An Analysis of Pre-Service Teachers’ Reflective Thinking for Tasks on Polar Coordinates
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It is the first time that there is a subject, advanced mathematics in the 2009 revised high school curriculum. Therefore it is posing a challenge to the teachers who are teaching it. At the advanced level, it is important for learners to reflect on their mental mathematical activities. This research analysed pre-service secondary teachers’ reflective thinking in solving the tasks specific for the teaching and learning of polar coordinates. We report how and through what process mathematical tasks that can create disequilibrium for pre-service secondary teachers enable reflective thinking and expand pre-service secondary teachers’ thoughts and recognition of defining reflective thinking in looking back on one’s problem solving and thinking processes.
Abstract
It is the first time that there is a subject, advanced mathematics in the 2009 revised high school curriculum. Therefore it is posing a challenge to the teachers who are teaching it. At the advanced level, it is important for learners to reflect on their mental mathematical activities. This research analysed pre-service secondary teachers’ reflective thinking in solving the tasks specific for the teaching and learning of polar coordinates. We report how and through what process mathematical tasks that can create disequilibrium for pre-service secondary teachers enable reflective thinking and expand pre-service secondary teachers’ thoughts and recognition of defining reflective thinking in looking back on one’s problem solving and thinking processes.
참고문헌 (19)
- Boyer, C. B, "Newton as an originator of polar coordinates", Amer. Math. Mon, 56(2), pp.73~78 (1949)
- Coolidge, J. L, "The origin of polar coordinates", Amer. Math. Mon, 59(2), pp.78~85 (1952)
- Davis, E. A., "Scaffolding students’ knowledge integration: Prompts for re-flection in KIE", International Journal of Science Education, 22(8), pp.819~837 (2000)
- Dewey, J., "How we think: a restatement of the relation of reflective thinking to the educa-tive process" (1933), Henry Regnery Company
- Dewey, J., "The relation of theory to practice in education, In Teacher education in America: A documentary history", pp.140~171 (1965), Teacher College Press
- Doyle, W., "Themes in teacher education research, In Handbook of research on teacher education", pp.3~24 (1990), Macmillan
- Dubinsky, E., "Reflective abstraction in advanced mathematical thinking, In Advanced mathematical thinking", pp.95~123 (1991), Kluwer
- Freudenthal, H., "Weeding and sowing: Preface to a science of mathematical education" (1978), D. Reidel Publishing Company
- Freudenthal, H., "Revisiting mathematics education, In China lectures" (1991), Kluwer Academic Publishers
- Gagatsis, A, "Using geometrical models in a process of reflective thinking in learning and teaching mathematics", Educ. Stud. Math, 21(1), pp.29~54 (1990)
- Ge, X., "Scaffolding students’ problem-solving processes in an ill-structured task using question prompts and peer interactions", Educational Technology Research and Development, 51(1), pp.21~38 (2003)
- Kwon, O. N., "Fundamentals of advanced mathe-matics (in Korean)" (2011), Seoul Textbook
- Kwon, O. N, "Mathematical Tasks in the Advanced Mathematics Class for Nurturing Reflection, In Nurturing Reflective Learners, Yearbook 2013, Association of Mathematics Educators" (2013), World Scientific
- King, A., "Effects of training in strategic questioning on children’s problem-solving per-formance", Journal of Educational Psychology, 83(3), pp.307~317 (1991)
- Piaget, J., "The grasp of consciousness" (1976), Harvard University Press
- Piaget, J., "The development of thought: Equilibration of cognitive structures" (1977), Viking
- Piaget, J., "Psychogenesis and the history of science" (1989), Columbia University Press
- Polya, G., "How to Solve It: A New Aspect of Mathematical Method" (1985), Princeton University Press
- Skemp, R., "Intelligence, learning, and action" (1979), Wiley
