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Challenging Mathematics In and Beyond the Classroom pp 243–283Cite as

Challenging Mathematics: Classroom Practices

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References

  • Arons, A.B.: Historical and philosophical perspectives attainable in introductory physics courses. Educational Philosophy and Theory 20, 2, pp. 13–23 (1988)

    Article  Google Scholar 

  • Amit, M., Fried, M.N., Abu-Naja, M.: The mathematics club for excellent students as common ground for Bedouin and other Israeli youth. In: Sriraman, B. (ed.) International perspectives on social justice in mathematics education. Monograph 1, The Montana Mathematics Enthusiast. Montana Council of Teachers of Mathematics and The University of Montana Press, Missoula (2007)

    Google Scholar 

  • Askew, M., Brown, M., Rhodes, V., Johnson, D., Wiliam, D.: Effective teachers of numeracy. Final Report. School of Education, King’s College, London (1997)

    Google Scholar 

  • Baba, T.: How is lesson study implemented? In: Isoda, M., Stephens, M., Ohara, Y., Miyakawa T. (eds.) Japanese lesson study in mathematics: Its impact, diversity and potential for educational improvement, pp. 2–7. World Scientific, Singapore (2007)

    Chapter  Google Scholar 

  • Blum, W., Leiss, D.: How do students and teachers deal with modeling problems? In: Haines, C., Galbraith, P., Blum, W., Khan S. (eds.) Mathematical Modelling (ICTMA12): Education, Engineering and Economics, pp. 222–231. Horwood, Chichester, UK (2007)

    Chapter  Google Scholar 

  • Borba, M.C., Villarreal, M.E.: Humans-with-media and the reorganization of mathematical thinking. Springer, New York (2005)

    Google Scholar 

  • Brändström, A.: Differentiated tasks in mathematics textbooks: An analysis of the levels of difficulty. Lulea University of Technology, Sweden (2005)

    Google Scholar 

  • Brousseau, G.: Theory of didactical situations in mathematics: Didactique des Mathématiques, 1970–1990. Kluwer, Dordrecht, The Netherlands (1997)

    Google Scholar 

  • Cheung, K.C.: Raindrops soothing amidst the spring wind: Exemplary case studies of multiple intelligences inspired education (in Chinese). Crystal Educational Publications, Hong Kong (2003)

    Google Scholar 

  • Cheung, K.C.: Mathematization and realistic mathematics education: An analysis of their contributions to exploratory mathematics project work (in Chinese). Journal of Mathematics Education 14, 1, pp. 35–37 (2005)

    Google Scholar 

  • Cheung, K.C.: Challenging mathematical problems in the classroom. Submitted paper, ICMI Study 16 (2006)

    Google Scholar 

  • Clarke, D.J. (ed.): Perspectives on practice and meaning in mathematics and science classrooms. Kluwer, Dordrecht (2001)

    Google Scholar 

  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., Schauble, L.: Design experiments in educational research. Educational Researcher 32, 1, pp. 9–13 (2003)

    Article  Google Scholar 

  • Collins, A., Brown, J. S. and Newman, S. E.: Cognitive apprenticeship: Teaching the craft of reading, writing, and mathematics. In: Resnick L.B. (ed.) Knowing, learning, and instruction: Essays in honor of Robert Glaser, pp. 453–494. Lawrence Erlbaum, Hillsdale, NJ (1989)

    Google Scholar 

  • Collins, A., Joseph, D., Bielaczyc, K.: Design research: Theoretical and methodological issues. The Journal of the Learning Sciences 13, 1, pp. 15–42 (2004)

    Article  Google Scholar 

  • Csikszentmihalyi, M.: The flow experience and its significance for human psychology. In: Csikszentmihalyi, M., Csikszentmihalyi, I.S. (eds.) Optimal experience: Psychological studies of flow in consciousness, pp. 15–35. Press Syndicate of the University of Cambridge, Cambridge (1992)

    Google Scholar 

  • Cuomo, S.: Pappus of Alexandria and the mathematics of late antiquity. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  • Czarnocha, B., Prabhu, V.: Teaching-research and Design experiment—Two methodologies of integrating research and classroom practice. e-Proceedings of epiSTEME-1, International Conference to review research on Science, Technology and Mathematics Education, pp. 78–80. Goa, India (2004) www.hbcse.tifr.res.in/episteme1/ Accessed 16 December 2007

  • Davydov, V. V.: Types of generalization in instruction: Logical and psychological problems in the structuring of school curricula. Soviet studies in mathematics education, Vol. 2. (J. Kilpatrick, ed., J. Teller, trans.). National Council of Teachers of Mathematics, Reston, VA (1990) (Original work published 1972)

    Google Scholar 

  • Dede, C.: If design-based research is the answer, what is the question? Commentary. The Journal of the Learning Sciences 13, 1, pp.105–114 (2004)

    Article  Google Scholar 

  • Diezmann, C.M., Watters, J.J.: Catering for mathematically gifted elementary students: Learning from challenging tasks. Gifted Child Today 23, 4, pp. 14–19 (2000)

    Google Scholar 

  • Diezmann, C. M., Watters, J. J.: The importance of challenging tasks for mathematically gifted students. Gifted and Talented International 17, 2, pp. 76–84 (2002)

    Google Scholar 

  • Dionne, J.: The perception of mathematics among elementary school teachers. In: Moser, J. (ed.) Proceedings of the 6th annual meeting of the North American chapter of the International group for the Psychology of Mathematics Education, pp. 223–228. University of Wisconsin, Madison, WI (1984)

    Google Scholar 

  • Doerr, H.M., English, L.D.: Middle grade teachers learning through students’ engagement with modeling tasks. Journal of Mathematics Teacher Education 9, 1, pp. 5–32 (2006)

    Article  Google Scholar 

  • English, L.: Reconciling theory, research and practice: A models and modelling perspective. Educational Studies in Mathematics 51, 2/3, pp. 225–248 (2003)

    Article  Google Scholar 

  • Ernest, P.: The impact of beliefs on the teaching of mathematics. In: Ernest, P. (ed.) Mathematics teaching: The state of the art, pp. 249–253. Falmer, New York (1989)

    Google Scholar 

  • Eves, H.: An introduction to the history of mathematics. Holt, Rinehart & Winston, New York (1960)

    Google Scholar 

  • Fernandez, C., Yoshida, M.: Lesson study: A Japanese approach to improving mathematics teaching and learning (Studies in mathematical thinking and learning). Erlbaum, Mahwah, NJ (2004)

    Google Scholar 

  • Festinger, L.: A theory of cognitive dissonance. Row Peterson, Evanston, IL (1957)

    Google Scholar 

  • French, D.: The calculus: Differentiation and integration. In: French, D. Teaching and learning algebra, pp. 174–190. Continuum, London (2002)

    Google Scholar 

  • Freudenthal, H.: Mathematics as an educational task. Reidel, Dordrecht, The Netherlands (1973)

    Google Scholar 

  • Furinghetti, F., Pehkonen, E.: A comparative study on students’ beliefs concerning their autonomy in doing mathematics. Nordisk matematikkdidaktikk [Nordic Studies in Mathematics Education] 8, 4, pp. 7–26 (2000)

    Google Scholar 

  • Galbraith, P. L., Stillman, G.A., Brown, J. P.: Turning ideas into modelling problems. In: Lesh, R., Galbraith, P., Blum, W., Hurford A. (eds.) Mathematical Modeling (ICTMA13): Education and the Design Sciences. Horwood, Chichester, UK (in press)

    Google Scholar 

  • Gardner, H.: Frames of mind: The theory of multiple intelligences. Basic Books, New York (1983)

    Google Scholar 

  • Gardner, H.: The last recreations. Springer-Verlag, New York (1997)

    Book  Google Scholar 

  • Gardner, H.: Intelligence reframed: Multiple intelligences for the 21st century. Basic Books, New York (1999)

    Google Scholar 

  • 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

  • Goos, M., Stillman, G., Vale, C.: Teaching secondary school mathematics: Research and practice for the 21st century. Allen and Unwin, Crows Nest, Australia (2007)

    Google Scholar 

  • Gravemeijer, K.: How emergent models may foster the constitution of formal mathematics. Mathematics Thinking and Learning 1, 2, pp. 155–177 (1999)

    Article  Google Scholar 

  • Guzdial, M.: Software-realised scaffolding to facilitate programming for science learning. Interactive Learning Environments 4, pp. 1–44 (1994)

    Article  Google Scholar 

  • Haggarty, L., Pepin, B.: An investigation of mathematics textbooks and their use in English, French and German classrooms: Who gets an opportunity to learn what? In: Winter, J. (ed.) Proceedings of the British Society for Research into Learning Mathematics (Proceedings of the BCME5) 21, 2, pp. 117–125 (2001)

    Google Scholar 

  • Haggarty, L., Pepin, B.: An investigation of mathematics textbooks and their use in English, French and German classrooms: Who gets an opportunity to learn what? British Educational Research Journal 28, 4, pp. 567–590 (2002)

    Article  Google Scholar 

  • Harvey, J.G., Waits, B.K., Demana, F.D.: The influence of technology on the teaching and learning of algebra. Journal of Mathematical Behavior 14, 1, pp. 75–109 (1995)

    Article  Google Scholar 

  • Hashimoto, Y., Becker, J.: The open approach to teaching mathematics—Creating a culture of mathematics in the classroom: Japan. In: Sheffield, L. (ed.) Developing mathematically promising students, pp. 101–120. National Council of Teachers of Mathematics, Reston, VA (1999)

    Google Scholar 

  • Henningsen, M., Stein, M.K.: Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education 28, 5, pp. 524–549 (1997)

    Article  Google Scholar 

  • Herbel-Eisenmann, B.A., Breyfogle, M.L.: Questioning our patterns of questioning. Mathematics Teaching in the Middle School 10, 9, pp. 484–489 (2005)

    Google Scholar 

  • Hiebert, J., Gallimore, R., Stigler, J.: A knowledge base for the teaching profession: What would it look like and how can we get one? Educational Researcher 31, 5, pp. 3–15 (2002)

    Article  Google Scholar 

  • Hino, K.: Toward the problem-centered classroom: Trends in mathematical problem solving in Japan. ZDM—The International Journal on Mathematics Education 39, 5–6, pp. 503–514 (2007)

    Article  Google Scholar 

  • Hoffman, P.: Archimedes' revenge: The joys and perils of mathematics. Fawcett Columbine, New York (1988)

    Google Scholar 

  • Isoda, M.: Where did lesson study begin, and how far has it come? In: Isoda, M., Stephens, M., Ohara, Y., Miyakawa, T. (eds.) Japanese lesson study in mathematics: Its impact, diversity and potential for educational improvement, pp. 8–15. World Scientific, Singapore (2007)

    Chapter  Google Scholar 

  • Isoda, M., Stephens, M., Ohara, Y., Miyakawa, T. (eds.): Japanese lesson study in mathematics: Its impact, diversity and potential for educational improvement. World Scientific, Singapore (2007)

    Google Scholar 

  • Julie, C.: Learners’ context preferences and mathematical literacy. In: Haines, C., Galbraith, P., Blum, W., Khan S. (eds.) Mathematical Modelling (ICTMA12): Education, Engineering and Economics, pp. 195–220. Horwood, Chichester, UK (2007)

    Google Scholar 

  • Kadijevich, Dj.: Suitable activities for and possible factors influencing the outcomes of challenging mathematics in and beyond the classroom. Submitted paper, ICMI Study 16 (2006)

    Google Scholar 

  • Kadijevich, Dj.: Towards relating procedural and conceptual knowledge by CAS. Invited presentation at CAME 5. (2007) www.lkl.ac.uk/research/came/events/CAME5/ Accessed 05 February 2008

  • Kadijevich, Dj., Marinković, B.: Challenging mathematics by “Archimedes”. The Teaching of Mathematics 9, 1, pp. 31–39 (2006)

    Google Scholar 

  • 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)

    Google Scholar 

  • Liu, P-H.: Do teachers need to incorporate the history of mathematics in their teaching? Mathematics Teacher 96, 6, pp. 416–421 (2003)

    Google Scholar 

  • Lobato, J.: How design experiments can inform a rethinking of transfer and vice versa. Educational Researcher 32, 1, pp. 17–20 (2003)

    Article  Google Scholar 

  • Loh, B., Reiser, B., Radinsky, J., Edelson, D., Gomez, L., Marshall, S.: Developing reflective inquiry practices: A case study of software, the teacher, and students. In: Crowley, K., Schunn, C., Okada, T. (eds.) Designing for science: Implications from everyday, classroom, and professional settings, pp. 279–323. Erlbaum, Mahwah, NJ (2001)

    Google Scholar 

  • Mason, J., Graham, A., Johnston-Wilder, S.: Developing thinking in algebra. Sage, London, UK (2005)

    Google Scholar 

  • Mason, R.T.: Teaching mathematics as a humanity. Colloquium, Department of Mathematics, University of Manitoba, Winnipeg (1999)

    Google Scholar 

  • Mason, R.T.: Mathematics—By invitation only. In: Simmt, E., Davis, B., McLoughlin, J.G. (eds.) Proceedings of the annual meeting of the Canadian Mathematics Education Study Group [Groupe Canadien d’Etude en Didactique des Mathematiques]. ERIC Document No. ED472904, Montreal, QC (2000)

    Google Scholar 

  • Mason, R.T.: Isaac Newton: An apple for the teacher. In: Mason, R.T., Stinner, A. (eds.) Proceedings of the Third Annual Seminar in the History of Science in Education. Deutsches Museum, Munich, Germany (2001)

    Google Scholar 

  • Mason, R.T.: Scientists as role models: making good examples from history’s exemplars. In: Mason R.T. (ed.) Proceedings of the Fourth Annual Seminar in the History of Science Education. University of Manitoba, Winnipeg, MB (2003)

    Google Scholar 

  • Mason, R.T., Janzen Roth, E.: The insight of Archimedes: Scaffolding students’ approximation of pi. International Institute on Units of Historical Presentation in Science Teaching. Deutsches Museum, Munich, Germany (2004)

    Google Scholar 

  • Mason, R., Janzen Roth, E.: Thinking like Archimedes: An instructional design experiment. Proceedings of the Eight International Congress of the History, Philosophy, Sociology and Science Teaching, Leeds, UK (2005) www.ihpst2005.leeds.ac.uk/papers.htm Accessed 11 January 2008

  • Mason, R., Janzen Roth, E.: Can high school students think mathematically like Archimedes? A design research experiment in challenging mathematics. Submitted paper, ICMI Study 16 (2006)

    Google Scholar 

  • Mason, R., Janzen Roth, E.: Why π? Instructional design experiment to incorporate history of science in student learning. Proceedings of the Ninth International History, Philosophy and Science Teaching Conference, Calgary, Canada, June 24–28 (2007) www.ucalgary.ca/ihpst07/ Accessed 11 January 2008

  • Mercier, A., Sensevy, G., Schubauer-Leoni, M-L.: How social interactions within a class depend on the teachers’ assessment of the pupils’ various mathematical capabilities: A case study. In: Schwank I. (ed.) European research in mathematics education 1, Proceedings of the first Conference of the European Society in Mathematics Education 1, pp. 342–353 (1999) www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/cerme1-proceedings.html . Accessed 11 January 2008

  • Mitchelmore, M., White, P.: Abstraction in mathematics learning. [Editorial] Mathematics Education Research Journal 19, 2, pp. 1–9 (2007)

    Google Scholar 

  • Neighbour, R.: The inner apprentice. Petroc Press, Plymouth, UK (1992)

    Google Scholar 

  • Netz, R., Noel, W.: The Archimedes codex: Revealing the secret of the world’s greatest palimpsest. Weidenfeld and Nicolson, London (2007)

    Google Scholar 

  • Nohda, N.: Learning and teaching through open approach method. In: Mathematics education in Japan, pp. 29–32. Japan Society of Mathematical Education, Tokyo (2000) (Original work published 1995)

    Google Scholar 

  • Palinscar, A. S.: Working theory into and out of design experiments. Learning Disabilities Research and Practice 20, 4, pp. 218–220 (2005)

    Article  Google Scholar 

  • Paris, S.G., Turner, J.C.: Situated motivation. In: Pintrich, P.R., Brown, D.R., Weinstein C.E. (eds.) Student motivation: Essays in honor of Wilbert J. McKeachie, pp. 213–237. Erlbaum, Hillsdale, NJ (1994)

    Google Scholar 

  • Pea, R.D.: Commentary: The social and technological dimensions of scaffolding and related theoretical concepts for learning, education and human activity. The Journal of the Learning Sciences 13, 3, pp. 423–451 (2004)

    Article  Google Scholar 

  • Pehkonen, L.: To change or not to change: How primary school teachers speak about stability and change. Nordic Studies in Mathematics Education NOMAD 12, 2, pp. 57–76 (2007)

    Google Scholar 

  • Piaget, J.: The psychology of intelligence. Routledge and Kegan Paul, London (1950)

    Google Scholar 

  • Pierce, R., Stacey, K.: Enhancing the image of mathematics by association with simple pleasures from real world contexts. Zentralblatt für Didaktik der Mathematik 38, 3, pp. 214–225 (2006)

    Article  Google Scholar 

  • Ponte, J.P.: Investigations and explorations in the mathematics classroom. ZDM—The International Journal on Mathematics Education 39, 5–6, pp. 419–430 (2007)

    Article  Google Scholar 

  • Reiss, K., Törner, G.: Problem solving in the mathematics classroom: The German perspective. ZDM—The International Journal on Mathematics Education 39, 5–6, pp. 431–442 (2007)

    Google Scholar 

  • Rudge, D.W., Howe, E.M.: Incorporating history into the science classroom. Science Teacher 71, 9, pp. 52–57 (2004)

    Google Scholar 

  • Seligman, M.: The optimistic child. Griffin Press, Adelaide, Australia (1995)

    Google Scholar 

  • Sheffield, L.: Extending the challenge in mathematics: developing mathematical promise in K–8 students. Corwin, Thousand Oaks, CA (2003)

    Google Scholar 

  • Shimada, S. (ed.) The open-ended approach in arithmetic and mathematics—A new proposal toward teaching mathematics (in Japanese). Mizuumishobo, Tokyo (1977)

    Google Scholar 

  • Silver, E.A., Stein, M.K.: The QUASAR project: The “Revolution of the possible” in mathematics instructional reform in urban middle schools. Urban Education 30, 4, pp. 476–521 (1996)

    Article  Google Scholar 

  • Skovsmose, O.: Critical mathematics education. In: Alsina, C., Alvarez, J.M., Hodgson, B., Laborde, C., Pérez, A. (eds.) Proceedings of the 8th International Congress on Mathematical Education: Selected Lectures, Seville, pp. 413–426. SAEM Thales, Seville, Spain (1998)

    Google Scholar 

  • Sriraman, B.: Generalisation processes in combinatorial problem-solving situations. In: Mewborn, D.S., Szrajn, P., White, D.Y., Wiegel, H.G., Bryant, R.L, Nooney, K. (eds.) Proceedings of 24th annual meeting of the North American chapter of the International group for the Psychology of Mathematics Education, Athens, Georgia, 3, pp. 1411–1414. ERIC/CSMEE Publications, Columbus, OH (2002)

    Google Scholar 

  • Sriraman, B.: Mathematical giftedness, problem solving, and the ability to formulate generalisations. Journal of Secondary Gifted Education 14, 3, pp. 151–165 (2003a)

    Google Scholar 

  • Sriraman, B.: Can mathematical discovery fill the existential void? The use of conjecture, proof and refutation in a high school classroom. Mathematics in School 32, 2, pp. 2–6 (2003b)

    Google Scholar 

  • Sriraman, B.: Discovering a mental principle: The case of Matt. Mathematics in School 33, 2, pp. 25–31 (2004a)

    Google Scholar 

  • Sriraman, B.: Discovering Steiner Triple Systems through problem solving. Mathematics Teacher 97, 5, pp. 320–326 (2004b)

    Google Scholar 

  • Sriraman, B.: Reflective abstraction, uniframes and the formulation of generalizations. The Journal of Mathematical Behavior 23, 2, pp. 205–222 (2004c)

    Google Scholar 

  • Sriraman, B.: The challenge of discovering mathematical structures: Some research based pedagogical recommendations for the secondary classroom. Submitted paper, ICMI Study 16 (2006)

    Google Scholar 

  • Sriraman, B., English, L.D.: Combinatorial mathematics: Research into practice. Mathematics Teacher 98, 3, pp. 182–191 (2004)

    Google Scholar 

  • Sriraman, B., Strzelecki, P.: Playing with powers. International Journal for Technology in Mathematics Education 11, 1, pp. 29–34 (2004)

    Google Scholar 

  • Stein, M. K., Grover, B. W., Henningsen, M.: Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal 33, 2, pp. 455–488 (1996)

    Google Scholar 

  • Stephens, M., Isoda, M.: Introduction to the English translation. In: Isoda, M., Stephens, M., Ohara, Y., Miyakawa, T. (eds.) Japanese lesson study in mathematics: Its impact, diversity and potential for educational improvement, pp. xv–xxiv. World Scientific, Singapore (2007)

    Google Scholar 

  • Stillman, G.: The role of challenge in engaging lower secondary students in investigating real world tasks. Submitted paper, ICMI Study 16 (2006)

    Google Scholar 

  • Stillman, G., Brown, J.: Challenges in formulating an extended modelling task at Year 9. In: Reeves, H., Milton, K., Spencer, T. (eds.) Mathematics: Essential for learning, essential for life. Proceedings of the twenty-first biennial conference of the Australian Association of Mathematics Teachers (AAMT), pp. 224–231. AAMT, Adelaide, Australia (2007)

    Google Scholar 

  • Stillman, G., Galbraith, P.: Towards constructing a measure of the complexity of application tasks. In: Lamon, S.J., Parker, W.A., Houston, K. (eds.) Mathematical modelling: A way of life, pp. 179–188. Horwood, Chichester, UK (2003)

    Google Scholar 

  • Stillman, G., Brown, J., Galbraith, P.: Identifying challenges within transition phases of mathematical modelling activity at Year 9. Paper presented at the Thirteenth International Conference on The Teaching of Mathematical Modeling and Applications, Bloomington, IN (2007) site.educ.indiana.edu/Papers/tabid/5320/Default.aspx. Accessed 10 January 2008

    Google Scholar 

  • Stillman, G., Edwards, I., Brown, J.: Mediating the cognitive demand of lessons in real-world settings. In: Tadich, B., Tobias, S., Brew, C., Beatty, B., Sullivan P. (eds.) Towards excellence in mathematics, pp. 489–500. Mathematical Association of Victoria, Melbourne (2004)

    Google Scholar 

  • Stinner, A., Williams, H.: History and philosophy of science in the science curriculum. In: Fraser, B.J., Tobin, K.G. (eds.) The international handbook of science education. Kluwer, London (1998)

    Google Scholar 

  • Stone, C. A.: What is missing in the metaphor of scaffolding? In: Forman, E., Minick, N., Stone, C. (eds.) Contexts for learning: Sociocultural dynamics in children’s development, pp. 169–183. Oxford University Press, New York (1993)

    Google Scholar 

  • Sullivan, P., Clarke, D.: Communication in the classroom: The importance of good questioning. Deakin University Press, Geelong, Australia (1991)

    Google Scholar 

  • Takahashi, A.: Characteristics of Japanese mathematics lessons. APEC Symposium: Innovative Teaching in mathematics through lesson study. Tokyo, Japan (2006)

    Google Scholar 

  • Tall, D.: A theory of mathematical growth through embodiment, symbolism and proof. Annales de Didactique et de Sciences Cognitives 11, pp. 195–215 (2006)

    Google Scholar 

  • Tejima, K.: Open-ended approach and improvement of classroom teaching. In: Mathematics education in Japan, pp. 29–32. Japan Society of Mathematical Education, Tokyo (2000) (Original work published 1997)

    Google Scholar 

  • Vinner, S.: Mathematics education—Procedures, rituals and man’s search for meaning. Abstract. Proceedings of the 10th International Congress on Mathematical Education: Plenary and Regular Lectures, pp. 120–121. International Commission on Mathematics Instruction, Copenhagen, Denmark (2000)

    Google Scholar 

  • Vinner, S., Dreyfus, T.: Images and definitions for the concept of function. Journal for Research in Mathematics Education 20, 4, pp. 356–366 (1989)

    Article  Google Scholar 

  • 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)

    Google Scholar 

  • Watson, A.: Red herrings: Post 14 ‘best’ mathematics teaching and curricula. British Journal of Educational Studies 52, 4, pp. 359–376 (2004)

    Article  Google Scholar 

  • Williams, G.: Associations between student pursuit of novel mathematical ideas and resilience. In: Bragg, L., Campbell, C., Herbert, G., Mousley, J. (eds.) Mathematics education research: Innovation, networking, opportunity 2, pp. 752–759. MERGA, Melbourne, Australia (2003a)

    Google Scholar 

  • Williams, G.: Student inclination to work with unfamiliar challenging problems: The role of resilience. In: Clarke, B., Bishop, A., Cameron, R., Forgasz, H., Seah, W.T. (eds.) Making Mathematicians, pp. 374–385. Mathematical Association of Victoria, Brunswick, Victoria (2003b)

    Google Scholar 

  • Williams, G.: Impetus to explore: Approaching operational deficiency optimistically. In: Novotna, J., Moraova, H., Kratka, M., Stehlikova, N. (eds.) Proceedings of the 30th conference of the International Group for the Psychology of Mathematics Education 5, pp. 393–400. PME, Prague, Czech Republic (2006)

    Google Scholar 

  • Wood, D., Bruner, J., Ross, G.: The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry 17, pp. 89–100 (1976)

    Article  Google Scholar 

  • Woodward, J., Brown, C.: Meeting the curricular needs of academically low-achieving students in middle grade mathematics. The Journal of Special Education 40, 3, pp. 151–159 (2006)

    Article  Google Scholar 

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    Gloria Stillman

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    Stillman, G., Cheung, Kc., Mason, R., Sheffield, L., Sriraman, B., Ueno, K. (2009). Challenging Mathematics: Classroom Practices. 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_8

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