A research framework for creative and imitative reasoning
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Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergratduate mathematics education. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education II, CBMS issues in mathematics education (pp. 1–32). American Mathematical Society.
Balacheff, N. (1988). Aspects of proof in pupils practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216–235). London: Hodder and Stoughton.
Balacheff, N. (1990). Towards a problematique for research on mathematics teaching. Journal for Research in Mathematics Education, 21(4), 258–272.
Ball, D., & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 27–44). Reston, VA: National Council of Teachers of Mathematics.
Bergqvist, T., & Lithner, J. (2005). Simulating creative reasoning in mathematics teaching. Research Reports in Mathematics Education 2, Dept. of Mathematics, Umeå University.
Bergqvist, T., Lithner, J., & Sumpter, L. (2007). Upper secondary students task reasoning. International Journal of Mathematical Education in Science and Technology (in press).
Bloom, B. S. (Ed.) (1956). Taxonomy of Educational Objectives, Part 1: The Cognitive Domain. New York: David McKay.
Boesen, J., Lithner, J., & Palm, T. (2005). The mathematical reasoning required by national tests and the reasoning actually used by students. Research Reports in Mathematics Education 4, Dept. of Mathematics, Umeå University.
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.
Churchman, C. W. (1971). The design of inquiring systems: Basic concepts of system and organization. New York: Basic Books.
Doyle, W. (1988). Work in mathematics classes: The context of students thinking during instruction. Educational Psychologist, 23, 167–180.
Duval, R. (2002). Proof understanding in mathematics: What ways for students? Proceedings of 2002 international conference on mathematics: Understanding proving and proving to understand (pp. 61–77).
Ernest, P. (1999). Forms of knowledge in mathematics and mathematics education: Philosophical and rhetorical perspectives. Educational Studies in Mathematics, 38(1), 67–83.
Fischbein, E. (1999). Intuitions and schemata in mathematical reasoning. Educational Studies in Mathematics, 38(1), 11–50.
Harel, G. (2006). Mathematics education research, its nature and its purpose: A discussion of Lester’s paper. Zentralblatt fuer Didaktik der Mathematik, 38(1), 58–62.
Haylock, D. (1997). Recognising mathematical creativity in schoolchildren. Zentralblatt fuer Didaktik der Mathematik, 29(3), 68–74.
Hegarty, M., Mayer, R., & Monk, C. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18–32.
Hiebert, J. (2003). What research says about the NCTM Standards. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A Research companion to principles and standards for school mathematics (pp. 5–26). Reston, VA: National Council of Teachers of Mathematics.
Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 65–97). New York: Macmillan.
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge (pp. 1–27). Hillsdale, NJ: Erlbaum.
Huckstep, P., & Rowland, T. (2000). Creative mathematics – real or rhetoric? Educational Studies in Mathematics, 42(1), 81–100.
Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229–269). Hillsdale, NJ: Erlbaum.
Leron, U., & Hazzan, O. (1997). The world according to Johnny: A coping perspective in mathematics education. Educational Studies in Mathematics, 32, 265–292.
Lester, F. (2005). On the theoretical, conceptual, and philosophical foundations for research in mathematics education. Zentralblatt fuer Didaktik der Mathematik, 37(6), 457–467.
Lithner, J. (2000a). Mathematical reasoning and familiar procedures. International Journal of Mathematical Education in Science and Technology, 31, 83–95.
Lithner, J. (2000b). Mathematical reasoning in task solving. Educational Studies in Mathematics, 41, 165–190.
Lithner, J. (2002). Lusten att lära, Osby (The motivation to learn, Osby). Skolverkets nationella kvalitetsgranskningar (Quality inspections of the Swedish National Agency for Education), in Swedish.
Lithner, J. (2003). Students mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52, 29–55.
Lithner, J. (2004). Mathematical reasoning in calculus textbook exercises. Journal of Mathematical Behavior, 23, 405–427.
Långström, P., & Lithner, J. (2007). Students learning strategies and mathematical reasoning in textbook-related metacognitive processes (in press).
McGinty, R., VanBeynen, J., & Zalewski, D. (1986). Do our mathematics textbooks reflect what we preach? School Science and Mathematics, 86, 591–596.
Monaghan, J., & Ozmantar, M. (2006). Abstraction and consolidation. Educational Studies in Mathematics, 62(3), 233–258.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: The Council.
Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. Third Mediterranean conference on mathematics education (pp. 115–124).
Palm, T., Boesen, J., & Lithner, J. (2005). The requirements of mathematical reasoning in upper secondary level assessments. Research Reports in Mathematics Education 5, Dept. of Mathematics, Umeå University.
Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26, 165–190.
Pólya, G. (1954). Mathematics and plausible reasoning (Vols. I and II). Princeton, NJ: Princeton University Press.
Schoenfeld, A. (1985). Mathematical problem solving. Orlando, FL: Academic.
Schoenfeld, A. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. Voss, D. Perkins, & J. Segal (Eds.), Informal reasoning and education (pp. 311–344). Hillsdale, NJ: Erlbaum.
Schoenfeld, A. (2007). Method. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 69–107). Charlotte, NC: Information Age Publishing.
Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4–36.
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.
Sierpinska, A. (1996). Understanding in mathematics. Routledge: Falmer.
Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt fuer Didaktik der Mathematik, 29(3), 75–80.
Skemp, R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9–15.
Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34.
Stacey, K., & MacGregor, M. (1999). Taking the algebraic thinking out of algebra. Mathematics Education Research Journal, 11, 24–38.
Tall, D. (1991). Reflections. In D. Tall (Ed.), Advanced mathematical thinking (pp. 251–259). Dordrecht: Kluwer.
Tall, D. (1996). Functions and calculus. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 289–325). Dordrecht: Kluwer.
Tall, D. (2004). Thinking through three worlds of mathematics. In M. J. Høines & A. B. Fuglestad (Eds.), 28th Conference of the international group for the psychology of mathematics education. vol. 4 (pp. 281–288). Bergen.
van Hiele, P. (1986). Structure and insight. A theory of mathematics education. Orlando: Academic.
Vinner, S. (1997). The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Educational Studies in Mathematics, 34, 97–129.
Wedege, T., & Skott, J. (2006). Changing views and practices? A study of the Kapp-Abel mathematics competition. Trondheim: NTNU.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.
Yackel, E., & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 227–236). Reston, VA: National Council of Teachers of Mathematics.