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HISTORY AS A PLATFORM FOR DEVELOPING COLLEGE STUDENTS’ EPISTEMOLOGICAL BELIEFS OF MATHEMATICS

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Abstract

The present study observed how Taiwanese college students’ epistemological beliefs about mathematics evolved during a year-long historical approach calculus course. On the basis of the characteristics of initial accounts, seven students were invited to participate in this study and were divided into two groups. An open-ended questionnaire, mathematics biographies, in-class reports, and follow-up semi-structured interviews served as instruments for identifying their epistemological beliefs. Furthermore, four randomly selected students from another calculus class constituted the control group. Results indicated that most of the students receiving this course exhibited relatively significant changes in their epistemological beliefs of mathematics, but trends and extents in their epistemological development varied across groups as well as individuals. This study identifies the potential relationships among the course features, initial beliefs, and the tendency of belief development, followed by a discussion of the mechanism of belief change and an afterthought on HPM approach.

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References

  • Ball, D.L. (2000). Working on the inside: using one’s own practice as a site for studying teaching and learning. In A.E. Kelly & R.A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 365–402.) Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Baxter-Magolda, M.B. (2004). Evolution of a constructivist conceptualisation of epistemological reflection. Educational Psychologist, 39(1), 31–42.

    Article  Google Scholar 

  • Bendixen, L.D. & Rule, D.C. (2004). An integrative approach to personal epistemology: a guiding model. Educational Psychologist, 39(1), 69–80.

    Article  Google Scholar 

  • Beth, E.W. & Piaget, J. (1966). Mathematical epistemology and psychology. Dordrecht: D. Reidel Publishing Company.

    Google Scholar 

  • Butterfield, H. (1931). The Whig interpretation of history. London: G. Bell and Sons.

    Google Scholar 

  • Carlson, M.P. (1999). The mathematical behavior of six successful mathematics graduate students: influences leading to mathematical success. Educational Studies in Mathematics, 40(3), 237–258.

    Article  Google Scholar 

  • Dennis, D. (2000). The role of historical studies in mathematics and science educational research. In D. Lesh & A. Kelly (Eds.), Research design in mathematics and science education. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Fried, M. (2001). Can mathematics education and history of mathematics coexist? Science and Education, 10, 391–408.

    Article  Google Scholar 

  • Furinghetti, F. & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G.C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: a hidden variable in mathematics education? (pp. 39–58. ) Dordrecht: Kluwer.

    Google Scholar 

  • Garofalo, J. & Lester, F.K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176.

    Article  Google Scholar 

  • Glas, E. (1998). Fallibilism and the use of history in mathematics education. Science and Education, 7, 361–379.

    Article  Google Scholar 

  • Grugnetti, L. & Rogers, L. (2000). Philosophical, multicultural and interdisciplinary issues. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education (pp. 39–62.) Dordrecht: Kluwer.

    Google Scholar 

  • Hofer, B. (1999). Instructional context in the college mathematics classroom: epistemological beliefs and student motivation. Journal of Staff, Program, & Organizational Development, 16(2), 73–82.

    Google Scholar 

  • Hofer, B. (2004). Epistemological understanding as a metacognitive process: thinking aloud during online searching. Educational Psychologist, 39(1), 43–55.

    Article  Google Scholar 

  • Hofer, B. & Pintrich, P. (1997). The development of epistemological theories: beliefs about knowledge and knowing and their relation to learning. Review of Educational Research, 67, 88–140.

    Google Scholar 

  • Horng, W.-S. (2000). Euclid versus Liu Hui: a pedagogical reflection. In V. Katz (Ed.), Using history of mathematics in teaching mathematics (pp. 37–47.) Washington, DC: Mathematical Association of America.

    Google Scholar 

  • Kitcher, P. (1984). The nature of mathematical knowledge. New York: Oxford University Press.

  • Kline, M. (1980). Mathematics: the loss of certainty. New York: Oxford University.

    Google Scholar 

  • Kloosterman, P. & Stage, F.K. (1991). Relationships between ability, belief and achievement in remedial college mathematics classrooms. Research and Teaching in Developmental Education, 8(1), 27–36.

    Google Scholar 

  • Lakatos, I. (1976). Proofs and refutations: the logic of mathematical discovery. N.J.: Cambridge University Press.

    Google Scholar 

  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: mathematical knowing and teaching. American Educational Research Journal, 27, 29–63.

    Google Scholar 

  • Leder, G.C., Pehkonen, E. & Törner, G. (Eds.) (2002). Beliefs: a hidden variable in mathematics education? Dordrecht: Kluwer.

  • Legrand, M. (2001). Scientific debate in mathematics courses. In D. Holton (Ed.), The teaching and learning of mathematics at university level: an ICMI study (pp. 127–135.) Netherlands: Kluwer.

    Google Scholar 

  • Leng, N.-W. (2006). Effects of an ancient Chinese mathematics enrichment programme on secondary students’ achievement in mathematics. International Journal of Science and Mathematics Education, 4(2), 485–511.

    Article  Google Scholar 

  • Lester, F.K., Garofalo, J. & Kroll, D.L. (1989). Self-confidence, interest, beliefs, and metacognition. In D.B. McLeod & V.M. Adams (Eds.), Affect and mathematical problem solving (pp. 75–88.) Berlin Heidelberg New York: Springer.

    Google Scholar 

  • Liu, P.-H. (2007). Exploring the relationship between a history oriented calculus course and the development of students’ views on mathematics. Chinese Journal of Science Education, 15(6), 703–723.

    Google Scholar 

  • Liu, P.-H. & Niess, M. (2006). An exploratory study of college students’ views of mathematical thinking in a historical approach calculus course. Mathematical Thinking and Learning, 8(4), 373–406.

    Article  Google Scholar 

  • MacLeod, D.B. (1992). Research on affect in mathematics education: a reconceptualization. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596.) New York: Macmillan.

    Google Scholar 

  • National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Op ‘t Eynde, P., De Corte, E. & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs: a quest for conceptual clarity and a comprehensive categorization. In G.C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: a hidden variable in mathematics education? (pp. 13–37.)Dordrecht: Kluwer.

    Google Scholar 

  • Pajares, F. (1992). Teachers’ beliefs and educational research: cleaning up a messy construct. Review of Educational Research, 62(3), 307–332.

    Google Scholar 

  • Piaget, J. & Garcia, R. (1989). Psychogenesis and the history of science. New York: Columbia University Press.

    Google Scholar 

  • Pintrich, P.R. (2002). Future challenges and directions for theory and research on personal epistemology. In B.K. Hofer & P.R. Pintrich (Eds.), Personal epistemology: the psychology of beliefs about knowledge and knowing (pp. 389–414.) Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Presmeg, M. (2002). Beliefs about the nature of mathematics in the bridging of everyday and school mathematical practice. In G.C. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: a hidden variable in mathematics education? (pp. 293–311.) Dordrecht: Kluwer.

    Google Scholar 

  • Radford, L. (1997). On psychology, historical epistemology, and the teaching of mathematics: towards a socio-cultural history of mathematics. For the Learning of Mathematics, 17(1), 26–33.

    Google Scholar 

  • Schoenfeld, A.H. (1985). A framework for the analysis of mathematical behavior. In A.H. Schoenfeld (Ed.), Mathematical problem solving (pp. 11–45.) New York: Academy Press.

    Google Scholar 

  • Schoenfeld, A.H. (1987). What’s all the fuss about metacognition? In A.H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189–215.) Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Schoenfeld, A.H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 340–370.). New York: Macmillan.

    Google Scholar 

  • Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18, 371–397.

    Article  Google Scholar 

  • Sierpinska, A. & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. In A.J. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Eds.), International handbook of mathematics education (pp. 827–876). Dordrecht: Kluwer.

  • Thompson, A. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105–127.

    Article  Google Scholar 

  • Waldegg, G. (1997) Histoire, épistémologie et méthodologie dans la recherche en didactique. For the Learning of Mathematics, 17(1), 43–46.

    Google Scholar 

  • Whitemire, E. (2004). The relationship between undergraduates’ epistemological beliefs, reflective judgment, and their information-seeking behavior. Information Processing Management, 40, 97–111.

    Article  Google Scholar 

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Liu, PH. HISTORY AS A PLATFORM FOR DEVELOPING COLLEGE STUDENTS’ EPISTEMOLOGICAL BELIEFS OF MATHEMATICS. Int J of Sci and Math Educ 7, 473–499 (2009). https://doi.org/10.1007/s10763-008-9127-x

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  • DOI: https://doi.org/10.1007/s10763-008-9127-x

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