Metaphor or Met-Before? The effects of previouos experience on practice and theory of learning mathematics
Tài liệu tham khảo
Ashcraft, 2001, The relationships among working memory, math anxiety and performance, Journal of Experimental Psychology: General, 130, 224, 10.1037/0096-3445.130.2.224
Ausubel, 1968
Bachelard, G. (1938, reprinted 1983). La Formation de l’esprit Scientifique, J. Vrin. Paris, France.
Black, 1998, Inside the black box: Raising standards through classroom assessment, Phi Delta Kappan, 80, 139
Behr, 1992, Rational number, ratio, and proportion, 308
Betz, 1978, Prevalence, distribution, and correlates of math anxiety in college students, Journal of Counselling Psychology, 25, 441, 10.1037/0022-0167.25.5.441
Bright, 2003
Brousseau, 1983, Les obstacles épistémologiques et les problèmes en mathématiques, Recherches en didactique des Mathématiques, 4, 164
Burns, 1998
Byers, 2007
Davis, 2007, Formative feedback and the mindful teaching of mathematics, The Australian Senior Mathematics Journal, 21, 19
DeMarois, P. (1998). Facets and layers of function for college students in beginning algebra. Ph.D. Dissertation, University of Warwick, Coventry, UK.
Fauconnier, 2002
Fischbein, 1985, The role of implicit models in solving verbal problems in multiplication and division, Journal for Research in Mathematics Education, 16, 3, 10.2307/748969
Gray, 1994, Duality, ambiguity, and flexibility: A “proceptual” view of simple arithmetic, Journal for Research in Mathematics Education, 25, 116, 10.2307/749505
Hadamard, 1945
Jones, 2001, Applying psychology to the teaching of basic math: A case study, Inquiry, 6, 60
Lakoff, 2000
McGowen, M. A. (1998). Cognitive units, concept images, and cognitive collages: An examination of the process of knowledge construction. Ph.D. Dissertation, University of Warwick, Coventry, UK.
McGowen, M. A. (2006). Developmental algebra: In Nancy B.-H. (Ed.), MAA Notes 69: A fresh start for collegiate mathematics (pp. 369–375).
McGowen, 2001, Changing pre-service elementary teachers’ attitudes to algebra
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA.
Skemp, 1987
Skemp, 1979
Sowder J. (2000). Mathematics in the middle grades: Linking research and practice. Invited plenary address. In National conference on curriculum, instruction, and assessment in the middle grades: Linking research and practice (pp. 3–4). Sponsored by the National Educational Research Policy and Priorities Board, U.S. Department of Education.
Sowder, 1988, Capturing the major themes, 1
Takagi, 1903, A simple example of the continuous function without derivative, Proceedings of the Physico-Mathematical Society of Japan, 1, 176
Tall, 1982, The blancmange function, continuous everywhere but differentiable nowhere, Mathematical Gazette, 66, 11, 10.2307/3617301
Tall, 1985, Understanding the calculus, Mathematics Teaching, 110, 49
Tall, 1993, Real mathematics rational computers and complex people, 243
Tall, 2004, The three worlds of mathematics, For the Learning of Mathematics, 23, 29
Tall, 2008, The transition to formal thinking in mathematics, Mathematics Education Research Journal, 20, 5, 10.1007/BF03217474
Tall, 2009, Dynamic mathematics and the blending of knowledge structures in the calculus, ZDM: The International Journal on Mathematics Education, 41, 481, 10.1007/s11858-009-0192-6
Tall, 2000, The function machine as a cognitive root for the function concept, 255
Tobias, 1978