The math teachers know: Profound understanding of emergent mathematics

The Math Teachers Know: Profound Understanding of Emergent Mathematics

Volumn , Issue , 2013, Pages 1-141

  Davis, Brent ^a   Renert, Moshe ^b  

^a UNIVERSITY OF CALGARY   (Canada)

^b NONE   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84917173235     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203797044     Document Type: Book

References (117)

1. Adler, J., & Davis, Z. (2006) Opening another black box: research mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(4), 270–296.
2. Ainsworth, S. (1999) The functions of multiple representations. Computers & Education, 33, 131–152.
3. Ainsworth, S., & van Lebeke, N. (2004) Multiple forms of dynamic representation. Learning and Instruction, 14, 235–357.
4. Arnold, V.I. (1997 March 7) Discussion on the teaching of mathematics. Paris, FR: Palais de Découverte.
5. Baker, S. (2008) The numerati. Boston: Houghton Mifflin.
6. Ball, D.L., & Bass, H. (2000) Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport, CT: Ablex.
7. Ball, D.L., & Bass, H. (2003) Toward a practice-based theory of mathematical knowledge for teaching. In E. Simmt & B. Davis (Eds), Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 3–14). Edmonton, AB: CMESG/GCEDM.
8. Ball, D.L., Blömkeke, S., Delaney, S., & Kaiser, G. (Eds) (2102) Measuring teacher knowledge – approaches and reselts from a cross-national perspective. Special issue of ZDM: The International Journal of Mathematics Education, 44(3).
9. Ball, D.L., Hill, H.C., & Bass, H. (2005) Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, Fall, 14–46.
10. Ball, D.L., Lubienski, S.T., & Mewborn, D.S. (2001) Research on teaching mathematics: the unsolved problem of teachers’ mathematical knowledge in V. Richardson (Ed.), Handbook of research on teaching (pp. 433–456). Washington, DC: American Educational Research Association.
11. Ball, D.L., Thames, M.H., & Phelps, G. (2008) Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389–407.
12. Bauerserfeld, H. (1992) Integrating theories for mathematics education. for the Learning of Mathematics, 12(2), 19–28.
13. Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., Tsai, Y. (2010) Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47, 133–180.
14. Begle, E.G. (1972) SMSG Reports No. 9: Teacher knowledge and student achievement in algebra. Palo Alto, CA: Stanford University.
15. Begle, E.G. (1979) Critical variables in mathematics education: findings from a survey of the empirical literature. Washington, DC: Mathematical Association of American and National Council of Teachers of Mathematics.
16. Bejan, A., & Zane, J.P. (2012) Design in nature: how the constructal law governs evolution in biology, physics, technology, and social organization. New York: Doubleday.
17. Brousseau, G. (1997) Theory of didactical situations in mathematics: didactiques des mathématiques, 1970–1990. (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Trans.). Dordrecht, NL: Kluwer.
18. Brunner, M., Kunter, M., Krauss, S., Klusmann, U., Baumert, J., Blum, W., et al. (2006) Die professionalle kompetenz von Mathematiklehrkräften: Konzeptualisierung, erfassung und bedeutung für den unterricht. Eine zwischenbilanz des COACTIVE-Projekts. In M. Prenzel & L. Allolio-Näcke (Eds), Untersuchungen zur Bildungsqualität von Schule (pp. 54–83). Münster, DE: Waxmann.
19. Bruner, J. (1966) Toward a theory of instruction. Cambridge, MA: Harvard University Press.
20. Burger, E.B., & Starbird, M. (2005) The heart of mathematics: an invitation to effective thinking (2nd edn.). Emeryville, CA: Key College Publishing
21. Capra, F. (2002) The hidden connections. London: HarperCollins.
22. Chase, W.G., & Simon, H.A. (1973) The mind’s eye in chess. In W. G. Chase (Ed.), Visual information processing (pp. 215–281). New York: Academic Press.
23. Cobb, P. (1994) Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13–20.
24. Cobb, P. (1999) Individual and collective mathematics development: the case of statistical data analysis. Mathematics Thinking and Learning, 1(1), 5–43.
25. Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992) Characteristics of classroom mathematics traditions: an interactional analysis. American Educational Research Journal, 29, 573–604.
26. Cooney, T.J., & Wilson, M.R. (1993) Teachers’ thinking about functions; historical and research perspectives. In T. Romberg, E. Fennema, & T. Carpenter (Eds), Integrating research on the graphical representation of function (pp. 131–158). Hillsdale, NJ: Erlbaum.
27. Davidson, N. (2011) Now you see it: how the brain science of attention will transform the way we live, work, and learn. New York: Viking.
28. Davis, B. (1989) Meaningful talk in the mathematics classroom. Unpublished master’s thesis. Edmonton, AB: University of Alberta.
29. Davis, B. (1994) Mathematics teaching: moving from telling to listening. Journal of Curriculum and Supervision, 9(3), 267–283.
30. Davis, B. (1996) Teaching mathematics: toward a sound alternative. New York: Garland Publishing.
31. Davis, B. (1997) Listening for differences: an evolving conception of mathematics teaching. Journal for Research in Mathematics Education, 28(3), 355–376.
32. Davis, B. (2008) Is 1 a prime number? Developing teacher knowledge through concept study. Mathematics Teaching in the Middle School, 14(2), 86–91.
33. Davis, B. (2011) Mathematics teachers’ subtle, complex disciplinary knowledge. Science, 332, 1506–1507.
34. Davis, B., & Renert, M. (2009) Mathematics for teaching as shared, dynamic participation. for the Learning of Mathematics, 29(3), 37–43.
35. Davis, B., & Renert, M. (2012) Profound understanding of emergent mathematics: broadening the construct of teachers’ disciplinary knowledge. Educational Studies in Mathematics, 82, 245–265.
36. Davis, B., & Simmt, E. (2003) Understanding learning systems: Mathematics teaching and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.
37. Davis, B., & Simmt, E. (2006) Mathematics-for-teaching: an ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61(3), 293–319.
38. Davis, B., & Sumara, D. (2006) Complexity and education: inquiries into learning, teaching, and research. Mahwah, NJ: Lawrence Erlbaum Associates.
39. Davis, B., Sumara, D., & Luce-Kapler, R. (2008) Engaging minds: changing teaching in complex times (2nd edn.). New York: Routledge.
40. Davis, P.J., & Hersh, R. (1986) Descartes’ dream: the world according to mathematics. Boston: Houghton Mifflin.
41. Deacon, T.W. (1997) The symbolic species: the co-evolution of language and the human brain. New York: W.W. Norton
42. diSessa, A.A. (2004) Metarepresentation: native competence and targets for instruction. Cognition and Instruction, 22(3), 293–331.
43. Dweck, C.S. (2006) Mindset: the new psychology of success. New York: Random House.
44. English, L. (Ed.) (1997) Mathematical reasoning: analogies, metaphors, and images Hillsdale, NJ: Erlbaum.
45. Ericsson, K.A., Charness, N., Feltovich, P., & Hoffman, R.R., (2006) Cambridge handbook on expertise and expert performance. Cambridge, UK: Cambridge University Press.
46. Even, R. (1998) Factors involved in linking representations of function. Journal of Mathematical Behavior, 17(1), 105–121.
47. Even, R., & Li, Y. (Eds) (2011) Approaches and practices in developing teachers’ expertise in mathematics instruction. Special issue of ZDM: The International Journal of Mathematics Education, 43(6–7).
48. Even, R., & Tirosh, D. (2002) Teacher knowledge and understanding of students’ mathematical learning. In L.D. English (Ed.), Handbook of International Research in Mathematics Education (pp. 219–240). Mahwah, NJ: Lawrence Erlbaum Associates.
49. Fauconnier, G., & Turner, M. (2003) The way we think: cnceptual blending and the mind’s hidden complexities. New York: Basic Books.
50. Fauvel, J., & van Maanen, J. (Eds) (2000) History in mathematics education: the 10th ICME study. Dordrecht, NL: Kluwer.
51. Fernandez, C., & Yoshida, M. (2004) Lesson study: a Japanese approach to improving mathematics teaching and learning. Mahwah, NJ: Erlbaum.
52. Fischbein, E. (1989) Tacit models and matheamtical reasoning. for the Learning of Mathematics, 9(2), 9–14.
53. Fischbein, E. (1993) The theory of figural concepts. Educational Studies in Mathematics, 24, 129–162.
54. Foote, R. (2007) Mathematics and complex systems. Science, 318, 410–412.
55. Freudenthal, H. (1983) Didactical phenomenology of mathematical structures. Dordrecht, NL: D. Reidel.
56. Gibbs, Jr., R.W., & Colston, H.L. (2007) Irony in language and thought: a cognitive science reader. New York: Routledge.
57. Gick, M.L., & Holyoak, K.J. (1983) Schema induction and analogical transfer. Complexity and Organization, 1(1), 49–72.
58. Goldin, G.A., & Janvier, C. (Eds) (1998) Representations and the psychology of mathematics education, Parts I and II (special issues). Journal of Mathematical Behavior, 17(1 & 2).
59. Goldstein, J. (1999) Emergence as a construct: history and issues. Emergence: Complexity and Organization 1(1), 49–72.
60. Gowers, T. (2002) Mathematics: a very short introduction. New York: Oxford University Press.
61. Greer, B. (1994) Extending the meaning of multiplication and division. In G. Harel & J. Confrey (1994), The development of multiplicative reasoning in the learning of mathematics (pp. 61–87). Albany, NY: State University of New York Press.
62. Harel, G., & Confrey, J. (Eds) (1994) The development of multiplicative reasoning in the learning of mathematics Albany, NY: State University of New York Press.
63. Harel, G., & Dubinsky, E. (Eds). (1992) The concept of function; aspects of epistemology and pedagogy. MAA Notes, no. 28.
64. Hattie, J. (2009) Visible learning: a synthesis of over 800 meta-analyses relating to achievement. New York: Routledge
65. Hiebert, J., Gallimore, R., Garnier, H., Bogard Givvin, K., Hollingsworth, H., Jacobs, J., Miu-Ying Chui, A., Wearne, D., Smith, M., Kersting, N., Manaster, A., Tseng, E., Etterbeek, W., Manaster, E., Gonzales, P., & Stigler, J.W. (2003) Teaching mathematics in seven countries: the results of the TIMSS 1999 Video Study. Washington, DC: National Center for Education Statistics. Department of Education.
66. Hill, H., Ball, D.L., & Schilling, S. (2008) Unpacking “pedagogical content knowledge”: conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.
67. Hill, H.C., Rowan, B., & Ball, D.L. (2005) Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.
68. Hitt, F. (1998) Difficulties in the articulation of different representations linked to the concept of function. Journal of Mathematical Behavior, 17(1), 123–134.
69. Janvier, C. (Ed.) (1987) Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
70. Jenkins, H., Clinton, K., Purushotma, R., Robison, A. J., & Weigel, M. (2006) Confronting the challenges of participatory culture: Media education for the 21st century. Available at www.digitallearning.macfound.org/atf/cf/%7B7E45C7E0- A3E0-4B89-AC9C-E807E1B0AE4E%7D/jenkins_white_paper, pdf
71. Johnson, S. (2001) Emergence: the connected lives of ants, brains, cities, and software. New York: Scribner.
72. Kahneman, D. (2011) Thinking, fast and slow. New York: Farrar, Straus and Giroux.
73. Kieran, C. (2001) The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges. Educational Studies in Mathematics, 46, 187–228.
74. Kieren, T.E. (2000) Dichotomies or binoculars: reflections on the papers by Steffe and Thompson and by Lerman. Journal for Research in Mathematics Education, 31, 228–233.
75. Kilpatrick, J., Swafford, J., & Findell, B. (2001) Adding it up: helping children learn mathematics. Washington, DC: National Academy Press.
76. Lakoff, G., & Johnson, M. (1999) Philosophy in the flesh: the embodied mind and its challenge to western thought. New York: Basic Books.
77. Lakoff, G., & Núñez, R. (2000) Where mathematics comes from: how the embodied mind brings mathematics into being. New York: Basic Books.
78. Leinhardt, G. (1989) Math lessons: a contrast of novice and expert competence. Journal for Research in Mathematics Education, 20(1), 52–75.
79. Leinhardt, G., Putnam, R., & Hattrup, R.A. (1992) Analysis of arithmetic for mathematics teaching. Hillsdale, NJ: Lawrence Erlbaum Associates.
80. Lesh, R., Post, T., & Behr, M. (1987) Representations and translations among representations in matheamtics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33–40). Hillsdale, NJ: Lawrence Erlbaum Associates.
81. Ma, L. (1999) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
82. Marton, F. & Säljö, R (1976a) On qualitative differences in learning – 1: outcome and process. British Journal of Educational Psychology, 46, 4–11.
83. Marton, F. & Säljö, R (1976b) On qualitative differences in learning – 2: outcome as a function of the learner’s conception of the task. British Journal of Educational Psychology, 46, 115–127.
84. Mazur, B. (2003) Imagining numbers (particularly the square root of minus fifteen). New York: Farrar Straus Giroux.
85. Mewborn, D. (2001) Teachers’ content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States. Mathematics Education Research Journal, 3, 28-36.
86. Mitchell, M. (2009) Complexity: a guided tour. Oxford, UK: Oxford University Press.
87. Monk, D.H. (1994) Subject area preparation of secondary mathematics and science teachers and student achievement. Economics of Education Review, 13(2), 125–145.
88. NCTM (National Council of Teachers of Mathematics). (1989) Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
89. NCTM (National Council of Teachers of Mathematics). (2000) Principles and standards for school mathematics. Reston, VA: NCTM.
90. Peterson, L.G. (1996) Mathematics: grade 1, part 2. Moscow: Yuventa.
91. Pirie, S.E.B., & Kieren, T.E. (1994) Growth in mathematical understanding: how can we characterize it and how can we represent it? Educational Studies in Mathematics, 26, 165–190.
92. Polanyi, KM. (1966) The tacit dimension. New York: Doubleday.
93. Presmeg, N.C. (1986) Visualization in high school mathematics. for the Learning of Mathematics, 6(3), 42–46.
94. Renert, M., & Davis, B. (2010a) An open way of being: Integral reconceptualization of mathematics for teaching. In Esbjörn-Hargens, S., Reams, J. & Gunnlaugson, O. (Eds), Integral education: New directions for higher learning (pp.193-215). Albany, NY: SUNY Press
95. Renert, M., & Davis, B. (2010b) Life in mathematics: evolutionary perspectives on subject matter. In Walshaw, M. (Ed.), Unpacking pedagogy: new perspectives for mathematics classrooms (pp. 177-200). Charlotte, NC: Information Age.
96. Richland, L.E., Morrison, R.G., & Holyoak, K.J. (2006) Children’s development of analogical reasoning: Insights from scene analogy problems. Journal of Experimental Child Psychology, 94, 249–273.
97. Rowland, T., & Ruthven, K. (Eds) (2011) Mathematical knowledge in teaching. Dordrecht, NL: Springer.
98. Scardamalia, M., & Bereiter, C. (2003) Knowledge building. In J.W. Guthrie (Ed.), Encyclopedia of Education. 2nd edition. New York: Macmillan Reference.
99. Schoenfeld, A.H. (1985) Mathematical problem solving. New York: Academic Press.
100. Schoenfeld, A.H., Herrmann, D.J. (1982) Problem perception and knowledge structure in expert and novice mathematical problem solvers. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8(5), 484–494.
101. Seufert, T. (2003) Supporting coherence formation in learning from multiple representations. Learning and Instruction, 13, 227–237.
102. 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, 1–36.
103. Sfard, A. (2008) Thinking as communicating: human development, the growth of discourses, and mathematizing. New York: Cambridge University Press.
104. Sfard, A., & Kieran, C. (2001) Cognition as communication: rethinking learningby- talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture, and Activity, 8(1), 42–76.
105. Shulman, L.S. (1986) Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
106. Surowiecki, J. (2004) The wisdom of crowds. New York: Doubleday.
107. Tall, D.O. (2004) Thinking through three worlds of mathematics, Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergen, Norway, vol. 4, 281–288.
108. Usiskin, Z., Peressini, A., Marchisotto, E.A., & Stanley, D. (2003) Mathematics for high school teachers: an advanced perspective. Upper Saddle River, NJ: Pearson
109. Van de Walle, J., Karp, K.S., & Bay-Williams, J.M. (2012) Elementary and middle school mathematics: teaching developmentally (8th edn.). Upper Saddle River, NJ: Pearson.
110. von Glasersfeld, E. (1990) An exposition of constructivism: why some like it radical. In R.B. Davis, C.A. Maher, & N. Noddings (Eds), Constructivist views on the teaching and learning of mathematics (pp. 19–29). Reston, Virginia: National Council of Teachers of Mathematics.
111. Waldrop, M.M. (1992) Complexity: the emerging science on the edge of order and chaos. New York: Simon & Schuster.
112. Wilber, K. (1995) Sex, ecology, spirituality: The spirit of evolution. Boston: Shambhala
113. Wilber, K. (2006) Integral spirituality: A startling new role for religion in the modern and postmodern world. Boston: Integral Books.
114. Wilson, S.M., Floden, R.E., & Ferrini-Mundy, J. (2002) Teacher preparation research: an insider’s view from the outside. Journal of Teacher Education, 53(3), 190–204.
115. Zack, V., & Graves, B. (2001) Making mathematical meaning through dialogue: once you think of it, the z minus three seems pretty weird. Educational Studies in Mathematics, 46, 229–271.
116. Zazkis, R. (2011) Relearning mathematics: a challente for prospective elementary school teachers. Charlotte, NC: Information Age Publishing.
117. Zook, K.B. (1991) Effects of analogical processes on learning and misrepresentation. Educational Psychology Review, 3, 41–72.