数学的知識の二重性に関わる文献リスト
- Ali, M. B. & Tall, D. (1996). Procedural and conceptual aspects of standard algorithms in calculus. In L. Puig & A. Gurierrez (Eds.), Proceedings of the 20th International Conference for the Psychology of Mathematics Education (vol. II, pp. 19-26). Valencia, Spain.
- Arnon, I., Dubinsky, E., Nesher, P. (1994). Actions which can be performed in the learner's imagination. In J. P. Ponte & J. F. Matos (Eds.), Proceeding of the 18th International Conference for the Psychology of Mathematics Education (vol. III, pp. 32-39). Lisbon, Portugal.
- Coady, C. (1995). Students' responses utilising the procedural and structural aspects of algebra. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th International Conference for the Psychology of Mathematics Education (Vol. II, pp. 50-57). Brazil.
- Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Dordrecht: Kluwer.
- Ferrari, P. L. (1996). On some factors affecting advanced algebraic problem solving. In L. Puig & A. Gurierrez (Eds.), Proceedings of the 20th International Conference for the Psychology of Mathematics Education (vol. II, pp. 345-352). Valencia, Spain.
- Foster, R. (1994). Counting on success in simple addition tasks. In J. P. Ponte & J. F. Matos (Eds.), Proceeding of the 18th International Conference for the Psychology of Mathematics Education (vol. III, pp. 360-367). Lisbon, Portugal.
- Garancon, M., Kieran, C., & Boileau, A. (1993). Using a discrete computer graphing environment in algebra problem solving: Notinos of infinity / continuity. In I. Hirabayashi et al. (Eds.), Proceedings of the 17th International Conference for the Psychology of Mathematics Education (Vol. II, pp. 25-32). Tsukuba, Japan.
- Goodson-Epsy, T. (1998). The roles of reification and reflective abstraction in the development of abstract thought: Transition from arithmetic to algebra. Educational Studies in Mathematics, 36 (3), 219-245.
- Gray, E. (1993). Count-on: The parting of the ways for simple arithmetic. In I. Hirabayashi et al. (Eds.), Proceedings of the 17th International Conference for the Psychology of Mathematics Education (Vol. I, pp. 204-211). Tsukuba, Japan.
- Gray, E., Pinto, M., Pitta, D., & Tall, D. (1999). Knowledge construction and diverging thinking in elementary advanced mathematics. Educational Studies in Mathematics, 38, 111-133.
- Gray, E. & Pitta, D. (1996). Number processing: Qualitative differences in thinking and the role of imagery. In L. Puig & A. Gurierrez (Eds.), Proceedings of the 20th International Conference for the Psychology of Mathematics Education (vol. III, pp. 35-42). Valencia, Spain.
- Gray, E. M. & Tall, D. O. (1993). Success and failure in mathematics: The flexible meaning of symbols as process and concept. Mathematics Teaching, 142, 6-10.
- Gray, E. M. & Tall, D. O. (1994). Duality, ambiguity, and flexibility: A "proceptual" view of simple arithmetic. Journal for Research in Mathematics Education, 25 (2), 116-140.
- Harel, G. & Dubinsky, E. (1991). The development of the concept of function by preservice secondary teachers: From action conception to process conception. In F. Furinghetti (Ed.), Proceedings of the 15th International Conference for the Psychology of Mathematics Education (vol. II, pp. 133-140). Assisi, Italy.
- Harel, G. & Kaput, J. J. (1990). The role of conceptual entities in learning mathematical concept at the undergraduate level. Proceedings of the 14th International Conference for the Psychology of Mathematics Education (vol. 1, pp. 53-60). Mexico.
- Harel, G. & Kaput, J. J. (1991). The role of conceptual entities and their symbols in building advanced mathematical concept. In D. Tall (Ed.), Advanced mathematical thinking (pp. 82-94). Dordrecht: Kluwer.
- Hunter, M. & Monaghan, J. (1996). Some issues in assessing proceptual understanding. In L. Puig & A. Gurierrez (Eds.), Proceedings of the 20th International Conference for the Psychology of Mathematics Education (vol. III, pp. 97-104). Valencia, Spain.
- 井上芳文. (1998). 数学的概念の認識における二面性に関する考察(4):指導原理の関数における適用可能性について. 全国数学教育学会誌, 4, 187-195.
- Kieran, C. (1991). A procedural-structural perspective on algebra research. In F. Furinghetti (Ed.), Proceedings of the 15th International Conference for the Psychology of Mathematics Education (vol. 2, pp. 245-254). Assisi, Italy.
- Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 380-419). New York, NY: Macmillan.
- Kieran, C. (1994). A functional approach to the introduction of algebra: Some pros and cons. In J. P. Ponte & J. F. Matos (Eds.), Proceeding of the 18th International Conference for the Psychology of Mathematics Education (vol. I, pp. 157-175). Lisbon, Portugal.
- Kutscher, B. (1996). Application of reification thoery in translating verbal expressions and statements into algebraic expressions. In L. Puig & A. Gurierrez (Eds.), Proceedings of the 20th International Conference for the Psychology of Mathematics Education (vol. III, pp. 201-208). Valencia, Spain.
- Li, L. & Tall, D. (1993). Constructing different concept image of sequences & limits by programming. In I. Hirabayashi et al. (Eds.), Proceedings of the 17th International Conference for the Psychology of Mathematics Education (Vol. II, pp. 41-48). Tsukuba, Japan.
- Linchevski, L. & Sfard, A. (1991). Rules without reasons as processes without objects: The case of equations and inequalities. In F. Furinghetti (Ed.), Proceedings of the 15th International Conference for the Psychology of Mathematics Education (vol. 2, pp. 317-324). Assisi, Italy.
- Linchevski, L. & Willams, J. (1996). Situated intuitions, concrete manipulations and the construction of mathematical concepts: The case of integers. In L. Puig & A. Gurierrez (Eds.), Proceedings of the 20th International Conference for the Psychology of Mathematics Education (vol. III, pp. 265-272). Valencia, Spain.
- 牧野眞裕. (1996). 文字式に関する認知的ギャップについての一考察. 日本数学教育学会第29回数学教育論文発表会論文集, 37-42.
- Mesa, V.-M. & Gomez, P. (1996). Graphing calculators and pre-calculus: An exploration of some aspects of students' understanding. In L. Puig & A. Gurierrez (Eds.), Proceedings of the 20th International Conference for the Psychology of Mathematics Education (vol. III, pp. 391-398). Valencia, Spain.
- Monaghan, J., Shyashiow, S., & Tall, D. (1994). Construction of the limit concept with a computer algebra system. In J. P. Ponte & J. F. Matos (Eds.), Proceeding of the 18th International Conference for the Psychology of Mathematics Education (vol. III, pp. 279-286). Lisbon, Portugal.
- 森本明, 江森英世. (1999). 数学的概念の構造的意味の伝達に伴う二重の困難性. 科学教育研究, 23 (5), 357-364.
- 布川和彦. (1995, 11月). 数学の知識の二重性:文字式を例として. 教育科学数学教育, 456, 102-105.
- Schwingendorf, K., Hawks, J., & Beineke, J. (1992). Horizontal and vertical growth of the students' conception of function. In G. Harel & E. Dubinsky (Eds.),The concept of function: Aspects of epistemology and pedagogy (pp. 133-149). Wahington, DC: Mathematical Association of America.
- Sfard, A. (1987). Two conceptions of mathematical notions: Operational and structural. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th International Conference for the Psychology of Mathematics Education. Montreal, Canada.
- Sfard, A. (1988). Operational versus structural methods of teaching mathematics: A case study. Proceedings of the 12th International Conference for the Psychology of Mathematics Education. Budapest, Hyngary.
- Sfard, A. (1989). Transition from operational to structural conception: The notion of function revisited. In G. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th International Conference for the Psychology of Mathematics Education. Paris, University of Paris.
- Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects on different sides of the same coin. Educational Studies in Mathematics, 22 (1), 1-36.
- Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification: the case of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 59-84). Wahington, DC: Mathematical Association of America.
- Sfard, A. (1994). Reification as the birth of metaphor. For the Learning of Mathematics, 14 (1), 44-55.
- Sfard, A. (1995). The development of algebra. Journal of Mathematical Behavior, 14, 15-39.
- Sfard, A. & Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191-228.
- 清水宏幸. (1997). 中学校数学における文字式の理解に関する研究:文字式をひとまとまりと見ることの困難性に焦点をあてて. 日本数学教育学会第30回数学教育論文発表会論文集, 247-252.
- Slavitt, D. (1997). An alternative route to the reification of function. Educational Studies in Mathematics, 33 (3), 259-282.
- 横田 誠. (1995). 文字式の二元性 (duality) に関する研究. 数学教育研究 (上越教育大学数学教室), 10, 133-142.