Epistemologies of Mathematics and of Mathematics Education

This chapter addresses issues concerning epistemology, as they relate to mathematics and education. It commences with an examination of some of the main epistemological questions concerning truth, meaning and certainty, and the different ways they can be interpreted. It examines epistemologies of the ‘context of justification’ and of the ‘context of discovery’, foundationalist and non-foundationalist epistemologies of mathematics, historico-critical, genetic, socio-historical and cultural epistemologies, and epistemologies of meaning.

[1]  Paul Cobb,et al.  Small-group interactions as a source of learning opportunities in second-grade mathematics. , 1991 .

[2]  Alan H. Schoenfeld,et al.  Mathematical Problem Solving , 1985 .

[3]  J. Forgas.  Language and Social Situations , 1985 .

[4]  E. Skaalvik.  Gender differences in general academic self-esteem and in success expectations on defined academic problems , 1990 .

[5]  Emily M. Wadsworth,et al.  Women's Activities and Women Engineers: Expansions over Time. , 1992 .

[6]  Herbert J. Walberg,et al.  Educational Psychology's First Century , 1992 .

[7]  L. Steffe,et al.  Constructivism in education. , 1995 .

[8]  Paul Ernest,et al.  The philosophy of mathematics and mathematics education , 1985 .

[9]  Donald Gillies,et al.  Revolutions in Mathematics , 1975 .

[10]  Imre Lakatos,et al.  Mathematics, science and epistemology: A renaissance of empiricism in the recent philosophy of mathematics? , 1978 .

[11]  Leone Burton,et al.  Moving towards a feminist epistemology of mathematics , 1995 .

[12]  Cândida Maria de Almeida Paupério Queiroz Moreira,et al.  Primary teachers' attitudes towards mathematics and mathematics teaching with special reference to a Logo-based in-service course , 1992 .

[13]  S. Brainard.  Student Ownership: The Key to Successful Intervention Programs. , 1992 .

[14]  Claudie Solar,et al.  An inclusive pedagogy in mathematics education , 1995 .

[15]  Imre Lakatos,et al.  Mathematics, science and epistemology: Indexes , 1978 .

[16]  C. Silver,et al.  The Limits of Intervention: Lessons from Eureka, a Program to Retain Students in Science and Math-Related Majors. , 1992 .

[17]  I. Lakatos,et al.  Proofs and Refutations: Frontmatter , 1976 .

[18]  Jean Piaget,et al.  Psychogenesis and the History of Science , 1988 .

[19]  C. Matthews.  Underrepresented Minorities and Women in Science, Mathematics, and Engineering: Problems and Issues for the 1990s. CRS Report for Congress. , 1990 .

[20]  A. Sfard.  On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin , 1991 .

[21]  L. Steffe,et al.  Toward a Working Model of Constructivist Teaching: A Reaction to Simon. , 1995 .

[22]  G. Hanna.  Chapter 6 Cross-cultural gender differences in mathematics education , 1994 .

[23]  C. Gilligan.  In a Different Voice: Psychological Theory and Women''s , 1982 .

[24]  E. Goffman.  Frame analysis: An essay on the organization of experience , 1974 .

[25]  A. Bishop.  Mathematical Enculturation: A Cultural Perspective on Mathematics Education , 1988 .

[26]  Leslie P. Steffe,et al.  Cognitive Play and Mathematical Learning in Computer Microworlds. , 1994 .

[27]  R. Fischer.  Didactics, Mathematics, and Communication* , 1988 .

[28]  J. Piaget.  Science of education and the psychology of the child , 1970 .

[29]  Paul Ernest.  Constructing Mathematical Knowledge: Epistemology and Mathematics Education , 1996 .

[30]  Paul Ernest,et al.  The Philosophy of Mathematics Education , 2003 .

[31]  A. N. Leont’ev.  The Problem of Activity in Psychology , 1974 .

[32]  Hélène Massam.  Les femmes font des maths , 1993 .

[33]  Paul Cobb,et al.  Constructivist, emergent, and sociocultural perspectives in the context of developmental research , 1996 .

[34]  Thomas Tymoczko.  New Directions in the Philosophy of Mathematics , 1985 .

[35]  Peter F. Strawson,et al.  Logico Linguistic Papers , 1974 .

[36]  J. Lave.  Cognition in Practice: Outdoors: a social anthropology of cognition in practice , 1988 .

[37]  Sara Delamont,et al.  Inside Schools: Ethnography in Educational Research , 1987 .

[38]  Neil Mercer,et al.  Common Knowledge: The Development of Understanding in the Classroom , 1987 .

[39]  G. Bachelard,et al.  La formation de l'esprit scientifique. , 1940 .

[40]  Carol B. Muller,et al.  The Women in Science Project at Dartmouth , 2006 .

[41]  E. Fennema.  Increasing Women's Participation in Mathematics: An Intervention Study. , 1981 .

[42]  Henri Poincaré,et al.  Science et méthode , 1934 .

[43]  Etienne Wenger,et al.  Situated Learning: Legitimate Peripheral Participation , 1991 .

[44]  Gabriele Kaiser-Messmer.  Results of an empirical study into gender differences in attitudes towards mathematics , 1993 .

[45]  Maria Giuseppina Bartolini,et al.  Theoretical and Empirical Approaches To Classroom Interaction , 1994 .

[46]  Valerie Walkerdine,et al.  The Mastery Of Reason: Cognitive Development And The Production Of Rationality , 1990 .

[47]  G. Kaiser,et al.  Equity In Mathematics Education: Influences Of Feminism And Culture , 1995 .

[48]  Anna Sierpinska,et al.  Understanding in Mathematics , 1994 .

[49]  E. Fennema,et al.  Gender and the JRME. , 1994 .

[50]  D. Bloor.  Wittgenstein: A Social Theory of Knowledge , 1985 .

[51]  J. Dieudonne.  Mathematics-- the music of reason , 1992 .

[52]  H. Stevenson,et al.  Gender differences in beliefs and achievement: A cross-cultural study. , 1990 .

[53]  Heinz Steinberg,et al.  Routine and Meaning in the Mathematics Classroom. , 1989 .

[54]  A. Sierpińska.  Some Remarks on Understanding in Mathematics. , 1990 .

[55]  Stephen Lerman,et al.  Cultural perspectives on the mathematics classroom , 1994 .

[56]  L. Wittgenstein.  Tractatus Logico-Philosophicus , 2021, Nordic Wittgenstein Review.

[57]  Stephen Lerman.  Alternative views on the nature of mathematics and their possible influence on the teaching of mathematics , 1986 .

[58]  A. Sierpińska.  Some Reflections on the Phenomenon of French didactique , 1995 .

[59]  R. Sayers.  Gender differences in mathematics education in Zambia , 1994 .

[60]  H. Maturana.  Biology of Language: The Epistemology of Reality , 2014 .

[61]  D. Bloor,et al.  Knowledge and Social Imagery , 1977 .

[62]  C. Tocci,et al.  Achievement, Parental Support and Gender Differences in Attitudes Toward Mathematics , 1991 .

[63]  E. Keller.  Secrets Of Life, Secrets Of Death , 1992 .

[64]  Noam Chomsky,et al.  Théories du Langage, Théories de l'Apprentissage le Débat Entre Jean Piaget Et Noam Chomsky , 1982 .

[65]  J. Wertsch.  The Concept of Activity in Soviet Psychology , 1981 .

[66]  Suzanne K. Damarin.  Rethinking Science and Mathematics Curriculum and Instruction: Feminist Perspectives in the Computer Era , 1991 .

[67]  Anna Sfard.  Mathematical Practices, Anomalies and Classroom Communication Problems , 1994 .

[68]  S. Restivo.  The Social Relations of Physics, Mysticism, and Mathematics , 1983 .

[69]  Yves Chevallard,et al.  La transposition didactique : du savoir savant au savoir enseigné / , 1985 .

[70]  William Aspray,et al.  History and Philosophy of Modern Mathematics , 1988 .

[71]  Leslie P. Steffe,et al.  Epistemological foundations of mathematical experience , 1991 .

[72]  Nicolas Balacheff.  Beyond a Psychological Approach: the Psychology of Mathematics Education , 1990 .

[74]  Peter Damerow.  Mathematics Education and Society , 1996 .

[75]  R. Hersh.  Some proposals for reviving the philosophy of mathematics , 1979 .

[76]  E. Glasersfeld.  Learning and adaptation in the theory of constructivism , 1993 .

[77]  Lev Vygotsky.  Mind in society , 1978 .

[78]  Y. Chevallard.  On mathematics education and culture: Critical afterthoughts , 1990 .

[79]  The concept of chance in everyday teaching: Aspects of a social epistemology of mathematical knowledge , 1991 .

[80]  M. McIver.  Putting theory into practice. , 1987, The Canadian nurse.

[81]  H. Poincaré.  La science et l'hypothèse , 1968 .

[82]  I. Lakatos.  PROOFS AND REFUTATIONS (I)*† , 1963, The British Journal for the Philosophy of Science.

[83]  Linda Shepherd.  Lifting the Veil: The Feminine Face of Science , 1993 .

[84]  H. Garfinkel.  Studies in Ethnomethodology , 1968 .

[85]  H. Reichenbach.  Experience and Prediction. An Analysis of the Foundations and the Structure of Knowledge , 1938 .

[86]  Stephen Lerman,et al.  Intersubjectivity in Mathematics Learning: A Challenge to the Radical Constructivist Paradigm?. , 1996 .

[87]  Heinz Steinbring,et al.  Problems in the development of mathematical knowledge in the classroom: the case of a calculus lesson , 2012 .

[88]  Paul Ernest.  The Meaning of Mathematical Expressions: Does Philosophy Shed Any Light on Psychology? , 1990, The British Journal for the Philosophy of Science.

[89]  Teaching Not Learning: Listening to Parents and Empowering Children. , 1995 .

[90]  P. Clarkson,et al.  Causal attributions for success and failure in mathematics: A cross cultural perspective , 1984 .

[91]  B. Russell.  The Principles of Mathematics , 1938 .

[92]  J. Confrey.  Chapter 8: What Constructivism Implies for Teaching , 1990 .

[93]  S. Haack,et al.  Progress and Rationality in Science , 1978 .

[94]  Elizabeth Fennema,et al.  Mathematics Learning and the Sexes: A Review. , 1974 .

[95]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[96]  Tommy Dreyfus.  Didactic Design of Computer-based Learning Environments , 1993 .

[97]  Philip J. Davis,et al.  The Mathematical Experience , 1982 .

[98]  K. Popper,et al.  La connaissance objective , 1982 .

[99]  Paul K. Feyerabend,et al.  In Defence of Aristotle: Comments on the Condition of Content Increase , 1978 .

[100]  The Prevalence and Nature of Mathematics, Science, and Computer Science Intervention Programs Serving Minority and Female Students in Grades Four Through Eight , 1991 .

[101]  Valerie Walkerdine.  Counting Girls Out , 1989 .

[102]  R. Carnap.  Der logische Aufbau der Welt , 1998 .

[103]  M. Lecompte.  The Handbook of Qualitative Research in Education , 1993 .

[104]  H. Poincaré.  La logique et l'intuition dans la science mathématique et dans l'enseignement , 1991 .

[105]  Alexander James Dawson.  Implications of the work of Popper, Polya, and Lakatos for a model of mathematics instruction , 1969 .

[106]  Teri Perl,et al.  Math equals : biographies of women mathematicians+related activities , 1978 .

[107]  Judith V. Grabiner,et al.  Is Mathematical Truth Time-Dependent? , 1974 .

[108]  Ernst von Glasersfeld,et al.  Environment and Communication. , 1988 .

[109]  Thomas J. Cooney.  A Beginning Teacher's View of Problem Solving. , 1985 .

[110]  T. Abel,et al.  Mind, Self, and Society , 1934 .

[111]  Martin A. Simon.  Reconstructing Mathematics Pedagogy from a Constructivist Perspective. , 1995 .

[112]  Gila Hanna,et al.  Mathematics achievement of girls and boys in grade eight: results from twenty countries , 1989 .

[113]  N. Noddings.  Chapter 8: Feminist Critiques in the Professions , 1990 .

[114]  Léon Brunschvicg,et al.  Les Etapes de la Philosophie mathematique , 1913, The Mathematical Gazette.

[115]  Yves Chevallard,et al.  Concepts fondamentaux de la didactique : perspectives apportées par une approche anthropologique , 1991 .

[116]  Stephen Lerman.  Problem‐solving or knowledge‐centred: the influence of philosophy on mathematics teaching , 1983 .

[117]  G. Arsac.  Différents types de savoirs et leur articulation , 1995 .

[118]  H. Blumer,et al.  Symbolic Interactionism: Perspective and Method , 1988 .

[119]  G. Vergnaud.  La théorie des champs conceptuels , 1989 .

[120]  J. Northam.  Girls and boys in primary maths books , 1982 .

[121]  Leslie P. Steffe,et al.  Schemes of action and operation involving composite units , 1992 .

[122]  R. Goodstein,et al.  Remarks on the Foundations of Mathematics , 1957, The Mathematical Gazette.

[123]  Nicolas Balacheff,et al.  TOWARDS A PROBLEMATIQUE FOR RESEARCH ON MATHEMATICS TEACHING , 1990 .

[124]  E. Goffman.  The Presentation of Self in Everyday Life , 1959 .

[125]  A. Morf.  Une épistémologie pour la didactique: spéculations autour d'un aménagement conceptuel : Constructivisme et éducation , 1994 .

[126]  M. Linn,et al.  Gender, Mathematics, and Science , 1989 .

[127]  T. Kuhn,et al.  The Structure of Scientific Revolutions. , 1964 .