What makes an example exemplary: Pedagogical and didactical issues in appreciating multiplicative structures

Number Theory in Mathematics Education: Perspectives and Prospects

Volumn , Issue , 2012, Pages 41-68

  Mason, John ^a  

^a OPEN UNIVERSITY   (United Kingdom)

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EID: 44349145803     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203053904     Document Type: Chapter

References (44)

1. Banwell, C., Tahta, D. & Saunders, K. (1986). Starting points for teaching mathematics in middle and secondary schools. Oxford, England: Oxford University Press. (Original work published 1972)
2. Bennett, J. (1956-1966). The dramatic universe (Vols. 1-4). London: Hodder & Stoughton.
3. Bills, L. (1996). Shifting sands: Students' understanding of the roles of variables in A level mathematics. Unpublished doctoral dissertation. Milton Keynes, England: Open University.
4. Brown, S., & Walter, M. (1983). The art of problem posing. Philadelphia: Franklin Press.
5. Chevallard, Y. (1985). La transposition didactique [The didactic transposition]. Grenoble, France: La Pensée Sauvage.
6. Courant, R. (1981). Reminiscences from Hilbert's Göttingen. Math Intelligencer, 3(4), 154-164.
7. Davydov, V (1990). Types of generalization in instruction (J. Teller, Trans.). Soviet studies in mathematics education (Vol. 2). Reston: NCTM.
8. Fischbein, E. (1993). Figural concepts. Educational Studies in Mathematics, 24(2), 139-162.
9. Flegg, G. (1985). Nicolas Chuquet, renaissance mathematician. Dordrecht, Netherlands: Reidel.
10. Gattegno, C. (1970). What we owe children: The subordination of teaching to learning. London: Routledge & Kegan Paul.
11. Goldenberg, P. (1996). "Habits of mind" as an organizer for the curriculum. Journal of Education, 178(1), 13-34.
12. Halmos P. R. (1983). In D. Sarasen & L. Gillman (Eds.), Selecta: Expository writing (pp. 157-186). New York: Springer-Verlag.
13. Kaczkowski, S. (2001). Factoring quadratics. College Mathematics Journal, 32(3), 203-204.
14. Lehrer, T. (1965). Retrieved 2005 from http://curvebank.calstatela.edu/newmath/newmath.htm
15. Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Lawrence Erlbaum Associates.
16. Marton, F., & Trigwell, K. (2000). Varatio est mater studiorum [Variation is the mother of learning]. Higher Education Research & Development, 19(3), 381-395.
17. Marton, F., & Tsui, A. (2004). Classroom discourse and the space of learning. Mahwah, NJ: Lawrence Erlbaum Associates.
18. Mason, J. (1988). Fragments: The implications for teachers, learners and media users/researchers of personal construal and fragmentary recollection of aural and visual messages. Instructional Science, 17, 195-218.
19. Mason, J. (1989). Teaching (pupils to make sense) and assessing (the sense they make). In E Ernest (Ed.), Mathematics teaching: The state of the art (pp. 153-166). London: Falmer.
20. Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednaiz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Dordrecht, Netherlands: Kluwer.
21. Mason, J. (1999). Incitación al estudiante para que use su capacidad natural de expresar generalidad: Las secuencias de Tunja [Provoking students to use their natural power to express generality: Tunja sequences]. Revista EMA, 4(3), 232-246.
22. Mason, J. (2001). Tunja sequences as examples of employing students' powers to generalize. Mathematics Teacher, 94(3), 164-169.
23. Mason, J. (2002). Researching your own practice: The discipline of noticing. London: Routledge-Falmer.
24. Mason, J. (2003a). Structure of attention in the learning of mathematics. In J. Novotná (Ed.), Proceedings of the International Symposium on Elementary Mathematics Teaching (pp. 9-16). Prague, Czech Republic: Charles University
25. Mason, J. (2003b). On the structure of attention in the learning of mathematics. Australian Association of Mathematics Teachers, 59(4), 17-25.
26. Mason, J. (2006). Advanced Factoring. Retrievd from http://mcs.open.ac.uk/jhm3
27. Mason, J., Graham, A., & Johnston-Wilder, S. (2005). Developing algebraic thinking. London: Sage.
28. Mason, J., & Johnston-Wilder, S. (2004). Fundamental constructs in mathematics education. London: Routledge-Falmer.
29. Mason, J., & Eimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15(3), 277-290.
30. Mason, J., & Watson, A. (2001). Stimulating students to construct boundary examples. Questiones Mathematicae, 24(Suppl. 1), 123-132.
31. Minor, L. (1988). Factoring twins as a teaching tool. In A. Coxford & A. Shulte (Eds.), The ideas of algebra K-12: 1988 Yearbook (pp. 192-198). Reston, VA: National Council on Teaching Mathematics.
32. Eimm, D. (1994). Mathematics classroom language: Form, function and force. In R. Biehler, R. W. Scholz, R. Strasser, & B. Winkelman (Eds.), Didactics of mathematics as a scientific discipline (pp. 159-169). Dordrecht, Netherlands: Kluwer
33. Eolya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving [Film]. New York: Wiley.
34. Eolya, G. (1965). Let us teach guessing (film). Washington: Mathematical Association of America.
35. Rowland, T. (2002). Generic proofs in number theory. In S. R. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp. 157-184). Westport, CT: Ablex.
36. Rowland, T., Martyn, S., Barber, P., & Heal, C. (2000). Primary teacher trainees' mathematics subject knowledge and classroom performance. In T. Rowland & C. Morgan (Eds.), Research in mathematics education. Vol2: Papers of the British Society for Research into Learning Mathematics (pp. 3-18). London: British Society for Research in the Learning of Mathematics.
37. Sangwin, C. (2003). New opportunities for encouraging higher level mathematical learning by creative use of emerging computer aided assessment. International Journal for Mathematical Education in Science and Technology, 34(6), 813-829.
38. Watson, A. (2000). Going across the grain: Mathematical generalisation in a group of low attainers. Nordisk Matematikk Didaktikk (Nordic Studies in Mathematics Education), 8(1), 7-22.
39. Watson, A., & Mason, J. (1998). Questions and prompts for mathematical thinking. Derby, Leicestershire, England: Association of Teachers of Mathematics.
40. Watson, A., & Mason, J. (2004, June). The exercise as mathematical object: Dimensions of possible variation in practice. Proceedings of British Society for Research in the Learning of Mathematics, Leeds, England.
41. Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: The role of learner-generated examples. Mahwah, NJ: Lawrence Erlbaum Associates.
42. Whitehead, A. (1948). An introduction to mathematics. London: Oxford University Press. (Original work published 1911)
43. Zazkis, R. (1999). Intuitive rules in number theory: Examples of "the more of A, the more of B" rule implementation. Educational Studies in Mathematics, 40, 197-209.
44. Zazkis, R., & Gadowsky, K. (2001). Attending to transparent features of opaque representations of natural numbers. In A. Cuoco (Ed.), The roles of representation in school mathematics (pp. 146-165). Reston, VA: NCTM.