweyan pragmatism has not been thoroughly analyzed in our field. 4 One reason for this [End Page 141] might be the bad report that 'hard' or reductive naturalism has been given in connection with the experimental paradigm of music education research. 5 I want to argue that the critical potential of Deweyan pragmatism should not (and cannot) be separated from a naturalist approach. Taken together, critical and naturalist views can contribute to any philosophy, especially in fields that have a long tradition of leaning on otherworldly explanations.In what follows, I begin by outlining (in broad brushstrokes) the historical position of pragmatism and its status in present day philosophy. Next, I focus on the implications of Deweyan naturalist pragmatism and the possibility of maintaining a critical pragmatist attitude with naturalist presumptions in a pedagogical context. In the final part of the essay, I outline an interpretative framework for a critical pragmatism of music education that takes advantage of the naturalizing tendencies in contemporary philosophy without losing its grasp on the things that matter musically. II For a while, pragmatism had a bad name in academic philosophy. This was especially true after the linguistic turn in the first half of the last century. 6 By making the linguistic turn, many philosophers hoped to disassociate themselves from the speculative tradition(s) once and for all. Logical analysts also made it more difficult for philosophers to ignore the findings of scientists. Thus they paved the way for contemporary reductive naturalism that takes science as the measure of what can be known. 7However, analytic philosophers were not alone in their attempt to provide philosophy with scientific rigor. Classical pragmatists, too, had integrated a naturalist penchant in their output. Embracing naturalism with an open-ended experimental spirit, they wanted to focus on "the problems of men" as the chief subject matter of philosophy. 8 To many analytic philosophers, this seemed like a return to armchair speculation with an ingredient of sentimental ethics thrown in for good measure. Worse still, it looked as though the classical pragmatists were giving in to the spirit of the corporate West: speaking of the truth as "cash-value" surely seemed like a blasphemy to intellectuals who sought from formal logic and mathematics a purity of mind to clear up the messiness of everyday experience. 9Logical analysis also had its shortcomings. While many mainstream philosophers turned to logical analysis for clarity and certainty, at the same time they submitted to Cartesian-Kantian mind-body dualism with its problematic epistemology. Thus, they kept supporting the tensions between the rationalist and empiricist or analytic and synthetic domains of knowledge that haunted modernist neo-Kantian arguments.These distinctions turned out to be easy targets for postanalytic critics. 10 [End Page 142]Classical pragmatists anticipated this... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 11.2 (2003) 141-156 [Access article in PDF] Music Education as Critical PracticeA Naturalist View Lauri Väkevä University Of Oulu, Finland I This essay defends naturalism as a framework for philosophy of music education. I have three general reasons for supporting naturalism. First, by taking naturalism seriously we can keep our philosophies up-to-date with scientific inquiry. Second, naturalism can emancipate us (...) from transcendental pseudo-questions and instead help us to deal with the empirical problems of everyday life. Third, with naturalism, we can free ourselves from a priori theories of morals and aesthetics and thus view the active part that normative and aesthetic concerns play in human praxis. Even if I endorse naturalism, I do not subscribe to scientism. 1 Rather, I submit to a pragmatist view that stresses the role of philosophy (and science) in dealing with the questions of our life practices. Of the recent perspectives in the philosophy of music education my approach comes closest to the critical praxialism discussed in the MayDay group. 2All in all, I find a lot in common with the praxialist discussion (within or outside the MayDay group) and the kind of pragmatism that follows John Dewey's mature philosophy. 3 However, it seems to me that the naturalist bent of Deweyan pragmatism has not been thoroughly analyzed in our field. 4 One reason for this [End Page 141] might be the bad report that 'hard' or reductive naturalism has been given in connection with the experimental paradigm of music education research. 5 I want to argue that the critical potential of Deweyan pragmatism should not (and cannot) be separated from a naturalist approach. Taken together, critical and naturalist views can contribute to any philosophy, especially in fields that have a long tradition of leaning on otherworldly explanations.In what follows, I begin by outlining (in broad brushstrokes) the historical position of pragmatism and its status in present day philosophy. Next, I focus on the implications of Deweyan naturalist pragmatism and the possibility of maintaining a critical pragmatist attitude with naturalist presumptions in a pedagogical context. In the final part of the essay, I outline an interpretative framework for a critical pragmatism of music education that takes advantage of the naturalizing tendencies in contemporary philosophy without losing its grasp on the things that matter musically. II For a while, pragmatism had a bad name in academic philosophy. This was especially true after the linguistic turn in the first half of the last century. 6 By making the linguistic turn, many philosophers hoped to disassociate themselves from the speculative tradition(s) once and for all. Logical analysts also made it more difficult for philosophers to ignore the findings of scientists. Thus they paved the way for contemporary reductive naturalism that takes science as the measure of what can be known. 7However, analytic philosophers were not alone in their attempt to provide philosophy with scientific rigor. Classical pragmatists, too, had integrated a naturalist penchant in their output. Embracing naturalism with an open-ended experimental spirit, they wanted to focus on "the problems of men" as the chief subject matter of philosophy. 8 To many analytic philosophers, this seemed like a return to armchair speculation with an ingredient of sentimental ethics thrown in for good measure. Worse still, it looked as though the classical pragmatists were giving in to the spirit of the corporate West: speaking of the truth as "cash-value" surely seemed like a blasphemy to intellectuals who sought from formal logic and mathematics a purity of mind to clear up the messiness of everyday experience. 9Logical analysis also had its shortcomings. While many mainstream philosophers turned to logical analysis for clarity and certainty, at the same time they submitted to Cartesian-Kantian mind-body dualism with its problematic epistemology. Thus, they kept supporting the tensions between the rationalist and empiricist or analytic and synthetic domains of knowledge that haunted modernist neo-Kantian arguments.These distinctions turned out to be easy targets for postanalytic critics. 10 [End Page 142]Classical pragmatists anticipated this... (shrink)

This essay addresses a critical epistemology of mathematics as an investigation into the epistemic limitations of mathematical thinking. After arguing for the relevance of a critical epistemology of mathematics, I discuss assumptions underlying standard arithmetic and assumptions underlying standard logic as examples for such epistemic limitations of mathematical thinking. Looking into the work of philosophically inte­res­ted scholars in mathematics education such as Alan Bishop and Ole Skovsmose, I discuss some early insights for a (...) class='Hi'>critical epistemology of mathematics. I conclude that these insights can only be the beginning, that we are yet far away from a proper under­standing of the epistemic limitations of mathematics, and that more research is needed. (shrink)

The goal of this paper is to highlight the fact that the Philosophy for Children Approach can be used to stimulate pupil’s reflection within the framework of school subjects such as mathematics. First we situate P4C within the field of socio-constructivist epistemology. Then, P4C as adapted to mathematics is introduced. Finally, we describe an experiment linked to five types of exchanges, manifested between the beginning and the end of a school year while the pupils were learning to philosophize (...) about mathematics. In the discussion, emphasis is placed on the educational interventions of the teachers who facilitate the P4CM workshops. (shrink)

Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues.

In the field of mathematics education, one of the main questions remaining under debate is whether students’ development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little (...) or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students’ math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students’ performance onpracticed test tasksandtransfer test tasks. Cognitive proficiency was shown to have an effect on students’ learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A Wittgensteinian Approach to Discerning the Meaning of Works of Art in the Practice of Critical and Contextual Studies in Secondary Art EducationLeslie Cunliffe (bio)In order to get clear about aesthetic words you have to describe ways of living.Wittgenstein, Lectures and Conversations on Aesthetics, Psychology and Religious Belief1Language is a labyrinth of paths. You approach from one side and know your way about; you approach the same place (...) from another side and no longer know your way about.Wittgenstein, Philosophical Investigations2IntroductionThis article explores a Wittgensteinian approach for dealing with the meaning of works of art in the practice of critical and contextual studies in art education. The article is aimed at developing a methodology for eleven to nineteen year olds, known in the UK as the secondary phase of education, but the approach could be generalized to other educational phases.Henry Finch3 interprets four references to meaning found in Ludwig Wittgenstein's philosophy of language as a quadrant that combines the horizontal axis of meaning as physiognomies (the experiential and visual) and meaning as constructions (concepts, uses, science, and mathematics), with a vertical axis of meaning as imperatives (rule following, obligations, and law) and meaning as custom (ceremonies, myths, and ritual).4 The quadrant represents Finch's understanding of Wittgenstein's views about how language serves a different but complementary role in the way human beings engage [End Page 65] with meaning in the world and their place in it.5 Such meanings are embedded in social practices, including first-person responses to a physiognomy, although these start off as biologically primed reactions.Michael Luntley argues that Wittgenstein's philosophy of language and the related remarks on perception should be understood as setting conditions for the possibilities of judgment in "seeing the world aright, in taking the right attitude to the world"6 rather than simply mapping the possibilities of meaning, as the former underscores the role of will7 in the way meaning is actively witnessed and ethically processed by an agent. Having the right view is still only a view, but for Wittgenstein this amounted to an immense ethical and philosophical project to see things accurately and in correct relationship to each other. Such perspectival stances result from an agent's capacity to selectively engage with meaning, with a more unitary understanding resulting from criss-crossing the same territory from different points of view. Wittgenstein's four references to meaning can be thought of as forming four different points on a compass that direct the "self-as-will engaged with that which is independent of will "8 in a quest to see things aright. By extension, such an approach could be used in art education to enable students to develop the dispositions to see works of art aright.Marcia Eaton describes the tension between epistemic and interpretative approaches to the meaning of works of art in this way: "In which direction should one go? In other words, how can judgments which seem so personal (relative, subjective, etc.) also play a role in interpersonal (absolute, objective, etc.) language games?"9 Michael Podro gives a similar description of the apparent tension between a context-bound analysis of works of art and their irreducible and autonomous qualities as like "constantly treading a tightrope."10 Ralph Smith highlights the difference "between having knowledge about art and personally experiencing its presence and power."11Ben Tilghman12 advocates a Wittgensteinian way of going beyond these twofold approaches for understanding and interpreting art by focusing on the role that ponderable and imponderable evidence play in achieving the right stance when attempting to condense the meaning of works of art. Following Wittgenstein, Tilghman argues that a judgment based on imponderable evidence can often be supported by ponderable evidence, a process that is always linked to the relative experience, knowledge, and wisdom of the person making the judgment. Wittgenstein's four references to meaning could be thought of as points on a compass for directing the will in fittingness when endeavoring to understand the role and relationship of ponderable and imponderable evidence in any attempt to see works of art aright. But before these ideas can be... (shrink)

Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues.

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

This article sheds new light on Karl Marx’s theoretical legacy to promote educational philosophy and theory in science, technology, engineering, arts, and mathematics (STEAM) education. Accordingly, this article selects Marxian thought as an exemplar case to elaborate critical pedagogy and aesthetics and culminate with an overview of the Marxian approach to the theoretical underpinnings of STEAM education. Hence, the article critically reviews Marx’s original works and earlier Marxian scholars’ contributions to extending critical pedagogy and its (...) applications to the STEAM paradigm and informational and communication technology (ICT) development. This article critiques notable structural problems of STEAM education that produce power differentials such as educational gaps and digital divides in the current age of digital capitalism. Given the context, this article refines art and communication theories through the lens of his biography and writings. Additionally, this article incorporates the Marxian viewpoints about reproduction and aesthetic literacy into STEAM education. Overall, this article reviews the theoretical legacy of Marx and his essential critical and pedagogical theory, calling on scholars to pay close attention to re-orienting STEAM pedagogy as an emerging multidisciplinary field. (shrink)

Values, moral values and democratic values are attracting the attention of education researchers in general and mathematics education researchers in particular. Little research has studied pre-service teachers’ perceptions of values in the classroom, their perceptions of the relationship between the different variables of values in the classroom, as well as their relationship with the democratic society. The present research attempts to do so. Twenty-two graduate pre-service teachers who participated in ‘New trends in mathematics education’ course (...) discussed how to cultivated values in the mathematics classroom. Moreover, they answered survey questions related to the cultivation of values in this classroom. We used a combination of deductive and inductive content analysis to characterize the pre-service teachers’ texts. The research results indicate that the pre-service teachers perceived values as encouraging students’ activity in the mathematics classroom. In addition, the pre-service teachers perceived values as encouraging specific categories of values needed as skills for the citizen in a democratic society, as creativity, critical thinking and metacognition. (shrink)

The theory of knowledge objectification, initially presented and developed by Luis Radford, has gained some traction in the field of mathematics education. As with any developing theory, its presentation contains statements that may contradict its stated intents; and these problems are exacerbated in its uptake into the work of other scholars. The purpose of this study is to articulate a Spinozist-Marxian approach, in which the objectification exists not in things—semiotic means that mediate interactions—but as real relation between people. (...) As a consequence, the concept of mediation is unnecessary and can be abandoned. A concrete classroom example from Radford’s own studies is used to exemplify and develop pertinent issues. In particular, the societal nature of the ideal—a synecdoche of relations between objects that reflect relations between people—should be added and the notion of mediation no longer is required. (shrink)

The critique of philosophical foundations of neoclassical economics is significant, because of its hegemony on economic education and research programs in Iran and worldwide academies. Due to an epistemological fallacy, methodological individualism plays a prominent role in the philosophy of economic; since the ontological aspects of economy are reduced to methodological considerations. Accordingly, critique of methodological individualism is regarded as the main entry for philosophical analysis of neoclassical economics. This article aims to analyze and appraise the methodological individualism from (...) critical realism’s point of view. Critical realism is taken as a stand for criticizing methodological individualism, because critical realism and neoclassical economics as a positive approach to economics, both share a realistic worldview. The critical realism’ critique of methodological individualism is bases on analyzing the concepts of formalism, syllogism, social atomism, isolation and reduction. From critical realism’ point of view because of unrealistic postulations of methodological individualism, neoclassical economics is turned to an abstract and deductive science such as mathematics with a low potentiality of explanation. (shrink)

Educational assessments, specifically standardized and normalized exams, owe most of their foundations to psychological test theory in psychometrics. While the theoretical assumptions of these practices are widespread and relatively uncontroversial in the testing community, there are at least two that are philosophically and mathematically suspect and have troubling implications in education. Assumption 1 is that repeated assessment measures that are calculated into an arithmetic mean are thought to represent some real stable, quantitative psychological trait or ability plus some error. (...) Assumption 2 is that aggregated, group-level educational data collected from assessments can then be interpreted to make inferences about a given individual person over time without explicit justification. It is argued that the former assumption cannot be taken for granted; it is also argued that, while it is typically attributed to 20th century thought, the assumption in a rigorous form can be traced back at least to the 1830s via an unattractive Platonistic statistical thesis offered by one of the founders of the social sciences—Belgian mathematician Adolphe Quetelet (1796–1874). While contemporary research has moved away from using his work directly, it is demonstrated that cognitive psychology is still facing the preservation of assumption 1, which is becoming increasingly challenged by current paradigms that pitch human cognition as a dynamical, complex system. However, how to deal with assumption 1 and whether it is broadly justified is left as an open question. It is then argued that assumption 2 is only justified by assessments having ergodic properties, which is a criterion rarely met in education; specifically, some forms of normalized standardized exams are intrinsically non-ergodic and should be thought of as invalid assessments for saying much about individual students and their capability. The article closes with a call for the introduction of dynamical mathematics into educational assessment at a conceptual level (e.g., through Bayesian networks), the critical analysis of several key psychological testing assumptions, and the introduction of dynamical language into philosophical discourse. Each of these prima facie distinct areas ought to inform each other more closely in educational studies. (shrink)

Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics, together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues.

This research investigates how pre-service teachers aim to bring awareness of environmental sustainability while learning mathematical modelling to their 5th-grade students. Theoretical perspectives from socio-critical modelling research can involve engaging students in societal issues, including focusing on action. Thematic coding of a mandatory task by a group of pre-service teachers, where they design, implement, and reflect on a modelling activity during practicum, is used to analyse how they combine environmental and mathematical aims. The findings show that the pre-service teachers (...) emphasise the authenticity of tasks and data, engage students in actions in littering, reflect on students’ critique of assumptions, and focus on the meaning-making of environmental numbers using students’ everyday language. Implications to teacher education suggest that teachers can combine focusing on environmental sustainability through mathematics education. Further, teacher education can support pre-service teachers and students in actions through socio-critical modelling activities. (shrink)

Abstract In the present article, we provide a critical overview of the emerging field of ‘neuroeducation’ also frequently referred to as ‘mind, brain and education’ or ‘educational neuroscience’. We describe the growing energy behind linking education and neuroscience in an effort to improve learning and instruction. We explore reasons behind such drives for interdisciplinary research. Reviewing some of the key advances in neuroscientific studies that have come to bear on neuroeducation, we discuss recent evidence on the brain (...) circuits underlying reading, mathematical abilities as well as the potential to use neuroscience to design training programs of neurocognitive functions, such as working memory, that are expected to have effects on overall brain function. Throughout this review we describe how such research can enrich our understanding of the acquisition of academic skills. Furthermore, we discuss the potential for modern brain imaging methods to serve as diagnostic tools as well as measures of the effects of educational interventions. Throughout this discussion, we draw attention to limitations of the available evidence and propose future avenues for research. We also discuss the challenges that face this growing discipline. Specifically, we draw attention to unrealistic expectations for the immediate impact of neuroscience on education, methodological difficulties, and lack of interdisciplinary training, which results in poor communication between educators and neuroscientists. We point out that there should be bi-directional and reciprocal interactions between both disciplines of neuroscience and education, in which research originating from each of these traditions is considered to be compelling in its own right. While there are many obstacles that lie in the way of a productive field of neuroeducation, we contend that there is much reason to be optimistic and that the groundwork has been laid to advance this field in earnest. Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s12152-011-9119-3 Authors Daniel Ansari, Numerical Cognition Laboratory, Department of Psychology, The University of Western Ontario, Westminster Hall, London, ON N6A 3K7, Canada Bert De Smedt, Parenting and Special Education Research Group, Katholieke Universiteit Leuven, Leuven, Belgium Roland H. Grabner, Institute for Behavioral Sciences, Swiss Federal Institute of Technology (ETH) Zurich, Zurich, Switzerland Journal Neuroethics Online ISSN 1874-5504 Print ISSN 1874-5490. (shrink)

One of the criticisms of standard teaching practices is that they support merely ‘ritual’ as opposed to ‘principled’ knowledge, that is, knowledge which is procedural rather than being founded on principled explanation. This paper addresses issues and assumptions in current debate concerning the nature of mathematical knowledge, focusing on the ritual/principle distinction. Taking a discussion of centralism in logic and mathematics as its start-point, it seeks to resolve these issues through an examination of mathematics as a community of (...) practice and the teacher's role as epistemological authority in inducting pupils into such practices. (shrink)

One of the criticisms of standard teaching practices is that they support merely ‘ritual’ as opposed to ‘principled’ knowledge, that is, knowledge which is procedural rather than being founded on principled explanation. This paper addresses issues and assumptions in current debate concerning the nature of mathematical knowledge, focusing on the ritual/principle distinction. Taking a discussion of centralism in logic and mathematics as its start-point, it seeks to resolve these issues through an examination of mathematics as a community of (...) practice and the teacher's role as epistemological authority in inducting pupils into such practices. (shrink)

Joseph Agassi is known primarily among fellow academics as an exemplary historian and philosopher of science; an ardent critic and disciple of Karl Popper; a critical admirer of the work of Michael Polanyi; and a Socratic fly with the “sting of a bee” for all those who wear the intellectual fashions of the day. To most of Agassi’s students he is known primarily as an exemplary model of the Socratic teacher. The question of most urgency for educators today who (...) care about the intellectual development of students is: How do we make ready our educational institutions for more Socratic teachers? The philosophical or theoretical question is: Why do we want Socratic teachers? In outline, of the many of Agassi’s educational essays selected for this book, Agassi answers those questions: authoritarianism (or anti-democracy) blocks the democratic reform of educational institutions where Socratic teachers and students could find a safe haven; and, Socratic teaching is the main anti-dote to authoritarianism. The removal of authoritarianism from education also removes the hazard that education has become to students; to their happiness, creativity, and dignity as autonomous individuals. See Less Copyright Year: 2014 E-Book (PDF) Availability: Published ISBN: 978-94-6209-626-4 Publication date: 01 Jan 2014 Hardback Availability: Published ISBN: 978-94-6209-624-0 Publication date: 01 Jan 2014 Paperback Availability: Published ISBN: 978-94-6209-623-3 Publication date: 01 Jan 2014 Login via Institution Prices from (excl. shipping): -/- $56.00 -/- ​ Available formats Add to Cart View PDF Flyer Get Permissions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Method and Mathematics:Peter Ramus's Histories of the SciencesRobert GouldingPeter Ramus (1515–72) was, at first sight, the least likely person to write an influential history of mathematics. For one thing, he was clearly no great mathematician himself. His sympathetic biographer Nicholas Nancel related that Ramus would spend the mornings being coached in mathematics by a team of experts he had assembled, and in the afternoon would lecture (...) on the very same subjects.1 But there can be no doubt that Ramus held mathematics in particular esteem and even played a crucial role in linking philosophical discourse to mathematics and in promoting the use of quadrivial reasoning in the study of the natural world.2The origins for his enthusiasm for mathematics are to be found in his account of the nature of the arts and critique of the curriculum of the universities. From his earliest career, Ramus was a logician and remained one in all his works, whether writing on mathematics or Virgil, and he conceived [End Page 63] of all the arts, especially mathematics, as unchanging structures of necessarily true propositions—not prima facie a position which lends itself to notions of historical change and development.3 His career as a historian of mathematics, I will argue, was directed by problems that arose in his theoretical understanding of mathematics as he began to immerse himself in the sciences of the ancient world.Ramus and the Reform of DialecticRamus set out his fundamental logical positions in his very first printed work, the Dialecticae institutiones (Education in Dialectic) of 1543, a contribution to the ongoing humanist attack on scholastic logic, in which Ramus rehearsed many of the commonplace criticisms of the university dialectic. Humanists complained that logic no longer concerned itself with real human reasoning; instead, it had become a discipline studied for its own sake, using its own incomprehensible jargon, and was of no practical interest. The new humanist dialectics of Lorenzo Valla and Rudolph Agricola attempted to teach the kind of practical reasoning useful for composing a speech or letter, and they borrowed extensively from rhetorical works of Cicero and Quintilian to develop a highly rhetoricized logic. Questions about the formal validity of arguments were of little interest; what mattered was whether the arguments were persuasive.4In his Dialecticae institutiones, Ramus took this humanist reformulation of dialectic a step further. Dialectic—or, in fact, any art or science—consisted of nature, doctrine, and exercise. The natural workings of the mind formed the most significant element. Doctrine was nothing more than a record of natural reasoning; in importance it paled next to nature and practice.5 The logic of the universities bore no resemblance to the true, natural dialectic, as he argued at length in the companion volume to the Institutiones, the innocuously titled but exuberantly offensive Aristotelicae animadversiones [End Page 64] (Observations on Aristotle).6 The question, then, remained: how can we gain access to this "natural reasoning"?Ramus's answer was surprising. He asks us to find a group of men—not scholars, but completely uneducated vineyard workers. Question them about the coming year: the fertility of the soil, the quality and quantity of the crop. "And then," he writes "from their minds as from a mirror an image of nature will be reflected."7 In the reasoned replies of these uneducated men, says Ramus, we discover every part of logic needed for any purpose, whether everyday discourse or composition of poetry: the invention of arguments, the assessment of their truth and their proper and orderly presentation. Other humanists had praised man's natural logical faculties, elevating them over artificial technique, but Ramus was the first to look beyond the walls of the university and the writings of the ancients to find natural dialectic at work.If even the uneducated have some possession of the arts, then the arts taught at the university should do no more than clear away the misleading junk in the mind, and allow its natural clarity to shine through.8 Logic should be easy to learn—not because this is a pedagogic ideal, but from the very nature of the art. And if logic as it is... (shrink)

First published in 1991, _In Praise of Cognitive Emotions_ comprises fourteen of Scheffler's most recent essays - all of which challenge contemporary notions of education and rationality. While defending the ideal of rationality, he insists that rationality not be identified with a mental faculty or a mechanism of inference but taken rather as the capactity to grasp principles and purposes and to evaluate them in the light of relevant reasons. Examining a broad range of issues - from computers in (...) school to math education, from metaphor to morality - these essays are unified by Scheffler's conviction of the primacy of critical thought in education. Scheffler is especially concerned to promote a broad interpretation of rationality to counteract the narrowing of vision accompanying the technological revolution now sweeping education. Addressing three specific areas of curriculum, the work offers a critique of computer applications to education, develops a notion of strategic rationality in understanding mathematical reasoning, and, contrary to prevalent notions of moral education, connects reason with care, thus emphasizing the intimate connection between emotion and reason and challenging the dominant perception of the two as oppositional. (shrink)

An Archaeology of Educational Evaluation: Epistemological Spaces and Political Paradoxes outlines the epistemology of the theories and models that are currently employed to evaluate educational systems, education policy, educational professionals and students learning. It discusses how those theories and models find their epistemological conditions of possibility in a specific set of conceptual transferences from mathematics and statistics, political economy, biology and the study of language. The book critically engages with the epistemic dimension of contemporary educational evaluation and is (...) of theoretical and methodological interest. It uses Foucauldian archaeology as a problematizing method of inquiry within the wider framework of governmentality studies. It goes beyond a mere critique of the contemporary obsession for evaluation and attempts to replace it with the opening of a free space where the search for a mode of being, acting and thinking in education is not over-determined by the tyranny of improvement. This book will appeal to academics, researchers and post-graduate students in the fields of educational philosophy, education policy and social science. (shrink)

In this article, we review approaches to modeling a connection between spatial and mathematical thinking across development. We critically evaluate the strengths and weaknesses of factor analyses, meta-analyses, and experimental literatures. We examine those studies that set out to describe the nature and number of spatial and mathematical skills and specific connections between these abilities, especially those that included children as participants. We also find evidence of strong spatial-mathematical connections and transfer from spatial interventions to mathematical understanding. Finally, we map (...) out the kinds of studies that could enhance our understanding of the mechanisms by which spatial and mathematical processing are connected and the principles by which mathematical outcomes could be enhanced through spatial training in educational settings. (shrink)

In the mathematics education research literature, there is a growing body of scholarship on how mathematicians practice their craft. The purpose of this chapter is to survey some of this literature and explain how it can contribute to the philosophy of mathematical practice. We first describe how mathematics educators use empirical methodologies to investigate the behaviors of mathematicians and argue that findings from these studies can inform the philosophy of mathematical practice. We then illustrate this by summarizing (...) research on mathematicians’ understandings and mathematicians’ proof reading. (shrink)

Purpose: One of my goals in the paper is to investigate why realists reject radical constructivism (RC) as well as social constructivism (SC) out of hand. I shall do this by means of commenting on Peter Slezak’s critical paper, Radical Constructivism: Epistemology, Education and Dynamite. My other goal is to explore why realists condemn the use of RC and SC in science and mathematics education for no stated reason, again by means of commenting on Slezak’s paper. (...) Method: I restrict my comments to Slezak’s paper and leave it to the reader to judge which, if any, of the reasons that I advance for these two states of affairs are not specific to Slezak’s paper. Other readers might not agree with my interpretations of Slezak’s paper, including Slezak himself, but I offer them after having worked with von Glasersfeld in interdisciplinary research in mathematics education for over 25 years. Findings: My findings are that Slezak: (1) rejects RC and SC on the basis of unjustified criticisms, (2) does not explore basic tenets of RC nor of SC beyond the unjustified criticisms, (3) rejects how SC and RC have been used in science and mathematics education, based at least in part on the unjustified criticisms, (3) dislikes how SC has been used in science and mathematics education, a dislike that fuels his rejection of any constructivism, and (4) doesn’t explore how RC has been used in scientific investigations in mathematics education. On the basis of these findings, I conclude that how epistemological models of knowing might be used in science or mathematics education would be better left to the educators who use them in interdisciplinary work. (shrink)

First published in 1991, In Praise of Cognitive Emotions comprises fourteen of Scheffler's most recent essays âe" all of which challenge contemporary notions of education and rationality. While defending the ideal of rationality, he insists that rationality not be identified with a mental faculty or a mechanism of inference but taken rather as the capactity to grasp principles and purposes and to evaluate them in the light of relevant reasons. Examining a broad range of issues âe" from computers in (...) school to math education, from metaphor to morality âe" these essays are unified by Scheffler's conviction of the primacy of critical thought in education. Scheffler is especially concerned to promote a broad interpretation of rationality to counteract the narrowing of vision accompanying the technological revolution now sweeping education. Addressing three specific areas of curriculum, the work offers a critique of computer applications to education, develops a notion of strategic rationality in understanding mathematical reasoning, and, contrary to prevalent notions of moral education, connects reason with care, thus emphasizing the intimate connection between emotion and reason and challenging the dominant perception of the two as oppositional. (shrink)

This dissertation concerns Plato's theory of education and the problem of how one can actually acquire knowledge of the Forms. Plato's theory of education aims to make one a good person, which requires knowledge of the Form of the Good. Yet, how exactly one would acquire such knowledge has remained a mystery. Various models of learning are presented by Plato: elenctic refutation ; hypothesis; recollection; the mathematical, dialectical, and political studies of the Republic's curriculum; and diairesis to name (...) just those that are explicit. I have argued here that as rich as these learning strategies are we need to augment our examination of Socratic pedagogy with a full exegesis of Platonic epistemology. ;In order finally to appreciate how they, Socratic education and Platonic epistemology, are meaningfully inseparable, I have explored the following questions: what kind of teacher Socrates is and the way in which he struggles against the sophistic methods of teaching; why Plato has Socrates include ten years of mathematical study in the ideal philosophical curriculum and how we can take the Republic's paradoxical curriculum seriously; how the philosopher utilizes the mathematical training in coming to know a Platonic Form; what role opposites play in Plato's metaphysical imagination; and what kind of person would one be if one actually knew the Form of the Good. I have shown that if one were to partake of a Socratic education, to pursue the requisite mathematical training, and to arrive finally at knowledge of the Platonic Forms, then one would be the sort of person that Socrates has in mind when he articulates the principles of Socratic intellectualism. ;What has been novel about this approach is its demonstration of how, despite the fact that Socratic learning and Platonic epistemology have separately been the object of perennial scholarly attention, the two taken genuinely together have been in need of fresh critical engagement. This inquiry reveals the metaphysical constraints on knowledge and in so doing reconciles Plato's theory of knowledge with Socrates' style of educating potential philosophers. (shrink)

This paper explores the nature of the language used when teaching mathematics to young children. It proposes that an important part of the teaching of a mathematical concept is the introduction of specific terminology. Children may need to be taught new meanings for already familiar words. The timing of these introductions to new words or meanings is critical to their understanding of the concepts being taught. It will be argued that there are two aspects of the children's learning (...) that need to be considered. First, their understanding of the concept being introduced, and secondly, their learning the appropriate word to describe that concept. By assessing children's understanding of new mathematical concepts through their own use of the terminology, the teacher can then negotiate new meanings with them through practical experiences, introducing new word meanings only when the concepts have been understood. (shrink)

This article argues that children represent one vanguard of an emergent shift in Western subjectivity, and that adult-child dialogue, especially in the context of schooling, is a key locus for the epistemological change that implies. Following Herbert Marcuse's invocation of a ‘new sensibility’, the author argues that the evolutionary phenomenon of neoteny—the long formative period of human childhood and the pedomorphic character of humans across the life cycle—makes of the adult-collective of school a primary site for the reconstruction of belief. (...) After exploring child-adult dialogue more broadly as a form of dialectical interaction between what Dewey called ‘impulse’ and ‘habit’, three key dimensions of dialogic schooling are identified, all of which are grounded in a fourth: the form of dialogical group discourse called community of philosophical inquiry (CPI), which is based on the problematisation and reconstruction of concepts through critical argumentation. As a discourse-model, CPI grounds practice in all of the dialogic school's emergent curricular spaces, whether science, mathematics, literature, art, or philosophy. Second, it opens a functional space for shared decision-making and collaborative governance, making of school an exemplary model of direct democracy. Finally, CPI as a site for critical interrogation of concepts encountered in the curriculum (e.g. ‘alive’, ‘justice’, ‘system’, ‘biosphere’) and as a site for democratic governance leads naturally to expression in activist projects that model an emergent ‘new reality principle’ through concrete solutions to practical problems on local and global levels. (shrink)

Recently within the critical accounting literature Funnell (1998) has argued that accounting was implicated in the Holocaust. This charge is primarily related to the technical, mathematical nature of accounting and its ability to dehumanise individuals. Broadbent (1998, see also DeMoss and McCann, 1997) has also contended that "accounting logic" excludes emotion. She suggests that a more emancipatory form of accounting could be possible if emotion were given a voice and allowed to be heard within accounting discourse (see also Kjonstad (...) and Wilmott, 1995). This paper contends that emotion should be introduced into accounting education and in particular emotional commitment to other individuals should be encouraged. It is suggested that one way to do this may be through business ethics education. It is also suggested that increasing ethical commitment to other individuals may go some way towards combating the tendency for accountancy to dehumanise other people. While there have been specific studies of ethics and accounting education there has, as yet, been little open debate about what the objectives of accounting ethics education should be or the specific techniques that could be used to meet the desired aims. This paper contends that accountancy has become dangerously dehumanised and that one of the most important objectives for any business ethics education must be to develop an empathy with "the other". The paper studies the developments within the medical, legal and engineering profession in order to suggest some specific methods which could be employed in order to re-humanise accountancy and develop a sense of moral commitment towards other individuals. (shrink)

The Mathematics Education and Neurosciences project is an interdisciplinary research program that bridges mathematics education research with neuroscientific research. The bidirectional collaboration will provide greater insight into young children's (aged four to six years) mathematical abilities. Specifically, by combining qualitative ‘design research’ with quantitative ‘experimental research’, we aim to come to a more thorough understanding of prerequisites that are involved in the development of early spatial and number sense. The mathematics education researchers are concerned (...) with kindergartner's spatial structuring ability, while the neuroscientists are studying kindergartner's automatic quantity processing and its effect on mathematical development. The outcomes of these investigations should contribute to practical ways of fostering and supporting young children's mathematical thinking and learning. (shrink)

The vision of integrating artificial intelligence in education is part of an ongoing push for harnessing digital solutions to improve teaching and learning. Drawing from Jasanoff (Future imperfect: Science, technology, and the imaginations of modernity. In S. Jasanoff, & S. H. Kim (Eds.), Dreamscapes of modernity: Sociotechnical imaginaries and the fabrication of power (pp. 1–33). The University of Chicago Press, 2015. 10.7208/9780226276663) and Hasse (Socratic ignorance in processes of learning with technology. In H. Bound, A. Edwards, & A. Chia (...) (Eds.), Workplace learning for changing social and economic circumstances (pp. 76–90). Routledge, 2023), this paper deliberates on how sociotechnical imaginaries are interrelated to the implications of new technologies, such as AI, in education. Complicating Hasses’s (Socratic ignorance in processes of learning with technology. In H. Bound, A. Edwards, & A. Chia (Eds.), Workplace learning for changing social and economic circumstances (pp. 76–90). Routledge, 2023) call for the development of Socratic ignorance to consider our predispositions about new technologies and open new prospects of thought, this paper revisits postphenomenology (Ihde, Technology and the lifeworld: From garden to earth. Indiana University Press, 1990; Ihde, Postphenomenology: Essays in the postmodern context. Northwestern University Press, 1993; Ihde, Postphenomenology and technoscience. The Peking University lectures. State University of New York Press, 2009) and Feenberg’s (Critical theory of technology, Oxford University Press, 1991; Between reason and experience, MIT Press, 2010; Techne: Res Philos Technol 24:27–40, 2020) critical constructivist theories. While embracing the notion of Socratic ignorance, this paper stresses the importance of developing a nuanced understanding of technology that realizes its lack of neutrality and supports the creation of a deeper understanding of how knowledge is produced, deployed, and interpreted in the digital age. Thus, this paper argues that an amalgam of Hasse’s call for advancing Socratic ignorance combined with postphenomenology and critical constructivism can support students in developing a critical understanding of technology and opening new landscapes of imaginaries. (shrink)