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Acevedo, M., de Losada, M.F.: Recorriendo el Algebra: de la solución de ecuaciones al álgebra abstracta. Universidad Nacional de Colombia, Colciencias, Bogotá (1997)
Acevedo, M., de Losada, M.F.: Formación del pensamiento algebraico de los docentes. Revista Latinoamericana de Investigación en Matemática Educativa 3, pp. 245–264 (2000)
Anthony, G., Walshaw, M.: Best Evidence Synthesis: Effective Pedagogy in Pangarau/ Mathematics. Ministry of Education, Wellington (2007) www.educationcounts.govt.nz/themes/BES. Accessed 15 January 2009
Artzt, A.F., Armour-Thomas, E.: Becoming a reflective mathematics teacher. Lawrence Erlbaum, Mahwah, NJ (2002)
Atkinson, T., Claxton, G. (eds.): The intuitive practitioner: On the value of not always knowing what one is doing. Open University Press, Philadelphia, PA (2000)
Ball, D.: Teaching mathematics for understanding: What do teachers need to know about the subject matter? In: Kennedy M. (ed.) Teaching Academic Subjects Diverse Learners, pp. 63–83. Teachers College, New York (1992)
Ball, D., Cohen, D.: Developing practice, developing practitioners. In: Darling-Hammond, L., Sykes, G. (eds.) Teaching as the learning profession: Handbook of policy and practice. 1st edn. Jossey Bass, San Francisco, CA (1999)
Bicknell, B., Anthony, G.: Thoughtful practice: Taking professional development a step further. Teachers and Curriculum 7, pp. 33–37 (2004)
Blanton, M. L.: Using an undergraduate geometry course to challenge pre-service teachers’ notions of discourse. Journal of Mathematics Teacher Education 5, 2, pp. 117–152 (2002)
Boaler, J., Wiliam, D., Brown, M.: Students’ experiences of ability grouping: Disaffection, polarisation and the construction of failure. British Educational Research Journal 26, pp. 631–648 (2000)
Brousseau, G.: Theory of didactical situations in mathematics. Kluwer Academic Publishers, Dordrecht, The Netherlands (1997)
Brown, M., Askew, M., Baker, D., Denvir, H., Millet, A.: Is the national numeracy strategy research-based? British Journal of Educational Studies 46, 4, 362–385 (1998)
Brown, S., Cooney, T., Jones, D.: Mathematical Teacher Education. In: Houston, W.R. (ed.), Handbook of Research on Teacher Education, pp. 639–656. Macmillan, New York (1990)
Chambers, D.L., Hankes, J.E.: Using knowledge of children’s thinking to change teaching. In: Aichele, D.B., Coxford, A.F. (eds.) Professional development for teachers of mathematics, pp. 286–295. National Council of Teachers of Mathematics, Reston, VA (1994)
Clarke, B. A., Clarke, D.M.: Painting a picture of challenging, supportive, and effective classrooms. In: Rubenstein, R., Bright, G. (eds.) Perspectives on the Teaching of Mathematics, pp. 67–81. National Council of Mathematics Teachers, Reston, VA (2004)
Cobb, P., Wood, T., Yackel, E.: Classrooms as learning environments for teachers and researchers. In: Davis, R., Maher, C., Noddings, N.: Constructivist Views on the Teaching and Learning of Mathematics 4, pp. 125–146. National Council of Mathematics Teachers, Reston, VA (1990)
Cooney, T.J.: Considering the paradoxes, perils, and purposes of conceptualizing teacher development. In: Lin, F.L., Cooney, T.J. (eds.) Making Sense of Mathematics Teacher Education, pp. 9–31. Kluwer Academic Publishers, Dordrecht, The Netherlands (2001)
Cooney, T. J., Krainer, K.: Inservice mathematics teacher education: The importance of listening. In: Bishop, A.J., Clements, K., Keitel, C., Kilpatrick, J., Laborde, C. (eds.) International Handbook of Mathematics Education, pp. 1155–1185. Kluwer Academic Publishers, Dordrecht, The Netherlands (1996)
Davydov, V. V.: Theory of Developing Education (in Russian). Intor, Moscow (1996)
DeLacy, M.: The ‘No Child’ law’s biggest victims? An answer that may surprise. Education Week 23, 41, p. 40 (23 June, 2004)
Ell, F., Higgins, J., Irwin, K.C., Thomas, G., Trinick, T., Young-Loveridge, J. (eds.): Findings from the New Zealand Numeracy Development Projects 2005. Learning Media Ltd, Wellington (2006)
English, L. (ed.): Mathematical Reasoning: Analogies, Metaphors and Images. Lawrence Erlbaum, Mahwah, NJ (1997)
Fischbein, E.: Intuition in Science and Mathematics. An Educational Approach. Kluwer Academic Publishers, Norwell, MA (1987)
Franks, D., Tuncali, M.: Building a relationship between undergraduate mathematics and mathematics teacher education: Innovation in Teacher Education. The Mathematics Education into the 21st Century Project, Pol. Tezniami, Ciechocinek, Poland (2004)
Frase, L.E.: Maximizing People Power in Schools: Motivating and Managing Teachers and Staff. Corwin Press, Inc, Newbury Park, CA (1992)
Freiman, V., Vézina, N.: Challenging virtual mathematics environments: The case of the CAMI project. Submitted paper, ICMI Study 16 (2006)
Freiman, V., Vézina, N., Langlais, M.: Le Chantier d’Apprentissages Mathématiques Interactifs (CAMI) accompagne la réforme au Nouveau-Brunswick: Revue: Mathématique virtuelle à l’attention du primaire, disponible en ligne (2005a) spip.cslaval.qc.ca/mathvip/rubrique.php3?id_rubrique=18. Accessed 24 December 2007
Freiman, V., Vézina, N., Gandaho, I.: New Brunswick pre-service teachers communicate with schoolchildren about mathematical problems: CAMI project. Zentralblatt für Didaktik der Mathematik 37, 3, pp. 178–190 (2005b)
Garden, R. (ed.): Mathematics and science performance in the middle primary school: Results from New Zealand’s participation in the Third International Mathematics and Science Study. Research and International Section, Ministry of Education, Wellington (1997)
Gavin, M.K., Sheffield, L.J., Chapin, S., Dailey, J.: Project M3: Mentoring Mathematical Minds (Series of 12 curriculum units). Kendall Hunt, Dubuque, IA (2006, 2007, and 2008) www.projectm3.org (2006). Accessed 22 December 2007
Grozdev, S.: The Dirichlet Principle. In: Makrides, G. (ed.) MATHEU: Identification, Motivation, and Support of Mathematical Talents in European Schools. European Comenius Project (2006)
Grugnetti, L., Jaquet, F.: The transalpine mathematics rally in primary and lower secondary school: A problem-solving and a maths education experience. Submitted paper, ICMI Study 16 (2006)
Gu, L.Y., Yang, Y.: Emphasis on methodology as basis of studies in mathematics education. Journal of Mathematics Education 13, 4, pp. 1–4 (2004)
Hadamard, J.S.: The Psychology of Invention in the mathematical field. Dover, New York (1945)
Hardy, G.H.: A Mathematician’s Apology. Cambridge University Press, London (1969)
Hiebert, J., Gallimore, R., Garnier, H., Givvin, K., Hollingsworth, H., Jacobs, J., Chui, A., Wearne, D., Smith, M., Kersting. N., Manaster, A., Tseng, E., Etterbeek, W., Manaster, C., Gonzales, P., Stigler, J.: Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study. National Center for Education Statistics, Washington, DC (2003)
Higgins, J., Bonne, L., Fraser, K.: An evaluation of the Advanced Numeracy Project 2003. Ministry of Education, Wellington (2004)
Hill, H., Rowan, B., Ball, D.: Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal 42, 2, pp. 371–406 (2005)
Holton, D.A.: Six circles: Almost the complete story. Teaching Mathematics and its Applications 22, 1, pp. 21–35 (2003)
Holton, D.A.: Holton on Problem Solving – 3: The Six Circles Problem. Mathematics in School 35, 4, pp. 21–23 (2006)
Holton, D.A., Clarke, D.: Scaffolding and metacognition. International Journal of Mathematical Education in Science and Technology 37, 2, pp. 127–143 (2006)
Holton, D.A., Ahmed, A., Williams, H., Hill, C.: On the importance of mathematical play. International Journal of Mathematical Education in Science and Technology 32, 3, pp. 401–405 (2001)
Houssart, J.: Simplification and repetition of mathematical tasks: a recipe for success or failure? The Journal of Mathematical Behavior 21, 2, pp. 191–202 (2002)
Jaworski, B.: Mathematics teaching: What is it? For the Learning of Mathematics 12, 1, pp. 8–14 (1992)
Jaworski, B.: Investigating Mathematics Teaching: A Constructivist Enquiry. The Falmer Press, London (1994)
Kahneman, D., Frederick, S.: A Model of Heuristic Judgement. In: Holyoak, K.J., Morrison, R.J. (eds.) The Cambridge Handbook of Thinking and Reasoning, pp. 267–293. Cambridge University Press (2005)
Karp, A.: An ordinary problem, but a difficult one…. Submitted paper, ICMI Study 16 (2006)
Kennedy, M. M.: Knowledge and teaching. Teacher and Teaching: theory and practice 8, pp. 355–370 (2002)
Krainer, K.: Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction. Educational Studies in Mathematics 24, 1, pp. 65–93 (1993)
Lakatos, I.: Proofs and Refutations. Cambridge University Press (1976)
Lakoff, G., Núñez, R.E.: Where Mathematics Comes from: How the Embodied Mind Creates Mathematics. Basic Books, New York (2000)
Leikin, R.: Problem-solving preferences of mathematics teachers: Focusing on symmetry. Journal of Mathematics Teacher Education 6, 4, pp. 297–29 (2003)
Leikin, R.: The wholes that are greater than the sum of their parts: Employing cooperative learning in mathematics teachers’ education. Journal of Mathematical Behavior 23, 2, pp. 223–256 (2004a)
Leikin, R.: Towards high quality geometrical tasks: Reformulation of a proof problem. In: Hoines, M.J., Fuglestad, A.B. (eds.) Proceedings of the 28th International Conference for the Psychology of Mathematics Education 3, pp. 209–216 (2004b)
Leikin, R.: Learning by teaching: The case of the Sieve of Eratosthenes and one elementary school teacher. In: Zazkis, R., Campbell, S. (eds.) Number Theory in Mathematics Education: Perspectives and Prospects, pp. 115–140. Lawrence Erlbaum, Mahwah, NJ (2006)
Leikin, R., Levav-Waynberg, A.: Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics 66, 3, pp. 349–371 (2007)
Leikin, R., Winicky-Landman, G.: Defining as a vehicle for professional development of secondary school mathematics teachers. Mathematics Teacher Education and Development 3, pp. 62–73 (2001)
Leontiev A.N.: Analysis of activity. Vestnik MGU (Moscow State University). 14: Psychology (1983)
Leron, U., Hazzan, O.: The Rationality Debate: Application of Cognitive Psychology to Mathematics Education. Educational Studies in Mathematics 62, 2, pp. 105–126 (2006)
Luria, A.: Lekzii po obschey psihologii [Lectures in General Psychology]. St. Petersburg (2004)
Ma, L.: Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Lawrence Erlbaum, Mahwah, NJ (1999)
McGatha, M., Sheffield, L.J.: Mighty Mathematics: Using Problem Posing and Problem Solving to Develop Mathematical Power. Teaching Children Mathematics 13, pp. 79–85 (2006)
McNeal, B., Simon, M.A..: Mathematics Culture Clash: Negotiating New Classroom Norms with Prospective Teachers. Journal of Mathematical Behavior 18, 4, pp. 475– 509 (2000)
Meissner, H.: Teacher Students as Researchers. In: European Research Conference on the Psychology of Mathematics Education (CERME 1), pp. 50–53, Osnabrueck, Germany (1995)
Meissner, H.: Mit Video besser lernen? In: Beiträge zum Mathematikunterricht. Franzbecker Verlag, Hildesheim, Germany (1996)
Meissner, H.: Einstellung, Vorstellung, and Darstellung. In: Cockburn, A.D., Nardi, E. (eds.) Proceedings of the 26th International Conference for the Psychology of Mathematics Education 1, pp.156–161. University of East Anglia, Norwich, UK (2002)
Moreira, P., David, M.M.: Mathematics In: Teacher Education Versus Mathematics In Teaching Practice: A Revealing Confrontation. ICMI Study 15, Brazil (2004)
National Center for Education Statistics: Job Satisfaction among America’s Teachers: Effects of Workplace Conditions, Background Characteristics, and Teacher Compensation. US Deptartment of Education, Washington, DC (1997) nces.ed.gov/pubsearch/pubsinfo.asp?pubid=97471. Accessed 22 December 2007
National Council of Teachers of Mathematics (NCTM): An Agenda for Action: Recommendations for School Mathematics of the 1980s. NCTM, Reston, VA (1980)
Pólya, G.: How to Solve It. Princeton University Press, Princeton, NJ (2004)
Rasmussen, S.: From Induction to Deduction with The Geometer’s Sketchpad. Paper presented at the 74th Annual NCTM Meeting, 25–28 April 1996, San Diego, CA (1996)
Scharm, P., Lappan, G.: Paper presented at the annual meeting of the American Educational Research Association, New Orleans (1988)
Scheffler, I.: Conditions of knowledge. An introduction to epistemology and education. Scott, Foresman and Company, Glenview, Illinois (1965)
Schoenfeld, A. H.: On Mathematics as Sense-Making: An Informal Attack on the Unfortunate Divorce of Formal and Informal Mathematics. In: Voss, J., Perkins, D.N., Segal, J. (eds.) Informal Reasoning and Education, pp. 311–343. Lawrence Erlbaum, Hillsdale, NJ (1991)
Sfard, A.: Reification as the birth of metaphor. For the Learning of Mathematics 14, pp. 44–55 (1994)
Sheffield, L. J.: Extending the Challenge in Mathematics: Developing Mathematical Promise in Students. Corwin Press, Thousand Oaks, CA (2003)
Shroyer, G., Hancock, M.: Facing the challenges: Further discussion of the factors influencing the successful implementation of professional development in schools. AETS Conference Proceedings, Session 905, pp. 726–736 (1997)
Shulman, L.S.: Those who understand: Knowledge growth in teaching. Educational Researcher 15, 2, pp. 4–14 (1986)
Shulman, L.S.: Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review 57, 1, pp. 1–22 (1987)
Siber, E.M.: Isolating students with mathematical learning difficulties for teaching purposes: The New Zealand experience. Unpublished Masters thesis, Massey University, Auckland (2003)
Sierpinska, A.: The Notion of “Didactic Contract”. Lecture at Concordia University, Montreal (1999) alcor.concordia.ca/˜sierp/TDSLecture%203.pdf. Accessed 22 December 2007
Simon, A. M.: Developing new models of mathematics teaching: An imperative for research on mathematics teacher development. In: Fennema, E., Scott-Nelson B. (eds.) Mathematics Teachers in Transition, pp. 55–86. Lawrence Erlbaum, Mahwah, NJ (1997)
Steinbring, H.: Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education 1, 2, pp. 157–189 (1998)
Stigler J. W., Hiebert J.: The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. The Free Press, New York (1999)
Tall, D.O.: The anatomy of a discovery in mathematical research. For the Learning of Mathematics 1, 2, pp. 25–30 (1980)
Thomas, G., Tagg, A.: Evidence for expectations: Findings from the Numeracy Project longitudinal study. In: Findings from the New Zealand Numeracy Development Project 2004, pp. 21–34. Ministry of Education, Wellington (2005)
Thomas, M.O.J., Holton, D.A.: Technology as a tool for teaching undergraduate mathematics. In: Bishop A.J., Clements M.A., Keitel C., Kilpatrick, J., Leung F.K.S. (eds.) Second International Handbook of Mathematics Education, pp. 351–394. Kluwer Academic Publishers, Dordrecht, The Netherlands (2003)
Vygotsky, L.S.: Mind in society: The development of higher psychological processes (Cole, M., John-Steiner, V., Scribner, S., Souberman, E. trans.). Harvard University Press, Cambridge, MA (1978)
Watson, A.: Red herrings: Post-14 ‘best’ mathematics teaching and curricula. British Journal of Educational Studies 52, 4, pp. 359–376 (2004)
Watson, A., De Geest, E.: Principled teaching for deep progress: improving mathematical learning beyond methods and materials. Educational Studies in Mathematics 58, 2, pp. 209–234 (2005)
Watson, A., De Geest, E., Prestage, S.: Deep progress in mathematics: The Improving Attainment in Mathematics Project. Universities of Oxford and Birmingham, Oxford (2003)
Wells, G.: Dialogic Inquiry: Towards a Sociocultural Practice and Theory of Education. Cambridge University Press (1999)
Wilson, S., Shulman, L., Richert, A. E.: “150” Different ways of knowledge in teaching. Representations of knowledge in teaching. In: Calderhead, J. (ed.) Exploring Teachers’ Thinking, pp. 1–37. Cassell, London (1987)
Wright, V.: The New Zealand Numeracy Project: Where it’s at. In: Ocean, J., Walta, C., Breed, M., Virgona, J., Horwood, J. (eds.) Mathematics—the way forward. Proceedings of the forty-third annual conference of the Mathematics Association of Victoria, MAV, Melbourne, Australia (2006)
Yeap, B. H.: Good practices in mathematics teaching and teacher development. Tsukuba Journal of Educational Study in Mathematics 25, pp. 233–236 (2006)
Yerushalmy, M.: Does technology transform the content of algebra curricula? An analysis of critical transitions for learning and teaching. Paper presented at the TSG9—Teaching and Learning of Algebra, ICME (July 2004)
Yerushalmy, M., Chazan, D., Gordon, M.: Mathematical problem posing: Implications for facilitating student inquiry in classrooms. Instructional Science 19, 3, pp. 219–245 (1990)
Zevenbergen, R.: Grouping by ability: A self-fulfilling prophecy? Australian Mathematics Teacher 59, 4, pp. 2–7 (2003)
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Holton, D. et al. (2009). Teacher Development and Mathematical Challenge. In: Taylor, P., Barbeau, E. (eds) Challenging Mathematics In and Beyond the Classroom. New ICMI Study Series, vol 12. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09603-2_7
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