Bibliography
Ahmed, A. (1987) Better Mathematics: a curriculum development study based on
the Low Attainers in Mathematics Project (LAMP) HSMO, London.
Ainley, J. (1982) ME234 Using Mathematical Thinking, Unit 9 Mathematical
Thinking in the Primary Curriculum, Open University, Milton Keynes.
Ainley, J. (1987) Telling Questions, Mathematics Teaching, 118 p24-26.
Ainley J. (1995) 'Re-viewing graphing: traditional and intuitive approaches' in For
the learning of mathematics, 15 (2) 10-16.
Ainley, J. (2000) Constructing Purposeful Mathematical Activity In Primary
Classrooms, in C. Tickley and A. Wolf, The Maths We Need Now: demands,
deficits and remedies. Bedford Way Papers, London Institute of Education,
London, p138-153.
Allen, B. (1994) ‘How can I improve my practice to enable the girls within my
classroom to develop and maintain a more positive attitude to mathematics?’,
Unpublished M.Ed. thesis, Worcester College of Higher Education, Worcester.
Allen, B. & Johnston-Wilder, S. (eds) (2004) Mathematics Education: exploring
the culture of learning, Routledge Falmer, London.
Anthony, G. (1994) The Role Of The Worked Example In Learning Mathematics,
SAME Papers (1994) p129-143, University of Waikato, Hamilton.
Armstrong, M. (1980) Closely Observed Children: the diary of a primary
classroom, Writers and Readers, Richmond.
Artigue, M. (1993) Didactical Engineering as a Framework for the Conception of
Teaching Products, in Biehler, R. Scholz, R. Straßer R. and Winkelman, B. (eds)
Didactics of Mathematics as a Scientific Discipline, Kluwer, Dordrecht, p27-39.
Askew, M., Brown, M., Rhodes, V., Johnson, D. and William D. (1997) Effective
Teachers of Numeracy, London, Kings College.
Atherton, J. webref, Learning and Teaching: learning from experience,
www.dmu.ac.uk/~jamesa/learning/experien.htm.
Atkinson, R., Derry, S., Renkl, A., and Wortham, D. (2000) Learning from
Examples: instructional principles from the worked examples research. Review of
Educational Research. 70(2) pp. 181-214
Ausubel, D. (1963) The Psychology of Meaningful Verbal Learning, Grune and
Stratton, New York.
Ausubel, D. (1978) In Defense Of Advance Organizers: a reply to the critics,
Review of Educational Research, 48, p251-257.
Ausubel, D. and Robinson, F. (1969) School Learning: an introduction to
educational psychology. Holt, Rhinehart and Winston. New York.
Bachelard, G. (1938) (reprinted (1980) La Formation de l’Esprit Scientifique, J.
Vrin, Paris.
Bachelard, G. (1958) The Poetics of Space, J. Maria, (Trans. (1969) Beacon Press,
Boston.
Bachelard, G. (1968) (G. Waterston, Trans.) The philosophy of no: a philosophy
of the new scientific mind, Orion Press, New York
Baird, J. & Mitchell, I. (1986) Improving The Quality of Teaching and Learning: an
Australian case – the PEEL project, Monash University, Melbourne.
Baird, J. & Northfield, F. (1992) Learning from the Peel Experience, Monash
University, Melbourne.
Balacheff, N. (1986) Cognitive Versus Situational Analysis of problem Solving
behaviours, For The Learning of Mathematics, 6 (3) p10-12.
Balacheff, N. (1990) Towards a Problématique For Research On Mathematics
Teaching, Journal for Research in Mathematics Education. 21 (4) p258-272.
Ball, D. (1992) Magical Hopes: manipulatives and the reform of math education,
American Educator 16 (2) p14-18, p46-47.
Ballard, P. (1928) Teaching The Essentials of Arithmetic, University of London
Press, London.
Banwell, C., Tahta, D. and Saunders, K. (1972) (updated (1986) Starting Points
for Teaching Mathematics in Middle and Secondary Schools, Diss, Tarquin.
Bartlett, F. (1932) Remembering: a study in experimental and social psychology,
Cambridge University Press, London.
Bartolini-Bussi, M. G. (1990) ‘Learning situations and experiential domains
relevant to early childhood mathematics’ in Steffe, L. P. and Wood, T. (eds)
Transforming Children's Mathematics Education: international perspectives,
Hillsdale, Lawrence Erlbaum Associates.
Bauersfeld, H. (1980) ‘Hidden dimensions in the so-called reality of a
mathematics classroom’, Educational Studies in Mathematics, no. 11, pp. 23–41.
Bauersfeld, H. (1988) ‘Interaction, construction, and knowledge—alternative
perspectives for mathematics education’ in Grouws, D.A. and Cooney, T.A. (eds)
Perspectives on Research on Effective Mathematics Teaching: research agenda for
mathematics education, vol. 1, pp. 27–46, Reston, Virginia, NCTM and Lawrence
Erlbaum Associates.
Bauersfeld, H. (1992) Integrating Theories for Mathematics Education, For the
Learning of Mathematics 12 (2) p19-28.
Bauersfeld, H. (1993) Theoretical perspectives on Interaction in the Mathematics
Classroom, in R. Biehler, R. Scholz, R. Straser, B. Winkelmann (eds) Didactics of
Mathematics as a Scientific Discipline, Dordrecht, Kluwer, p133-146
Bauersfeld, H. (1995) ‘Language Games’ in the Mathematics Classroom: their
function and their effects, in P. Cobb and H. Bauersfeld (eds) The Emergence Of
Mathematical Meaning: interaction in classroom cultures, Erlbaum, Mahwah,
p271-289.
Becker, J. and Shimada, S. (1997) The Open-Ended Approach: a new proposal for
teaching mathematics, Reston, Virginia, NCTM.
Belenky, M., Clinchy, B., Goldberger, N. and Tarule, J. (1986) Women’s Ways of
Knowing: the development of self, voice and mind, New York, Basic Books.
Bell, A. (1986) ‘Diagnostic teaching: 2—Developing conflict-discussion lessons’,
Mathematics Teaching, vol. 116, p. 26–29.
Bell, A. (1987) ‘Diagnostic teaching: 3—Provoking discussion’, Mathematics
Teaching, vol. 118, p. 21–23.
Bell, A. (1993) Principles For The Design of Teaching. Educational Studies in
Mathematics 24 p5-34
Bell, A., Brekke, G. and Swan, M. (1987a) ‘Diagnostic teaching: 4—Graphical
interpretation’, Mathematics Teaching, vol. 119, pp. 56–59.
Bell, A., Brekke, G. and Swan, M. (1987b) ‘Diagnostic teaching: 5—Graphical
interpretation, teaching styles and their effects’, Mathematics Teaching, vol. 120,
pp. 50–57.
Bell, A. and Purdy, D. (1986) ‘Diagnostic teaching’, Mathematics Teaching, vol.
115, pp. 39–41.
Benbachir, A. and Zaki, M. (2001) Production d’exemples et de contre-examples
en analyse: étude de cas en première d’université. Educational Studies in
Mathematics 47 pp.273-295.
Bennett, J. (1966) The Dramatic Universe, London, Routledge.
Bennett, J. (1993) Elementary Systematics: a tool for understanding wholes,
Santa Fe, Bennett Books.
Berne, E. (1964) Games People Play, Harmondsworth, Penguin.
Beth, E. W. and Piaget, J. (1966) Mathematical Epistemology and Psychology,
Reidel, Dordrecht.
Biggs, J. and Collis, K. (1982) Evaluating the Quality of Learning: the SOLO
taxonomy, New York, Academic Press.
Bills, L. (1996) The Use of Examples in the Teaching and Learning of
Mathematics, in L. Puig and A. Gutierrez (eds) Proceedings of PME XX, Vol 2
Valencia, Spain, p81-88.
Bills, L. and Rowland, T. (1999) ‘Examples, generalisation and proof’ in Brown, L.
(ed.) Making Meaning in Mathematics: visions of mathematics 2, advances in
mathematics education, no. 1, pp. 103–116, York, QED.
Black, P. and Wiliam, D. (1998) Inside the Black Box: raising standards through
classroom assessment, School of Education, Kings College, London.
Black, P., Harrison, C., Lee, C., Marshall, B. and Wiliam, D. (2002) Working Inside
The Black Box, Department of Education and Professional Studies, Kings College,
London.
Boaler, J. (1997) Experiencing School Mathematics: teaching styles, sex and
setting, Buckingham, Open University Press.
Boaler, J. (2000) Exploring Situated Insights into Research and Learning, Journal
for Research in Mathematics Education 31 (1) p113-119.
Boero, P., Garuti, R. and Mariotti, M. A. (1996) ‘Some dynamic mental processes
underlying producing and proving conjectures’, Proceedings of the 20th
Conference of the International Group for the Psychology of Mathematics
Education, Valencia, vol. 2, pp. 121–128.
Boero P., Rossella G. and Mariotti M. (1996) Some dynamic mental processes
underlying producing and proving conjectures, in Puig, L. and Gutiérrez, A. (eds)
Proceedings of PME XX, vol 2 p121-128.
Boero, P., Rossella, G. and Mariotti, M. webref, Some dynamic mental processes
underlying producing and proving conjectures, wwwdidactique.imag.fr/preuve/Resumes/Boero/Boero96.html.
Boole, M. (1901) Indian Logic and Western Science In The Nineteenth Century, in
M. Boole (1931, E. Cobham (Ed.) Collected Works, vol. 3, p947 – 967, C.W.
Daniel Co, London.
Boulton-Lewis, G. (1998) Children’s Strategy use and Interpretations of
Mathematical representations, Journal of Mathematical Behavior, 17 (2) p219237.
Bouvier, A. (1987) The Right To Make Mistakes. For the Learning of Mathematics.
7 (3) p17-25.
Brissenden, T. (1980) Mathematics Teaching: theory and practice, London,
Harper and Row.
Brookes, W. (1966) The Development of Mathematical Activity in Children: the
place of the problem in this development, Report prepared for the sub-committee
on mathematical instruction of the British National Committee for Mathematics,
Nelson, Lancs., ATM.
Brousseau, G. (1984) The Crucial Role of the Didactical Contract in the Analysis
and Construction of Situations in Teaching and Learning mathematics, in H.
Steiner (Ed.) Theory of Mathematics Education, Paper 54, Institut fur Didaktik der
Mathematik der Universitat Bielefeld p110-119.
Brousseau, G. (1997) Theory of Didactical Situations in Mathematics: didactiques
des mathématiques, (1970–1990 in Balacheff, N., Cooper, M., Sutherland, R. and
Warfield, V. (eds) Dordrecht, Kluwer.
Brousseau, G. and Otte, M. (1991) The Fragility of Knowledge, in A. Bishop, S.
Mellin-Olsen and J. van Dormolen, Mathematical Knowledge: its growth through
teaching, Kluwer, Dordrecht, p13-36.
Brown L. and Coles A. (1999) Needing to use algebra – a case study. in O.
Zaslavsky (Ed.) Proceedings of PME–XXIII. Haifa, Vol 2 p153-160.
Brown, L. and Coles, A. (2000) ‘Same/different: a ‘natural’ way of learning
mathematics’ in Nakahara, T. and Koyama, M. (eds) Proceedings of the 24th
Conference of the International Group for the Psychology of Mathematics
Education, Hiroshima, pp. 2–153.
Brown, L. and Coles, A. (2000) Same/different: a ‘natural’ way of learning
mathematics. In T. Nakahara and M. Koyama (eds) Proceedings of the 24th
Conference of the International Group for the Psychology of Mathematics
Education, Vol 2, Hiroshima, Japan, p153-160.
Brown, M., and Kuchemann D. (1976) Is it an ‘add', Miss?, Part 1, Mathematics in
School, 5 (5) p15-17.
Brown, M., and Kuchemann D. (1977) Is it an ‘add', Miss?, Part 2, Mathematics in
School, 6 (1) p9-10.
Brown, M., and Kuchemann D. (1981) Is it an ‘add', Miss?, Part 3, Mathematics in
School, 10 (1) p26-28.
Brown, S., Collins, A. and Duguid P. (1989) ‘Situated cognition and the culture of
learning’, Educational Researcher, vol. 18, no. 1, pp. 32–41.
Brown, S. and Walter, M. (1983) The Art of Problem Posing, Philadelphia, Franklin
Press.
Bruner, J. (1965) (reprint from (1962) On Knowing: essays for the left hand, New
York, Atheneum.
Bruner, J. (1966) Toward a Theory of Instruction, Cambridge, Harvard University
Press.
Bruner, J. (1986) Actual Minds, Possible Worlds, Cambridge, Harvard University
Press.
Bruner, J. (1996) The Culture of Education, Cambridge, Harvard University Press.
Bruner, J. Goodnow, J. and Austin, G. (1956) A Study of Thinking. New York:
Wiley.
Bryant, P. (1982) The Role of Conflict and of Agreement Between Intellectual
Strategies in Children’s Ideas About Measurement, British Journal of Psychology
73 p243-251.
Burger, W. and Shaunessy, J. (1986) ‘Characterizing the van Hiele levels of
development in geometry’, Journal for Research in Mathematics Education, pp.
31–48.
Burkhardt, H. (1981) The Real World of Mathematics, Blackie, Glasgow
Bussi, M. webref, Italian Research in Innovation: Towards a New Paradigm?
elib.zib.de/IMU/ICMI/bulletin/45/ItalianResearch.html
Butler, R. (1988) Enhancing and Undermining Intrinsic Motivation: the effects of
task-involving and ego-involving evaluation on interest and performance, British
Journal of Eduacational Psychology, 58 p1-14.
Byers and Herscovics (1977) Understanding School Mathematics, Mathematics
Teaching, 81 p24-27.
Caillot, M. (2002) French Didactiques, Canadian Journal; of Science, Mathematics
and Technology Education, 2 (3) p397-403.
Calkin, J. (1910) Notes on Education: a practical work on method and school
management, Mackinlay, Halifax.
Campbell, S. and Dawson, S. (1995) Learning As Embodied Action, in R.
Sutherland and J. Mason (eds) Exploiting Mental Imagery with Computers in
Mathematics Education, Springer, New York.
Chevallard, Y. (1985) La Transposition Didactique, Grenoble, La Pensée Sauvage.
Chi, M. and Bassok, M. (1989) Learning from examples via self-explanation, in L.
Resnick (Ed.) Knowing, Learning and Instruction: essays in honor of Robert
Glaser, Erlbaum, Mahwah.
Christiansen, B. and Walther, G. (1986) ‘Task and activity’ in Christiansen, B.,
Howson, G. and Otte, M., Perspectives in Mathematics Education, Dordrecht,
Reidel.
Clarke, D. webref, Assessment for Teaching and Learning,
www.acu.edu.au/mtlc/article2.html
Claxton, G. (webref) http://www.early-education.org.uk/1newsletter000699.htm
Cobb, P. (1986) Concrete can be Abstract: a case study, Educational Studies in
Mathematics 17 (1) p37-48.
Cobb, P. (1988) ‘The tension between theories of learning and instruction in
mathematics education’, Educational Psychologist, vol. 23, no. 2, pp. 87–103.
Cobb, P. (1994) ‘Where is the mind? Constructivism and sociocultural
perspectives on mathematical development’, Educational Researcher, vol. 23, no.
7, pp. 13–20.
Cobb, P. (1995) Learning and Small-Group Interaction, in P. Cobb and H.
Bauersfeld (eds) The Emergence of Mathematical Meaning: interaction in
classroom cultures, Erlbaum, Mahwah.
Cobb, P. and Merkel, G. (1989) Thinking Strategies: teaching arithmetic through
problem solving. In P. Trafton and A. Shulte (eds) New Directions for Elementary
School Mathematics: (1989 Yearbook, National Council of Teachers of
Mathematics, Reston, p70-81.
Cobb, P. McClain, K. and Whiteneck, J. (1997) Reflective Discourse and Collective
Reflection, Journal for Research in Mathematics Education, 28 (3) p258-277.
Cobb, P., Wood, T. and Yackel, E. (1990) ‘Classrooms as learning environments
for teachers and researchers’ in Davis, R., Maher, C. and Noddings, N. (eds)
Constructivist Views on the Teaching and Learning of Mathematics, Reston,
Virginia, NCTM.
Cobb, P. Wood, T. and Yackel E. (1991) A Constructivist Approach To Second
Grade Mathematics, in E. von Glasersfeld (Ed.) Radical Constructivism In
Mathematics Education, Reidel Dordrecht, pp. 157-76.
Cobb, P. Yackel, E. and Wood, T. (1992) A Constructivist Alternative to the
representational View of Mind in Mathematics education, Journal for Research in
Mathematics Education, 23 (1) p2-33.
Cobb, P., Yackel, E. and Wood, T. (1992) ‘Interaction and learning in
mathematics situations’, Educational Studies in Mathematics, no. 23, pp. 99–122.
Colburn, W. (1863) Intellectual Arithmetic, Upon the Inductive Method of
Instruction, Houghton, Cambridge.
Cole, M. (1985) The Zone of Proximal Development: where culture and cognition
create each other, in J. Wertsch (Ed.) Culture, Communication, and Cognition:
Vygotskian perspectives, Cambridge University Press, Cambridge, p141-161.
Coles, A. and Brown, L. (1999) ‘Meta-commenting: developing algebraic activity
in a ‘‘community of inquirers’’’ in Bills, L. (ed.) Proceedings of the British Society
for Research into Learning Mathematics, pp. 1–6, Warwick University, MERC.
Coles, A. and Brown, L. (1999) Meta-Commenting: developing algebraic activity
in a ‘Community of Inquirers’, in L. Bills (Ed.) Proceedings of the British Society
for Research into Learning Mathematics MERC, Warwick University, p1-6.
Confrey (1994) A Theory of Intellectual Development, For The Learning Of
Mathematics 14 (3) p2-8.
Confrey, J. (1990) What Constructivism Implies for Teaching, in R. Davis, C.
Maher, N. Noddings (eds) Constructivist Views on the Teaching of and Learning of
Mathematics (pp.107-122) NCTM Reston.
Confrey, J. (1991) Steering a Course Between Vygotsky and Piaget, Educational
Researcher 20 (2) 29-32.
Confrey, J. (1995) How Compatible are Radical Constructivism, Sociocultural
Approaches, and Social Constructivism? in L. Steffe, and J. Gale (eds)
Constructivism in Education, Erlbaum, Mahwah.
Cook, T. (1979) The Curves of Life, (reprint of (1914 edition) Dover, New York
Courant, R. (1981) Reminiscences from Hilbert’s Göttingen, Math Intelligencer, 3
(4) p 154-164.
Cremin, L. (1961) The Transformation of the School: progressivism in American
education, 1876-1957, Knopf, New York.
Crowley, M. (1987) The van Hiele Model of the Development of Geometric
Thought, in M. Lindquist and A. Shulte (eds) Learning And Teaching Geometry K12: (1987 yearbook, NCTM, Reston, p1-16.
Cuoco, A., Goldenberg, P. and Mark, J. (1996) Habits of Mind: an organizing
principle for mathematics curricula, Journal of Mathematical Behavior 15 p375402.
Da Vinci, L. webref, Leonardo Da Vinci, www-history.mcs.standrews.ac.uk/history/Quotations/Leonardo.html
Da Vinci, L. www.brainyquote.com/quotes/quotes/l/q140595.html
Dahlberg, R. and Housman, D. (1997) Facilitating Learning Events Through
Example Generation, Educational Studies in Mathematics 33, p283-299.
Davis, B. (1996) Teaching Mathematics: toward a sound alternative, London,
Garland.
Davis, B. (webref) Mathematics Teaching: moving from telling to listening,
phenomenological research paper, Textorium,
http://www.atl.ualberta.ca/po/main.cfm
Davis, B. (1996) Teaching Mathematics: toward a sound alternative, Garland,
London.
Davis, G. Tall, D. and Thomas, M. webref, What Is The Object Of The
Encapsulation Of A Process? www.warwick.ac.uk/staff/David.Tall/downloads.htm
Davis, P. and Hersh, R. (1981) The Mathematical Experience, Harvester, (1981.
Davis, R. (1966) ‘Discovery in the teaching of mathematics’ in Shulman, L. and
Keislar, E. (eds) Learning by Discovery: a reappraisal, Chicago, Rand McNally.
Davis, R. (1984) Learning Mathematics: the cognitive science approach, Croom
Helm, London.
Davis, R. Maher, C. and Noddings, N. (eds) (1990) Constructivist Views on the
Teaching of and Learning of Mathematics, Reston, Virginia, NTCM.
Davydov, V. (1990) Types of Generalisation in Instruction (trans. J. Teller)
Reston, Virginia, NTCM.
De Morgan, A. (1865) A Speech of Professor De Morgan, President, at the first
meeting of the London Mathematical Society, Proceedings of the London
Mathematical Society Jan 16, p1-9.
De Morgan, A. (1898) Of the Study and Difficulty of Mathematics, Open Court,
London.
Dearden R. (1976) Instruction And Learning By Discovery, in R. Peters (Ed.) The
Concept Of Education, Routledge and Kegan Paul, London, pp. 133-155.
Denvir, B. and Brown, M. (1986a) ‘Understanding number concepts in low
attaining 7–9-year-olds’, Educational Studies in Mathematics, vol. 17, no. 1, pp.
15–36.
Denvir, B. and Brown, M. (1986b) ‘Understanding number concepts in low
attaining 7–9-year-olds’ part II, Educational Studies in Mathematics, vol. 17, no.
2, pp. 143–164.
Denvir, B. and Brown, M. (1986) Understanding Number Concepts in Low
Attaining 7-9 year-olds, Educational Studies in Mathematics, 17 (1) p15-36.
Denvir, B. and Brown, M. (1986a) Understanding Number Concepts in Low
Attaining 7-9 Year-Olds: part II Educational Studies in Mathematics, 17 (2) p143164.
Detterman, D. and Sternberg, R. (eds) (1993) Transfer on Trial: intelligence,
cognition, and instruction, Abbex, Norwood, NJ p99-167.
Dewey, J. (1902) The Child and The Curriculum, (reprinted (1971 as The Child
and The Curriculum and The School and Society) Chicago, Chicago Press.
Dewey, J. (1933) How We Think: a restatement of the relation of reflective
thinking to the educative process, D.C. Heath and Co, London
Dewey, J. (1933) How We Think: a restatement of the relation of reflective
thinking to the educative process, Heath, Boston.
Dewey, J. (1938) Experience and Education, MacMillan, New York.
Dewey, J. webref, ‘My Pedagogic Creed’ by John Dewey
www.rjgeib.com/biography/credo/dewey.html
DfEE (1999a) National Numeracy Strategy: framework for teaching mathematics
from reception to year 6, London, DfEE.
DfEE (1999b) National Numeracy Strategy: mathematical vocabulary, London,
DfEE.
Dickson, L. Brown, M. & Gibson, O. (1984) Children learning Mathematics, Cassell
Education, Cassell, London.
Dienes, Z. (1963) An Experimental Study of Mathematics Learning, London,
Hutchinson.
Dienes, Z. P. (1963) An Experimental Study Of Mathematics. Hutchinson
Educational, London.
Donaldson, M. (1963) A Study of Children’s Thinking, Tavistock Publications,
London.
Dörfler, W, (1991) Meaning: Image Schemata and Protocols, Plenary Lecture, in
F. Furinghetti (Ed.) Proceedings of PME XV, vol I, p17-33. Assisi, Italy.
Dörfler, W. (2002) Formation of Mathematical Objects as Decision Making.
Mathematical thinking and learning 4 (4) p337-350.
Dubinsky, E. (1991) ‘Reflective abstraction in mathematical thinking’, in
Tall, D. (ed.) Advanced Mathematical Thinking, Dordrecht, Kluwer.
Dubinsky, E. (1991) Reflective Abstraction in Mathematical Thinking, in D. Tall
(Ed.) Advanced Mathematical Thinking, Dordrecht: Kluwer, p95-126.
Dubinsky, E. webref, Ed Dubinsky's Home Page, trident.mcs.kent.edu/~edd/
Duffin, J. (1996) Calculators in the Classroom, Manutius Press, Liverpool.
Duffin, J. and Simpson, A. (1999) A Search for Understanding. The Journal of
Mathematical Behaviour. 18 (4) p415-428.
Duffin, J.M. and Simpson, A.P. (2000) A search for understanding. Journal of
Mathematical Behavior, 18 (4) 1-13.
Duroux, A. (1982) (V. Warfield Trans) webref, Calculus By Scientific Debate As An
Application Of Didactique,
www.math.washington.edu/~warfield/articles/Calc&Didactique.html
Dweck, C. (1999) Self-Theories: their role in motivation, personality and
development, Philadelphia, Psychology Press.
Dweck, C. (1999) Self-Theories: Their role in motivation, personality and
development, Psychology Press, Philadelphia
Dyrszlag, Z. (1984) ‘Sposoby Kontroli Rozumienia Pojec Matematycznych’,
Oswiata i Wychowanie 9, B, pp. 42–43.
Earl, L., Fullan, M., Leithwood, K., & Watson, N. (2000) Watching and Learning,
OISE/UT Evaluation of the implementation of the National Literacy and National
Numeracy Strategies. First Annual Report, OISE, University of Toronto.
Earl, L., Fullan, M., Leithwood, K., & Watson, N. (2001) Watching and Learning 2,
OISE/UT Evaluation of the implementation of the National Literacy and National
Numeracy Strategies. Second Annual Report, OISE, University of Toronto.
Earl, L., Fullan, M., Leithwood, K., & Watson, N. (2003) Watching and Learning 3,
OISE/UT Evaluation of the implementation of the National Literacy and National
Numeracy Strategies. Third Annual Report, OISE, University of Toronto.
Edwards, D. and Mercer, N. (1987) Common Knowledge: The Development of
Understanding in the Classroom, Routledge, London.
Egan, K. (1986) Teaching as Story Telling: An Alternative Approach to Teaching
and Curriculum in the Elementary School, University of Chicago press, Chicago.
Egan, K. webref, Getting it wrong from the beginning: The mismatch between
school and children's minds at www.educ.sfu.ca/kegan/Wrong-article.html.
Egan, K. webref, Welcome to Kieran Egan's Home Page, www.educ.sfu.ca/kegan.
Elbaz, F. (1983) Teacher’s Thinking: a study of practical knowledge, Nichols, New
York.
Enright, M. & Cox, D. webref, Foundations Study Guide: Montessori education,
www.objectivistcenter.org/articles/foundations_montessori-education.asp.
Erlwanger, S. (1973) Benny's conception of rules and answers in IPI
Mathematics, Journal of Children's Mathematical Behavior, 1(2) p7-26.
Erlwanger, S. (1973) Benny's conception of rules and answers in IPI
mathematics, Journal of Children's Mathematical Behavior, 1 (2) p. 7-26.
Festinger, L. (1957) A Theory of Cognitive Dissonance, Stanford, Stanford
University Press.
Fielker, D. (1997) Extending Mathematical Ability through Interactive Whole Class
Teaching, Hodder & Stoughton, London.
Fischbein, E. (1987) Intuition in Science and Mathematics: an educational
approach, Reidel, Dordecht.
Flewelling, G. & Higginson, W. (2000) Realizing a Vision of Tomorrow’s
Classroom: a handbook on rich learning tasks, Centre for Mathematics, Science
and technology Education, Queen’s University, Kingston (Ontario).
Flewelling, G. & Higginson, W. webref, webstudio.educ.queensu.ca/faculty/tmc.
Floyd, A. (Ed.) (1981) Developing Mathematical Thinking, Addison Wesley,
London.
Floyd, A. et al (1982) EM235 Developing Mathematical Thinking, Open University,
Milton Keynes
Floyd, A., Burton, L., James, N. and Mason, J. (1981) Developing Mathematical
Thinking, Milton Keynes, The Open University.
Fox, D. (1983) Personal Theories of Teaching, Studies in Higher Education, 8 (2)
p151-163.
Frankenstein, M. (1989) Relearning Mathematics: a different third R— radical
math, London, Free Association.
Frankenstein, M. (1989) Relearning mathematics: a different R - radical math(s)
Free Association, London
Freudenthal, H. (1983) Didactical Phenomenology of Mathematical Structures,
Dordrecht, Reidel.
Freudenthal, H. (1991) Revisiting Mathematics Education: China lectures,
Dordrecht, Kluwer.
Freudenthal, H. (1973) Mathematics as an Educational Task, Reidel, Dordrecht.
Freudenthal, H. (1978) Weeding and Sowing: preface to a science of
mathematical education, Reidel, Dordrecht.
Freudenthal, H. (1983) Didactical Phenomenology of Mathematical Structures,
Reidel, Dordrecht.
Freudenthal, H. (1991) Revisiting Mathematics Education: China lectures, Kluwer,
Dordrecht.
Fullan, M., Earl, L., Leithwood, K., & Watson, N. (1999) Implementation of the
National Literacy and Numeracy Strategies: First interim report. Toronto: OISE,
University of Toronto.
Gadamer, H.-G. (1975) Truth and Method, New York, The Seabury Press.
Gadamer, H.-G. (1990) Truth and Method, New York, Continuum.
Gagne, R. (1985) The Conditions of Learning (4th edn.) Holt, Rinehart & Winston,
New York.
Gagne, R., Briggs, L. & Wager, W. (1992) Principles of Instructional Design (4th
edn.) HBJ College Publishers, Fort Worth.
Gattegno, C. (1970) What We Owe Children: the subordination of teaching to
learning, London, Routledge and Kegan Paul.
Gattegno, C. (1987) The Science of Education, Part I: Theoretical considerations,
New York, Educational Solutions.
Gattegno, C. (1963) For the Teaching of Mathematics, Educational Explorers,
Reading.
Gattegno, C. (1970) What We Owe Children: the subordination of teaching to
learning Routledge and Kegan Paul, London.
Gattegno, C. (1970a) The Human Element in Mathematics, in Mathematical
Reflections: contributions to mathematical thought and teaching, written in
memory of A. G. Sillito, Association of Teachers of Mathematics, Cambridge
University Press, Cambridge p131-138.
Gattegno, C. (1974) The Common Sense of Teaching Mathematics. Educational
solutions. New York.
Gattegno, C. (1981) Children and Mathematics: a new appraisal. Mathematics
Teaching 94 p5-7.
Gattegno, C. (1983) On Algebra, Mathematics Teaching 105 p34-35.
Gattegno, C. (1987) The Science of Education Part I: Theoretical considerations,
Educational Solutions, New York.
Gattegno, C. (1988) The Science of Education Part 2B: the awareness of
mathematization, Educational Solutions, New York.
Gibson webref, http://www.alamut.com/notebooks/a/affordances.html
Gibson, J. (1977) ‘The theory of affordances’ in Shaw, R. E. and Bransford, J.
(eds) Perceiving, Acting, and Knowing, Mahwah, Lawrence Erlbaum Associates.
Gibson, J. (1979) The Ecological Approach to Visual Perception, London,
Houghton Mifflin.
Gibson, J. (1977) The Theory of Affordances, in R. E. Shaw and J. Bransford (eds)
Perceiving, Acting, and Knowing, Erlbaum, Mahwah.
Gibson, J. (1977) The Theory of Affordances, in R. E. Shaw and J. Bransford (eds)
Perceiving, Acting, and Knowing, Erlbaum, Mahwah.
Gibson, J. (1979) The Ecological Approach to Visual Perception, Houghton Mifflin,
London.
Giles, G. (1966) Notes on Mathematical Activity in B. Atkin et al., The
development of Mathematical Ability in Children: the place of the problem in this
development, Association of Teachers of Mathematics, Nelson, p8-12.
Godfrey, C. and Siddons, A. W. (1931) The Teaching of Elementary Mathematics,
Cambridge, Cambridge University Press.
Goldenberg, P., Lewis, P. and O’Keefe, J. (1992) Dynamic Representation And
The Development Of A Process Understanding Of Function, in E. Dubinsky and G.
Harel, (eds) The Concept of Function: Aspects of Epistemology and Pedagogy,
MAA Monograph series, Washington, p235-260.
Goodman, N. (1978) Ways of World Making, Boston and London,
Harvester.Goodman, N. (1978) Ways of World Making, Harvester, Boston and
London.
Gravemeijer, K. (1994) Developing Realistic Mathematics Education, Utrecht,
Freudenthal Institute.
Gravemeijer, K. (1990) Context problems and realistic mathematics education, in
K. Gravemeijer, M. Van den Heuvel, and L. Streefland (eds) Contexts, Productions
Tests and Geometry in Realistic Mathematics Education, Technipress Culemborg.
Gravemeijer, K. (1994) Developing Realistic Mathematics Education, Freudenthal
Institute, Utrecht.
Gray, E. and Tall, D. (1994) Duality, Ambiguity, and Flexibility: A proceptual view
of simple arithmetic, Journal for Research in Mathematics Education, 25 (2)
p116–140.
Gray, E. M. and Tall, D. O. (1994) ‘Duality, ambiguity and flexibility: a proceptual
view of simple arithmetic’, The Journal for Research in Mathematics Education,
vol. 26, no. 2, pp.115–141.
Gray, E.M., & Tall, D.O., (1994) Duality, ambiguity and flexibility: A proceptual
view of simple arithmetic, Journal for Research in Mathematics Education, 25 (2)
p. 115-141.
Green, D. (1989) School Pupils’ Understanding of Randomness, in R. Morris (Ed.)
Studies In Mathematics Education: the teaching of statistics, Unesco, Paris, p2739.
Greeno, J. (1991) Number Sense as Situated Knowing in a Conceptual Domain,
Journal for Research in Mathematics Education 22 (3) p170-218.
Greeno, J. (1991) Number Sense as Situated Knowing in a Conceptual Domain,
Journal for Research in Mathematics Education 22 (3) p. 170-218.
Greeno, J. Smith, D. and Moore, J. (1993) Transfer of Situated Learning in D.
Detterman and R. Sternberg (eds) Transfer on Trial: intelligence, cognition, and
instruction, Abbex, Norwood, p99-167.
Griffin, P. (1989) Teaching Takes Place in Time, Learning Takes Place Over Time,
Mathematics Teaching 126, p12-13.
Griffin, P. and Gates, P. (1989) Project Mathematics UPDATE: PM753A,B,C,D,
Preparing To Teach Angle, Equations, Ratio and Probability, Open University,
Milton Keynes.
Groves, S. and Doig, B. (2002) ‘Developing Conceptual Understanding: the role of
the task in communities of mathematical inquiry’, PME26.
Hadas, N., Hershkowitz, R. and Schwarz, B. (2002) ‘Analyses of activity design in
geometry in the light of student actions’, Canadian Journal of Science,
Mathematics and Technology Education, vol. 2, no. 4, pp. 529–552.
Hall, E. (1981) The Silent Language, Anchor Press, Doubleday, New York.
Halmos, P. (1975) The Problem of Learning to Teach, American Mathematical
Monthly. 82 (5) p466-476.
Halmos, P. (1980) The Heart of Mathematics, American Mathematical Monthly 87
(7) p519–524.
Halmos, P., (1994) What is Teaching? American Mathematical Monthly 101 (9)
p848-854.
Hamilton, E. and Cairns, H. (eds) (1961) (trans. Guthrie, W.) Plato: the collected
dialogues including the letters, Bollingen Series LXXI, Princeton, Princeton
University Press.
Hamilton, E. and Cairns, H. (1961) Plato: the collected dialogues, Bollingen Series
LXXI, Princeton University Press, Princeton.
Hamming, R. (1980) The Unreasonable Effectiveness of Mathematics, The
American Mathematical Monthly, Vol 87 (2) p81-90.
Hamming, R. webref, The Unreasonable Effectiveness of Mathematics,
www.lecb.ncifcrf.gov/~toms/Hamming.unreasonable.html
Hanson, N. (1958) Patterns of Discovery: an enquiry into the conceptual
foundations of science
Harel, G. and Kaput, J. (1992) The Role of Conceptual Entities and Their Symbols
in Building Advanced mathematical Concepts, in D. Tall (Ed.) Advanced
Mathematical Thinking, Kluwer, Dordrecht, p82-94.
Harré, R. & Lamb, R. (eds) (1983) The Encyclopedic Dictionary of Psychology,
MIT Press, Cambridge.
Harré, R. and van Langenhove, L. (eds) (1999) Positioning Theory: Moral
Contexts of Intentional Action, Blackwell, Oxford.
Harré, R. and van Langenhove, L. (1992) Varieties of Positioning, Journal for the
Theory of Social Behaviour, 20, 393-407.
Hart, K. (Ed.) (1981) Children’s Understanding of Mathematics: 11-16, John
Murray, London.
Hart, K. (1984) Ratio: children’s strategies and errors, NFER-Nelson, Windsor.
Hart, K. (1993) Confidence in Success, in I. Hirabayashi, N. Nohda, K.
Shigematsu and F.-L. Lin (eds) Psychology of Mathematics Education, PME XVII,
Vol 1, p17-31, University of Tsukuba, Tsukuba.
Hart, K. Kerslake, D. Brown, M. Ruddock, G. Küchemann, D. and McCartney, M.
(eds) (1981) Children’s Understanding of Mathematics 11-16, John Murray,
London.
Hart, K., Brown, M. Kuchemann, D. Kerlsake, D. Ruddock, G. and McCartney, M.
(1981) Children’s Understanding of Mathematics, John Murray, London.
Hauser, M. (2001) Wild Minds: what animals really think, Harmondsworth,
Penguin.
Healy, L. and Hoyles, C. (2000) ‘Study of proof conceptions in algebra’, Journal
for Research in Mathematics Education, vol. 31, no. 4, pp. 396–428.
Healy, L. and Hoyles, C. (2000) Study of Proof Conceptions in Algebra. Journal for
Research in Mathematics Education, 31, 4, pp396-428.
Hewitt, D. (1996) ‘Mathematical fluency: the nature of practice and the role of
subordination’, For the Learning of Mathematics, vol. 16, no. 2, pp. 28–35.
Hewitt, D. (1994) The Principle of Economy in the Learning and Teaching of
Mathematics, unpublished PhD dissertation, Open University, Milton Keynes.
Hewitt, D. (1999) Arbitrary and Necessary Part 1: a way of viewing the
mathematics curriculum, For The learning of Mathematics (19 (3) p2-9.
Hiebert, J. and Carpenter, T. (1992) Learning and Teaching with Understanding,
in D. Grouws (Ed.) Handbook of Research on Mathematics Teaching and learning,
MacMillan, New York. p65-93.
Hiebert, J. and Wearne, D. (1992) Links Between Teaching and Learning Place
Value With Understanding in First Grade, Journal for Research in Mathematics
education, 23 p98-122.
Hogben, L. (1938) Clarity Is Not Enough: an address on the needs and difficulties
of the average pupil, Mathematical Gazette XXII (249) p105-123.
Holt, J. (1964) How Children Fail, Harmondsworth, Penguin.
Holt, J. (1967) How Children Learn, Pitman, New York.
Holt, J. (1970) What Do I Do Monday?, Dutton, New York.
Holton, D. webref, Personal Thoughts on an ICMI Study, Department of
Mathematics and Statistics, University of Otago, New Zealand,
www.maths.otago.ac.nz/ICMI_Study.doc.
Hopkins, C. (1990) ‘A conference tale’, Mathematics Teaching, no. 132, pp. 20–
21.
Houssart, J. (1999) ‘Seeing the pattern and seeing the point’ in Bills, L. (ed.)
Proceedings of the British Society for Research into Learning Mathematics, pp.
73–78, Warwick University, MERC.
Houssart, J. (2001) Rival Classroom Discourses and Inquiry mathematics: ‘the
whisperers’, For the Learning of Mathematics 21 (3) p2-8.
Hughes, M. (1986) Children and Number: difficulties in learning mathematics,
Blackwell, Oxford.
Jackson, P. (1992) Untaught Lessons, Teachers College Press, Columbia
University, New York.
James, W. (1899) (reprinted Dover (1961) Talks to Teachers on Psychology and
to Students on Some of life’s Ideals, Henry Holt, New York.
Jaworski, B. (1994) Investigating Mathematics Teaching: a constructivist enquiry,
London, Falmer Press.
Johnson, D., Adhami, M. and Shayer, M. (1997) ‘Does ‘CAME’ work? Summary
report on Phase 2 of the Cognitive Acceleration in Mathematics Education (CAME)
Project’ in Morgan, C. (ed.) Proceedings of the British Society for Research into
Learning Mathematics, pp. 26–31, and Bristol, Bristol University.
Johnson-Laird, P. and Wason, P. (1977) A theoretical analysis of insight into a
reasoning task. in P. Johnson-Laird and P Wason (eds) Thinking: readings in
cognitive science, Cambridge University Press, Cambridge p143-151.
Johnston-Wilder, S. & Pimm, D. (eds) (2004) Teaching Mathematics with ICT,
Open University Press.
Jong, T. and Ferguson-Hessler, M. (1996) Types and Qualities of Knowledge,
Educational Psychologist 31 (2) p105-113.
Jowett, B. (1871) The Dialogues of Plato Vol II, Oxford University Press, Oxford.
Kaheneman D. and Tversky, A. (1982) Subjective Probability: a judgement of
representativeness, in D. Kahneman, P. Slovic, A. and Tversky, (eds) Judgement
Under Uncertainty: Heuristics and Biases, Cambridge University Press, Cambridge
p32-47.
Kangshen, S., Crossley, J. and Lun, A. (1999) The Nine Chapters on the
Mathematical Art: companion and commentary, Oxford, Oxford University Press.
Kant, I. (1781) (Smith, N. Trans. 1929) Critique of Pure Reason, MacMillan,
London.
Kilpatrick, J., Swafford, J. and Findell, B. (eds) (2001) Adding It Up: helping
children learn mathematics, Washington, National Academy Press.
King, A. (1993) From Sage on the Stage to Guide on the Side in College
Teaching, 41 (1) p30-35.
Kitcher, P. (1983) The Nature of Mathematical Knowledge, Oxford University
Press, Oxford.
Kline, M. (1980) Mathematics: the loss of certainty, Oxford University Press, New
York.
Kolb, D. A. (1984) Experiential Learning: experience as the source of learning and
development, Prentice-Hall, Englewood Cliffs.
Krainer, K. (1993) Powerful Tasks: a contribution to a high level of acting and
reflecting in mathematics instruction, Educational Studies in Mathematics 24,
p65-93.
Krutetskii, V. (1976) (Teller, J., trans.) in Kilpatrick, J. and Wirszup, I. (eds) The
Psychology of Mathematical Abilities in School Children, Chicago, University of
Chicago Press.
Kuchemann, D. (1981) Algebra, in K. Hart, M. Brown, D. Kuchemann, D.
Kerlsake, G. Ruddock, and M. McCartney, (eds) Children’s Understanding of
Mathematics, John Murray, London p102-119.
Laborde, C. (1989) ‘Audacity and reason: French research in mathematics
education’, For the Learning of Mathematics, vol. 9, no. 3, pp. 31–36.
Lakatos, I. (1976) Proofs and Refutations, Cambridge, Cambridge University
Press.
Lakoff, G. and Johnson, M. (1980) Metaphors We Live By, University of Chicago
Press, Chicago.
Lampert, M. (1986) ‘Knowing, Doing, and Teaching Multiplication,’ Cognition and
Instruction, vol. 3, p305-342.
Lampert, M. (1990) When the problem is not the question and the solution is not
the answer: mathematical knowing and teaching, American Educational Research
Journal, 27 (1) p29-63.
Lampert, M. (2001) Teaching Problems and the Problems of Teaching, Yale
University Press, New Haven.
Lave, J. (1988) Cognition in Practice: mind, mathematics and culture in everyday
life, Cambridge, Cambridge University Press.
Lave, J. (1993) The Practice of Learning, in S. Chalkin and J. Lave (eds)
Understanding Practice: perspectives on activity and context, Cambridge
University Press, Cambridge, p3-32.
Lave, J. (1996) Teaching as learning, in Practice, Mind, Culture and Activity 3 (3)
p149-164.
Lave, J. and Wenger, E. (1991) Situated Learning: legitimate peripheral
participation, Cambridge, Cambridge University Press.
Lave, J. and Wenger, E. (1991) Situated Learning: legitimate peripheral
participation, Cambridge University Press, Cambridge.
Lawler, R. (1981) The Progressive Construction of Mind, Cognitive Science 5 p130.
Lawton, D. & Gordon, P. (1993) Dictionary of Education, Hodder & Stoughton,
London.
Leapfrogs, (1982) Geometric Images, Association of Teachers of Mathematics,
Derby.
Leder, G. Pehkonen, E. & Törner, G. (2003) Beliefs: a hidden variable in
mathematics education?, Kluwer, Dordrecht.
Legrand, M. (1993) Débate Scientifique en Cour de Mathématiques, Repères
IREM, No. 10, Topiques Edition.
Legrand, M. (1993) Débate scientifique en cour de mathématiques. Repères
IREM, no 10, Topiques Edition.
Leont’ev (1979) The problem of Activity in Psychology, in J. Wertsch (Trans., Ed.)
The Concept of Activity in Soviet Psychology, Sharpe, New York, p37-71.
Leont’ev, A. (1981a) ‘The problem of activity in psychology’ in Wertsch, J. (ed.)
The Concept of Activity in Soviet Psychology, Sharpe, Armonk.
Leont’ev, A. (1981b) Psychology and the Language Learning Process, Oxford,
Pergamon.
Leont’ev, A. (1981) Psychology and the Language Learning Process, Pergammon,
Oxford.
Lerman, S. (1989) ‘Constructivism, mathematics and mathematics education’,
Educational Studies in Mathematics, vol. 20, pp. 211–223.
Lerman, S. (1996) ‘Intersubjectivity in mathematics learning: a challenge to the
radical constructivist paradigm’, Journal for Research in Mathematics Education,
vol. 27, no. 2, pp. 133–150.
Lerman, S. (2000) The Social Turn in Mathematics Education, in J. Boaler, (Ed.)
Multiple perspectives on Mathematics Teaching and Learning, International
Perspectives on Mathematics Education, Ablex, London, p20-44.
Li, S. (1999) ‘Does practice make perfect?’, For The Learning of Mathematics, vol.
(19, no. 3, pp. 33–35.
Li, S. (1999) Does Practice Make Perfect?, For The Learning of Mathematics (19
(3) p33-35.
Li, Y. and Dù, S. (1987) J. Crossley and A. Lun (Trans.) Chinese Mathematics: a
concise history, Clarendon Press, Oxford.
Locke, J. (1693) Conduct of Understanding, Quick Edition.
Love, E. and Mason, J. (1992) Teaching Mathematics: action and awareness,
Milton Keynes, The Open University.
Macgregor, M. (1991) Making Sense of Algebra: cognitive processes influencing
comprehension, Geelong, Deakin University.
MacGregor, M. and Stacey, K. (1993) Cognitive Models Underlying Students’
Formulation of Simple Linear Equations, Journal For Research In Mathematics
Education, 24 (3) p217-232.
Martino, A. and Maher, C. (1999) Teacher Questioning To Stimulate Justification
And Generalization In Mathematics: what research practice has taught us, Journal
of Mathematical Behavior, (18) 1, p53-78.
Marton, F. (1981) Phenomenography: describing conceptions of the world around
us, Instructional Science, 10, p177-200.
Marton, F. and Booth, S. (1997) Learning and Awareness, Mahwah, Lawrence
Erlbaum Associates.
Marton, F. and Saljo, R. (1976) On Qualitative Differences in Learning, British
Journal of Educational Psychology, 46, p4–11.
Mason J. (1998) Enabling teachers to be real teachers: necessary levels of
awareness and structure of attention, Journal of Mathematics Teacher Education,
1 (3) p243-267.
Mason J., Burton L. and Stacey K. (1982) Thinking Mathematically, London,
Addison Wesley.
Mason, J. & Johnston-Wilder, S. (eds) (2004) Fundamental Constructs of
Mathematics Education, London, RoutledgeFalmer.
Mason, J. & Johnston-Wilder, S. (2004) ‘Designing and using Mathematical Tasks’
ME825 Course book, Milton Keynes, The Open University.
Mason, J. (1979) ‘Which medium, which message’, Visual Education, Feb. (1979,
pp. 29–33.
Mason, J. (2001) ‘Mathematical teaching practices at tertiary level: Working
Group report’ in Holton, D. (ed.) The Teaching and Learning of Mathematics at
University Level: An ICMI Study, Dordrecht, Kluwer.
Mason, J. ‘Thinking mathematically with e-screens’ in Johnston-Wilder, S. and
Pimm D., (eds) (2004) Teaching Secondary Mathematics with Technology, Open
University Press, Buckingham.
Mason, J. (1979) Which Medium, Which message?, Visual Education Feb. p29-33.
Mason, J. (1980) When is a Symbol Symbolic? For the Learning of Mathematics
1(2) p8-12.
Mason, J. (1989) Mathematical Abstraction Seen as a Delicate Shift of Attention,
For the Learning of Mathematics 9 (2) p2-8.
Mason, J. (1989) ME234 Unit 3 Open University, Milton Keynes.
Mason, J. (1990) Supporting Primary Mathematics: Space and Shape, Open
University, Milton Keynes.
Mason, J. (1992) Doing and Construing Mathematics in Screen Space, in B.
Southwell, B. Perry, and K. Owens (eds) Space - The First and Final Frontier:
Proceedings of the Fifteenth Annual Conference of the Mathematics Education
Research Group of Australasia (MERGA-15) p1-17.
Mason, J. (1996) Expressing Generality and Roots of Algebra, in Berdnarz, N.
Kieran, C. and Lee, L.(eds) Approaches to Algebra: perspectives for research and
teaching, Kluwer, Dordrecht, p65-86.
Mason, J. (2001) Mathematical Teaching Practices At Tertiary level: Working
Group Report, in D. Holton (Ed.) The Teaching and Learning of Mathematics at
University Level: An ICMI Study, Kluwer, Dordrecht, p71-86.
Mason, J. (2001) Modelling Modelling: where is the centre of gravity of-for-when
modelling?, in J. Matos, W. Blum, S. Houston and S. Carreira (eds) Modelling and
Mathematics Education: ICTMA 9 applications in science and technology, Horwood
Publishing, Chichester, p39-61.
Mason, J. (2002) Mathematics Teaching Practice: a guide for university and
college lecturers, Horwood Publishing, Chichester.
Mason, J. (2002) Mathematics Teaching Practice: a guide for university and
college lecturers, Horwood Publishing, Chichester.
Mason, J. (2002) Researching Your Own Practice: The Discipline of Noticing,
RoutledgeFalmer, London.
Mason, J. (2002a) Generalisation and Algebra: exploiting children's powers, in L.
Haggerty (Ed.) Aspects of Teaching Secondary Mathematics: perspectives on
practice, RoutledgeFalmer, London, p105-120.
Mason, J. (2002b) Minding Your Qs and Rs: effective questioning and responding
in the mathematics classroom, in L. Haggerty (Ed.) Aspects of Teaching
Secondary Mathematics: perspectives on practice, RoutledgeFalmer, London,
p248-258.
Mason, J. (2002c) Researching Your Own Practice: the discipline of noticing,
RoutledgeFalmer, London.
Mason, J. and Houssart, J. (2000) ‘Arithmogons: a case study in locating the
mathematics in tasks’, Primary Teaching Studies, vol. 11, no. 2, pp. 34–42.
Mason, J., Burton, L. and Stacey, K. (1982) Thinking Mathematically, London,
Addison Wesley.
Mathematical Association (1987) Maths Talk, Cheltenham, Stanley Thornes.
Maturana, H. (1978) Biology of Language: the epistemology of reality. In G. Miller
and E. Lenneberg, (eds) Psychology and Biology of Language and Thought:
essays in honor of Eric Lunneberg, Academic Press: New York. p27-63.
Maturana, H. and Varela, F. (1988) The Tree of Knowledge: the biological roots of
human understanding, Boston, Shambala.
Maturana, H. and Varela, F. (1988) The Tree of Knowledge: the biological roots of
human understanding, Shambala, Boston.
Maturana, H. webref, www.hum.auc.dk/~rasand/Artikler/M78BoL.html
McCague, W. (2003) A Mathematical Look at a Medieval Cathedral, Math
Horizons, April, pp. 11-15 and p. 31. See also www.maa.org.
McIntosh, A. (1977) When Will They Ever Learn? Forum (19 (3) p92-95.
Mcintosh, A. and Quadling, D. (1975) ‘Arithmogons’, Mathematics Teaching, no.
70, pp. 18–23.
Mehan, H. (1986) ‘“What time is it Denise?”: asking information questions in
classroom discourse’ in Hammersley, M. (ed.) Case Studies in Classroom
Research, Buckingham, Open University Press, pp. 85–103.
Meira, L. (1998) Making Sense of Instructional Devices: the emergence of
transparency in mathematical activity, Journal For Research In Mathematics
Education 29 (2) p121-142.
Mellin-Olsen, S. (1987) The Politics of Mathematics Education, Dordrecht, Reidel.
Mellin-Olsen, S. (1987) The Politics of Mathematics Education, Reidel, Dordrecht.
Merseth, K. (1993) How Old Is the Shepherd?: an essay about mathematics
education, Phi Delta Kappan, vol. 74 (March (1993) p548-554.
Merseth, K. webref, How Old Is the Shepherd?: an essay about mathematics
education, lsc-net.terc.edu/do.cfm/paper/8198/show/use_set-papers_pres
Michener, E. (1978) Understanding Understanding Mathematics, Cognitive science
2 p361-383.
Monroe, P. (1909) A Text-Book in the History of Education, MacMillan, New York.
Montaigne, M. de (1588) M. Screech (Trans.) (1987. Michel de Montaigne: the
complete essays, Penguin, London.
Montessori, M. (1912) A. George (Trans.) reprinted (1964) The Montessori
Method, Schocken Books, New York.
Morris R. (Ed.) (1989) Studies In Mathematics Education: the teaching of
statistics, Unesco, Paris
Moshovits-Hadar, N. (1988) Surprise, For the Learning Of Mathematics, 8 (3)
p34–40.
Movshovits-Hadar, N. (1988) ‘Surprise’, For the Learning of Mathematics, vol. 8,
no. 3, pp. 34–40.
Nesher, P. (1987) Towards an Instructional Theory: the role of student's
misconceptions, For the Learning of Mathematics 7 (3) : p33 - 40.
Nesher, P. and Winograd, T. (1992) What Fifth Graders Learn When They Write
Their Own Math Problems. Educational Leadership, 49 (7) 64-67.
Nesher, P. webref, Towards an Instructional Theory: the role of student's
misconceptions construct.haifa.ac.il/~nesherp/Public.ht.
Newman, J. (1956) The World of Mathematics: a small library of the literature of
mathematics from A’h-mosé the scribe to Albert Einstein, presented with
commentaries and notes (four vols.) Simon and Schuster, New York.
Nicholls, J. (1983) Conceptions of ability and achievement motivation: a theory
and its implications for education, in S. Paris, G. Olson and W. Stevenson (eds)
Learning and Motivation in the Classroom, Erlbaum, Mahwah.
Nickson, M. (2000) Teaching and Learning Mathematics: a teacher’s guide to
recent research and its application, Cassell Education, Cassell, London.
Nickson, M. (2000) Teaching and Learning Mathematics: a teacher’s guide to
recent research and its application, Cassell Education, Cassell, London.
Nolder, R. (1992) Bringing Teachers to the Centre of the Stage: A Study of
Secondary Teachers’ Responses to Curriculum Change in Mathematics,
Unpublished Ph.D. thesis, University of London, London.
Northfield, J. and Baird, J. (1992) Learning from the PEEL Experience, Monash
University Printing Service, Melbourne.
Nunes T. (1999) Mathematics Learning As The Socialization Of The Mind, Mind,
Culture, and Activity, 6(1) 33-52.
Nunes, T. webref, How Mathematics Teaching Develops Pupils’ Reasoning
Systems, Inaugural Lecture,
www.brookes.ac.uk/schools/social/psych/staff/tnicme2000/sld060.htm
Nunes, T., Schliemann, A. and Carraher, D. (1993) Mathematics in the Streets
and in Schools, Cambridge University Press, Cambridge.
Nunes, T., Schliemann, A. D. and Carraher, D.W. (1993) Street Mathematics and
School Mathematics, New York, Cambridge University Press.
Ollerton, M. and Watson, A. (2001) Inclusive Mathematics: 11-18, Sage, London.
Ollerton, M., (2002) Learning and Teaching Mathematics without a Textbook,
Association of Teachers of Mathematics, Derby.
Open University, (1978) M101 Mathematics Foundation Course, Block V Unit 1
p31, Milton Keynes.
Orage, A. (1966) (4th edn.) On Love: with some aphorisms and other essays,
Samuel Weiser, New York.
Paley, V. (1981) Wally’s Stories, Harvard University Press, Cambridge, MA.
Papert, S. (1980) Mind Storms, Basic Books, New York.
Papert, S. (1993) The Children's Machine: rethinking school in the age of the
computer, Basic Books, New York reproduced at
www.stemnet.nf.ca/~elmurphy/emurphy/papert.html
Papy, G. (1963) Modern Mathematics Vol. 1, Collier-Macmillan, London.
Peirce, C.S. (1902) The Essence of Mathematics, (reprinted (1956) in J. R.
Newman (Ed.) The World of Mathematics, Simon and Schuster, New York p1779.
Phillips, E and Crespo, S. (1996) ‘Developing written communication in
mathematics through math penpal letters’, For the Learning of Mathematics,
16(1) p. 15-22.
Piaget, J. (1950) The Psychology of Intelligence, London, Routledge and Kegan
Paul.
Piaget, J. (1971) Biology and Knowledge, Chicago, University of Chicago Press.
Piaget, J. (1972) (trans. Mays, W.) Principles of Genetic Epistemology, London,
Routledge and Kegan Paul.
Piaget, J. (1977) (Rosen, A., trans.) The Development of Thought: equilibration of
cognitive structures, New York, Viking.
Piaget, J. (1952) ‘Jean Piaget’, in Boring, Edwin et al. (eds) A History of
Psychology in Autobiography, Vol. IV, Clark University Press, Worcester, MA, pp.
237-256.
Piaget, J. (1970) Genetic Epistemology, Norton, New York.
Piaget, J. (1971) Biology and Knowledge: an essay on the relations between
organic regulations and cognitive processes, University of Chicago Press, Chicago.
(originally published in French (1963)
Piaget, J. (1972) The Principles of Genetic Epistemology (W. Mays Trans.)
Routledge and Kegan Paul, London.
Piaget, J. (1973) To Understand Is To Invent: the future of education, Grossman,
New York. (originally published in French (1948) .
Piaget, J. (1980) Adaptation and Intelligence: organic selection and phenocopy,
University of Chicago Press, Chicago. (originally published in French (1974)
Piaget, J. and Garcia, R. (1988) Psychogenesis And The History Of Science, by H.
Feider (Trans.) Columbia University Press, New York.
Pirie, S. and Kieren, T. (1989) ‘A recursive theory of mathematical
understanding’, For the Learning of Mathematics, vol. 9, no. 4, pp. 7–11.
Pirie, S. and Kieren, T. (1994) ‘Growth in mathematical understanding: how can
we characterise it and how can we represent it?’, Educational Studies in
Mathematics, vol. 26, no. 2–3, pp. 165–190.
Pirie, S. and Kieren, T. (1989) A Recursive Theory of Mathematical
Understanding, For the learning of Mathematics, 9 (3) p7-11.
Pirie, S. and Kieren, T. (1994) Growth in Mathematical Understanding: how can
we characterise it and how can we represent it? Educational Studies in
Mathematics, 26 (2-3) p165-190.
Pirie, S. E. B. and Schwarzenberger, R. L. E. (1988) ‘Mathematical discussion and
mathematical understanding’, Educational Studies in Mathematics, vol. 4, no. (19,
pp. 459–470.
Plowden, B. (1967) The Plowden Report: children and their primary schools,
HMSO, London.
Polanyi, M. (1958) Personal Knowledge, Routledge and Kegan Paul, London.
Pollard, A and Triggs, P. with Broadfoot, P, McNess, E. and Osborn, M (2000)
Changing Policy and Practice in Primary Education, Continuum, London.
Polya, G. (1954) Induction and Analogy, Princeton University Press, Princeton.
Polya, G. (1957) How to Solve it, Anchor, New York.
Polya, G. (1962) Mathematical Discovery: On understanding, learning, and
teaching problem solving (combined edition) Wiley, New York.
Pramling, I. (1994) Becoming able: testing a phenomenographic approach to
develop children’s ways of conceiving the world around us,
www.ped.gu.se/biorn/phgraph/civil/graphica/oth.su/praml94.html
Prestage, S. & Perks, P. (1992) Making Choices (part 1) Making Choices Explicit,
Mathematics in School 21 (3) pp. 46-48.
Prestage, S. & Perks, P. (1992) Making Choices (part 2) “... not if you’re a Bear”,
Mathematics in Schools, 21 (4) pp. 10-11.
Prestage, S. & Perks, P. (1992) Making Choices (part 3) Choices, Constraints &
Control, Mathematics in School 21 (5) p. 44-45.
Prestage, S. and Perks, P. (1992) ‘Making choices (part 2) : “... not if you’re a
bear”’, Mathematics in Schools, vol. 21, no. 4, pp. 10–11.
Raymond, L. (1972) To Live Within, London, George Allen and Unwin.
Renkl, A., Mandl, H. and Gruber, H. (1996) Inert Knowledge: analyses and
remedies, Educational Psychologist, 31 (2) p115-121.
Rg Veda, Samhita 1.164.20.
Rowland, T. (1999) ‘Pronouns in Mathematics Talk: Power, Vagueness and
Generalisation’ For the Learning of Mathematics (19, 2.
Rudduck, J., Chaplain, R., & Wallace, G. (1995) School Improvement. What Can
Pupils Tell Us? David Fulton Publishers Ltd., London.
Runesson, U. (1999) The Pedagogy of Variation: different ways of handling a
mathematical topic. Acta Univertsitatis Gothoburgensis. Göteborg:,University of
Göteborg.
Runesson, U. (2001) What matters in the mathematics Classroom? Exploring
critical differences in the space of learning. in C. Bergsten (Ed.) Proceedings of
NORMA01, Kristianstad.
Russell, B. (1926) On Education, George Allen and Unwin, London
Sáenz-Ludlow, A. and Walgamuth, C. (2001) ‘Question- and diagram-mediated
mathematical activity: a case in a fourth grade classroom’, Focus on Learning
Problems in Mathematics, vol. 23, no. 4, pp. 27–40.
Schmidt, W. H. (ed.) (1996) Characterizing Pedagogical Flow: an investigation of
mathematics and science teaching in six countries, Dordrecht, Kluwer.
Schoenfeld, A. (1985) Mathematical Problem Solving, Academic Press, New York.
Schoenfeld, A. (1987) Confessions of an Accidental Theorist, For the Learning of
Mathematics; 7 91) p30-38.
Searle, J. (1987) Minds and Brains Without Programs, in C. Blakemore and S.
Greenfield (eds) Mindwaves: thoughts on intelligence, identity and consciousness,
Blackwell, Oxford, p209-233.
Selden, A. and Selden, J. webref, Constructivism,
www.maa.org/t_and_l/sampler/construct.html.
Sfard, A. (1994) ‘Reification as the birth of metaphor’, For the Learning of
Mathematics, vol. 14, no. 1, pp. 44–55.
Sfard, A. (1991) On the Dual Nature of Mathematical Conceptions: Reflections on
processes and objects as different sides of the same coin, Educational Studies in
Mathematics, 22, p1–36.
Sfard, A. (1992) Operational origins of mathematical notions and the quandry of
reification: the case of function, in E. Dubinsky and G. Harel (eds) The Concept of
Function: aspects of epistemology and pedagogy, Mathematical Association of
America, Washington.
Sfard, A. (1994) The Gains and Pitfalls of Reification: the case of algebra,
Educational Studies in Mathematics, 26 p191-228.
Sfard, A. (1994a) Reification as the Birth of Metaphor, For the Learning of
Mathematics, 14 (1) p44–55.
Sfard, A., Nesher, P., Streefland, L., Cobb, P. and Mason, J. (1998) ‘Learning
mathematics through conversation: is it as good as they say?’, For the Learning
of Mathematics, vol. 18, no. 1, pp. 41–51.
Shiu, C. (1978) The Development of Some Mathematical Concepts in School
Children, unpublished Ph.D. thesis, University of Nottingham.
Shuard, H., Walsh, A., Goodwin, J. and Worcester, V. (1991) Calculators, Children
and Mathematics, Simon and Shuster, London
Shulman, L. (1987) Knowledge and teaching: foundations of the new reform,
Harvard Educational Review 57 (1) p1-14.
Shulman, L. webref, President of the Foundation: Lee Shulman,
www.carnegiefoundation.org/president/biography.htm
Sierpinska, A. (1994) Understanding in Mathematics, London, Falmer Press.
Sierpinska, A. (1994) Understanding in Mathematics, Falmer Press, London.
Skemp, R. (1976) ‘Relational understanding and instrumental understanding’,
Mathematics Teaching, no. 77 (December) pp. 20–26.
Skemp, R. (1979) Intelligence, Learning and Action, Chichester, Wiley.
Skemp, R. (1966) The Development of Mathematical Activity in Schoolchildren,,
in W. Brookes (Ed.) The Development of Mathematical Activity in Children: the
place of the problem in this development, ATM, Nelson, p76-78.
Skemp, R. (1971) The Psychology of Learning Mathematics, Penguin,
Harmondsworth.
Skemp, R. (1976) Relational Understanding and Instrumental Understanding.
Mathematics Teaching, 77, 20-26.
Skemp, R. (1979) Intelligence, Learning, and Action: a foundation for theory and
practice in education, Chichester, Wiley.
Skvovemose, O. (1994) Towards a Philosophy of Critical Mathematics Education,
Dordrecht, Kluwer.
Smith, A. (2004) Making Mathematics Count, the Report of Professor Adrian
Smith's Inquiry into Post-14 Mathematics Education, The Stationery Office,
London.
Smith, T. (1954) Number: an account of work in number with children throughout
the primary school stage, Basil Blackwell, Oxford.
Snyder, B. (1970) The Hidden Curriculum, New York, Alfred-Knopff.
Snyder, B. (1971) The Hidden Curriculum, Alfred-Knopff, New York.
Spencer, H. (1929) Education: intellectual, moral, and physical, Thinker’s Library
No. 2, London, Watts.
Spencer, H. (1878) Education: intellectual, moral, and physical, Williams and
Norgate, London.
Steffe, L. (1991) ‘The constructivist teaching experiment: illustrations and
implications’, in von Glasersfeld, Ernst (Ed.) Radical Constructivism in
Mathematics Education, Kluwer, Dordrecht, pp. 177-194.
Steffe, L. and Gale, J. (1995) Constructivism in Education, Erlbaum, Mahwah.
Steffe, L., Cobb, P. & Von Glasersfeld, E. (1988) Construction of arithmetical
meanings and strategies, Springer-Verlag, New York.
Steffe, L., Nesher, P., Cobb, P., Goldin, G. and Greer, B. (1996) Theories of
Mathematical Learning, Erlbaum, Mahwah.
Steffe, L., von Glasersfeld, E., Richards, J. and Cobb, P. (1983) Children’s
Counting Types: philosophy, theory, and application, New York, Praeger
Scientific.
Stein, S. (1987) ‘Gresham’s law: algorithm drives out thought’, For the Learning
of Mathematics, vol. 7, no. 2, pp. 2–4.
Stein, S. (1987) Gresham’s law: algorithm drives out thought, For The Learning
of Mathematics, 7 (2) p2-4.
Stigler J. and Hiebert, J. (1999) The Teaching Gap: best ideas from the world’s
teachers for improving education in the classroom, Free Press, New York.
Stigler, J. and Hiebert, J. (1999) The Teaching Gap: best ideas from the world’s
teachers for improving education in the classroom, New York, Free Press.
Stigler, J. and Hiebert, J. (1998) Teaching is a Cultural Activity, American
Educator, p4-11.
Streefland, L. (Ed.) (1991) Realistic Mathematics Education in Primary School,
CD-B Press/Freudenthal Institute, Utrecht, p63
Tahta, D. (1972) A Boolean Anthology: selected writings of Mary Boole on
mathematics education, Derby, Association of Teachers of Mathematics.
Tahta, D. (1981) ‘Some thoughts arising from the new Nicolet films’, Mathematics
Teaching, no. 94, pp. 25–29.
Tahta, D. (1991) ‘Understanding and Desire’ in Pimm, D. and Love, E. (eds)
Teaching and Learning School Mathematics, pp. 220–246, London, Hodder and
Stoughton.
Tahta, D. (1972) A Boolean Anthology: selected writings of Mary Boole on
mathematics education, Association of Teachers of Mathematics, Derby.
Tahta, D. (1981) Some Thoughts Arising From The New Nicolet Films,
Mathematics Teaching 94 p 25-29.
Tahta, D. (1991) Understanding and Desire, in D. Pimm and E. Love (eds)
Teaching and Learning School Mathematics, Hodder and Stoughton, London,
p220-246.
Tahta, D. and Brookes, W. (1966) The Genesis of Mathematical Activity, in W.
Brookes (Ed.) The Development of Mathematical Activity in Children: the place of
the problem in this development, ATM, Nelson, p3-8.
Tahta, D., (1980)About Geometry, For the Learning of Mathematics 1 p2-9
Tall, D. and Vinner, S. (1981) ‘Concept image and concept definition in
mathematics with particular reference to limits and continuity’, Educational
Studies in Mathematics, vol. 12, no. 2, pp. 151–169.
Tall, D. and Vinner, S. webref, Concept Image and Concept Definition,
www.warwick.ac.uk/staff/David.Tall/themes/concept-image.html
Tall, D. and Vinner, S. (1981) Concept Image and Concept Definition in
Mathematics with Particular Reference to Limits and Continuity, Educational
Studies in Mathematics, 12(2) p151-169, also published on the web at
www.warwick.ac.uk/staff/David.Tall/pdfs/dot1988e-concept-image-icme.pdf
Taylor, C. (1991) The Dialogical self in D. Hiley, J. Bohman and R. Shusterman
(eds) The Interpretive Turn: philosophy, science, culture, Cornell University
press, Ithaca.
Teplow, D. webref, Fresh Approaches: promoting teaching excellence,
www.acme-assn.org/almanac/jan97.htm.
The Open University (1980) PME233: Real Problem Solving, Milton Keynes, The
Open University,
The Open University, (2001) Research Methods in Educaton, Milton Keynes. The
Open University.
Theory Into Practice website http://tip.psychology.org/ (or at
Thom, A. (1967) Megalithic Sites in Britain, Oxford University Press, Oxford.
Thompson, P. and Thompson, A. (1990) Salient Aspects of Experience with
Concrete Manipulatives, in G. Booker, P. Cobb, and T de Mendicuti (eds)
Proceedings of PME XIV, Oaxtepec, Mexico, p46-52.
Thompson, P. and Thompson, A. (1990) Salient Aspects of Experience with
Concrete Manipulatives, in G. Booker, P. Cobb, and T de Mendicuti (eds)
Proceedings of PME XIV, Oaxtepec, Mexico, p. 46-52.
Thorndike, E. (1922) The Psychology of Arithmetic, Macmillan, New York.
Thurston, W. (1994) ‘Proof and progress in mathematics’, Bulletin of the
American Mathematical Society, vol. 30, no. 7, pp. 161–177; reprinted in For the
Learning of Mathematics, vol. 15, no. 1, (1995) pp. 29–37.
Thurston, W. (1990) Mathematical Education, Notices of the American
Mathematical Society, 37, p844-850; reprinted in For The Learning of
Mathematics, 15 (1) (February (1995) p29-37.
TIMSS (1997) Mathematics Achievement in the Primary School Years. Boston
College, Chestnut Hill, MA.
Tizard, B. and Hughes, M. (1984) Young Children Learning: talking and thinking
at home and at school, Fontana, London.
Treffers, A. (1986) Three Dimensions A Model of Goal and Theory Description in
Mathematics Instruction - The Wiskobas Project, Kluwer, Dordrecht.
Turing, A. (1950) Computing Machinery and Intelligence, Mind: a quarterly review
of philosophy and psychology, 59 (236) p433-460.
Tversky, A. and Kaheneman D. (1982) Judgement Under Uncertainty: heuristics
and biases, in D. Kahneman, P. Slovic, A. and Tversky, (eds) Judgement Under
Uncertainty: Heuristics and Biases, Cambridge University Press, Cambridge p320.
Ulich, R. (Ed.) (1999) Three Thousand years of Educational Wisdom: selections
from the great documents, Harvard University Press, London.
van den Brink, J. (1993) Different Aspects in Designing Mathematics Education:
three examples from the Freudenthal Institute, Educational Studies in
Mathematics. 24 (1) p35-64.
van Hiele, P. (1986) Structure and Insight: a theory of mathematics education,
Orlando, Academic Press.
van Hiele, P. (1986) Structure and Insight: a theory of mathematics education,
Academic Press, Orlando.
van Hiele-Geldof, D. (1957) The Didactiques of Geometry in the Lowest Class of
Secondary School, reprinted in D. Fuys, D. Geddes and R. Tichler (eds) (1984)
English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M.
van Hiele, National Science Foundation, Brooklyn College.
van Lehn, K. (1990) Mind Bugs: the origins of procedural misconceptions,
Bradford Book, MIT press, Cambridge.
van Maanen, J. (Ed.) (1977) Organizational Careers: some new perspectives,
Wiley, London.
Vergnaud, G. (1983) ‘Multiplicative structures’ in Lesh, R. and Landau, M. (eds)
Acquisition of Mathematics Concepts and Structures, pp. 127–174, New York,
Academic Press.
Vergnaud, G. (1981) Quelques Orientations Théoriques et Méthodologiques des
Recherches Françaises en Didactique des Mathématiques, Actes duVième
Colloque de PME, vol 2 p7-17, Grenoble: Edition IMAG.
Vergnaud, G. (1982) A Classification of Cognitive Tasks and Operations of
Thought Involved in Addition and Subtraction Problems, in T. Carpenter, J. Moser
and T. Romberg (eds) Addition and Subtraction: a cognitive perspective, Erlbaum,
Mahwah p39-59.
Vergnaud, G. (1982a) Cognitive Developmental Psychology and Research in
Mathematics Education: some theoretical and methodological issues, For The
Learning of Mathematics, 3 (2) p31-41.
Vergnaud, G. (1983) Multiplicative Structures in R. Lesh and M. Landau (eds)
Acquisition of Mathematics Concepts and Structures, Academic Press, New York,
p127-174.
Vico G-B. (1744) The New Science, (T. Bergin and M. Fisch Trans. (1961) Anchor
Books, New York.
Voight, J. (1985) Patterns and Routines in Classroom Interaction, Recherches en
Didactiques des Mathématiques, 6 (9) p69-118.
von Glasersfeld E. (1983) Learning as a Constructive Activity, In PME-NA
Proceedings, Montreal, (1983) p41-69.
von Glasersfeld, E. (1984) An Introduction to Radical Constructivism, in P.
Watzlawick, (Ed.) The Invented Reality, Norton, London, p17-40.
von Glasersfeld, E. (1995) Radical Constructivism: a way of knowing and
learning, London, Falmer Press.
von Glasersfeld, E. (1985) Reconstructing the Concept of Knowledge, Archives de
Psychologie 53 p91-101.
von Glasersfeld, E. (1991) Abstraction, Re-presentation, and Reflection in L.
Steffe (Ed.) Epistemological Foundations of Mathematical Experience, Springer,
New York, p45-67.
von Glasersfeld, E. (1996) Learning and Adaptation in Constructivism, in L.
Smith, (Ed.) Critical Readings on Piaget, Routledge, London, p22-27.
Vygotsky L. (1978) Mind in Society: the development of the higher psychological
processes, Harvard University Press, London.
Vygotsky, L. (1934/1986) Thought and Language, Cambridge, MIT Press.
Vygotsky, L. (1978) Mind in Society: the development of the higher psychological
processes, London, Harvard University Press.
Vygotsky, L. (1962) Thought and Language, M.I.T. Press, Cambridge.
Vygotsky, L. (1965) E. Hanfmann and G. Vakar (Trans.) Thought and Language,
MIT Press, Cambridge.
Vygotsky, L. (1979) The Genesis of Higher Mental Functions, in J. Wertsch
(Trans., Ed.) The Concept of Activity in Soviet Psychology, Sharpe, New York,
p144-188.
Walkerdine, V. (1988) The Mastery of Reason, London, Routledge and Kegan
Paul.
Warden, J. (1981) Making Space For Doing And Talking With Groups In A Primary
Classroom, in A. Floyd (Ed.) Developing Mathematical Thinking, Addison Wesley,
London, p248-257.
Warfield, V. webref, Calculus By Scientific Debate As An Application Of
Didactique, Department of Mathematics University of Washington on
www.math.washington.edu/~warfield/articles/Calc&Didactique.html
Watson A. and Mason, J. (2002) Student-Generated Examples in the Learning of
Mathematics, Canadian Journal of Science, Mathematics and Technology
Education, 2 (2) p. 237-249.
Watson, A. (2000) ‘Going across the grain: mathematical generalisation in a
group of low attainers’, Nordisk Matematikk Didaktikk (Nordic Studies in
Mathematics Education) vol. 8, no. 1, pp. 7–22.
Watson, A. (2002) ‘Instances of mathematical thinking among low attaining
students in an ordinary secondary classroom’, Journal of Mathematical Behaviour,
vol. 4, no. 20, pp. 461–475.
Watson, A. (2001) Low Attainers Exhibiting Higher-Order Mathematical Thinking,
Support for Learning 16 (4) Nov p179-183.
Watson, A. (2002) Working with Students On Questioning To Promote
Mathematical Thinking, Mathematics Education Review 15 p32-42.
Watson, A. (2003) 'Affordances, constraints and attunements in mathematical
activity' in Williams, J. (Ed.) Proceedings of the British Society for Research into
Learning Mathematics, Vol. 23, No. 2, Oxford, Oxford University, p. 103-108.
Watson, A. and Mason, J. (1998) Questions and Prompts for Mathematical
Thinking, Derby, Association of Teachers of Mathematics.
Watson, A. and Mason, J. (2002) ‘Student-generated examples in the learning of
mathematics’, Canadian Journal of Science, Mathematics and Technology
Education, vol. 2, no. 2, pp. 237–249.
Watson, A. and Mason, J. (1998) Questions and Prompts for Mathematical
Thinking, ATM, Derby.
Waywood A. (1992) Journal Writing and Learning Mathematics, For the Learning
of Mathematics 12 (2) p. 34-43.
Waywood, A. (1992) Journal Writing And Learning Mathematics, For the Learning
of Mathematics 12 (2) p34-43.
Waywood, A. (1994) Informal Writing-to-Learn as a Dimension of a Student
Profile. Educational Studies in Mathematics, 27, p321-340.
Waywood, A. (1994) Informal Writing-to-Learn as a Dimension of a Student
Profile. Educational Studies in Mathematics, 27, p. 321-340.
Wertheimer, M. (1961) Productive Thinking, enlarged edition, M. Wertheimer
(Ed.) Social Science Paperbacks with Tavistock Publications, London.
Wertsch, J. (ed.) (1981) The Concept of Activity in Soviet Psychology, Sharpe,
Armonk.
Wertsch, J. (1991) Voices of the Mind: a sociocultural approach to meditated
action, Harvard University Press, Cambridge.
Wheatley, G. (1992) The Role of Reflection in Mathematics Learning, Educational
Studies in Mathematics, 23 (5) p529-541.
Wheatley, G. webref, Quick Draw: a simple warm-up exercise helps students
develop mental imagery of mathematics.
www.learnnc.org/index.nsf/doc/quickdraw
Wheeler, D. (1965) Teaching for Understanding, Mathematics Teaching 33, p4750.
Wheeler, D. (1982) Mathematization Matters, For the Learning of Mathematics, 3
(1) p45-47.
Whitehead, A. (1919) (12th impression, reprinted (1948) An Introduction to
Mathematics, London, Oxford University Press.
Whitehead, A. (1911) (reset (1948) An Introduction to Mathematics, Oxford
University Press, London.
Whitehead, A. (1932) The Aims of Education and Other Essays, Williams and
Norgate, London.
Whiteside, D. (1968) The Mathematical Papers of Isaac Newton Volume II 16671670, Cambridge University Press, Cambridge.
Wigner E. webref, The Unreasonable Effectiveness of Mathematics in the Natural
Sciences, www-history.mcs.st-andrews.ac.uk/history/Quotations/Wigner.html
Wigner, E. (1960) The Unreasonable Effectiveness of Mathematics in the Natural
Sciences, Comm. Pure Appl. Math., 13, p1-14.
Winograd, T. and Flores, F. (1986) Understanding Computers and Cognition: a
new foundation for design, Ablex, Norwood.
Wood, D. and Middleton, D. (1975) A Study of Assisted Problem-Solving, British
Journal of Psychology, 66 (2) p181-191.
Wood, D., Bruner, J. and Ross, G. (1976) The Role of Tutoring in Problem
Solving, J. Child Psychology, 17, p89-100.
Wood, P., Bruner, J. and Ross, G. (1976) ‘The role of tutoring in problem solving’,
Journal of Child Psychology and Psychiatry, vol. 2, no. 17, pp. 89–100.
Yackel, E. (2001) Perspectives On Arithmetic From Classroom-Based Research In
The United States Of America in J. Anghileri (Ed.) Principles And Practices In
Arithmetic Teaching, Open University Press, Buckingham, p15-31.
Zaehner, R. (Trans.) (1966) Hindu Scriptures, Dent and Sons, New York.
Zammattio, C. Marinoni, A. and Brizio, A. (1980) Leonardo The Scientist,
McGraw-Hill, New York.
Zeichner, K. and Liston, D. (1987) Teaching Student Teachers to Reflect, Harvard
Educational Review, 57 (1) p23-48.
Zeichner, K. and Liston, D. (1996) Reflective Teaching, Erlbaum, Mahwah