A study of optimal periods in proportional reasoning
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Proportional reasoning is one of the most widely used concepts in everyday life. It could be the most important basic concept in science and mathematics. In research where the subjects were animals, it has been found that learning effect rapidly decreased with any stimulation given after a optimal period. Therefore, it is necessary to research about optimal periods in order to instruct about proportional reasoning. The purpose of this study is to investigate the optimal periods in proportional reasoning. The three programs for proportional reasoning instruction were developed by researchers. The titles of the programs were ‘Block’, ‘Balance scale’ and ‘Water glass’. The subjects of this present study were 131 3rd to 6th grade students who were not expected to have any proportional reasoning skills yet. In order to find out the optimal periods in proportional reasoning, the programs were applied to these students. After 4-5 weeks of treatment, the researchers investigated whether their proportional reasoning skills were formed or not through the instrument. The results indicated that it would be most effective to teach proportional reasoning to 6th grade students. Teaching of proportional reasoning is essential not only for mathematics but also for science. The findings could be used to investigate the optimal periods of controlling variables, probability, combinational and correlational logic.
Abstract
Proportional reasoning is one of the most widely used concepts in everyday life. It could be the most important basic concept in science and mathematics. In research where the subjects were animals, it has been found that learning effect rapidly decreased with any stimulation given after a optimal period. Therefore, it is necessary to research about optimal periods in order to instruct about proportional reasoning. The purpose of this study is to investigate the optimal periods in proportional reasoning. The three programs for proportional reasoning instruction were developed by researchers. The titles of the programs were ‘Block’, ‘Balance scale’ and ‘Water glass’. The subjects of this present study were 131 3rd to 6th grade students who were not expected to have any proportional reasoning skills yet. In order to find out the optimal periods in proportional reasoning, the programs were applied to these students. After 4-5 weeks of treatment, the researchers investigated whether their proportional reasoning skills were formed or not through the instrument. The results indicated that it would be most effective to teach proportional reasoning to 6th grade students. Teaching of proportional reasoning is essential not only for mathematics but also for science. The findings could be used to investigate the optimal periods of controlling variables, probability, combinational and correlational logic.
참고문헌 (37)
- Acredolo, C., "Children's ability to make probability estimates: Skills revealed through application of Anderson's functional measurement methodology", Child Development, 60, pp.933~945 (1998)
- Adey, P., "Science develops logical thinking-doesn't it? Part I: Abstract thinking and school science", School Science Review, 68, pp.622~622 (1987)
- Adey, P., "Really raising standards: Cognitive intervention and academic achievement" (1994), Nelson & Sons Ltd
- Adey, P., "Learning intelligence" (2002), Routledge
- Adey, P., "Thinking Science. (2nd ed.)" (1995), Nelson & Sons Ltd
- Cancedda, L., "Acceleration of visual system development by environmental enrichment", The Journal of Neuroscience, 24(20), pp.4840~4848 (2004)
- Capon, N., "Logical reasoning in the supermarket: Adult females' use of a proportional strategy in an everyday context", Developmental Psychology, 15(4), pp.544~573 (1979)
- Choi, B., "Relationships between the cognitive levels of students and understanding of concrete and formal science content", Journal of the Korean Association for Research in Science Education, 7(1), pp.19~33 (1987)
- Choi, B., "Effects of a cognitive acceleration program on secondary school students", Journal of the Korean Association for Research in Science Education, 22(4), pp.837~850 (2002)
- Choi, M., "The effects of thinking science activities on the cognitive acceleration of middle school students and the analysis of problem solving process of thinking science activities by the cognitive level and motivational style", 박사, pp.2002
- Chung, W., "A study on learner`s neurocognitive variables and an analysis of program effects for developing proportional reasoning ability", Journal of the Korean Association for Research in Science Education, 18(4), pp.503~516 (1998)
- Chung, W., "A study on the development of proportional reasoning strategies applied in elementary school students", Journal of Elementary Science Education, 17(2), pp.23~31 (1998)
- Garofalo, J., "Mathematics and reasoning in Implementing the K-8 Curriculum and evaluation standards" (1990), The National Council of Teachers of Mathematics., Inc
- Hines, E., "Interpreting middle school students' proportional reasoning strategies: Observations from preservice teachers", School Science and Mathematics, 105(2), pp.88~105 (2005)
- Huttenlocher, J., "Infants and toddlers discriminate amount: Are they measuring?", Psychological Science, 13(3), pp.244~249 (2005)
- Hwang. K., "A study, on scientific thinking of Korean high school students-with reference to logical thinking and reasoning power", Journal of the Korean Association for Research in Science Education, 9(1), pp.19~38 (1989)
- Inhelder, B., "The growth of logical thinking from childhood to adolescence" (1958), Basic Book
- Jeon, W., "A comparative study on scientific reasoning skills in Korean and the US college students", Journal of the Korean Association for Research in Science Education, 19(1), pp.117~127 (1999)
- Jeong, Y., "Two dissociable systems of proportional reasoning: Implications for learning and education", The Korean society for developmental psychology 2006 Annual meeting (2006), Kyungpook National University
- Karplus, E. F., "Intellectual development beyond elementary school ?: Ratio, the influence of cognitive style", School Science and Mathematics, 74(6), pp.476~482 (1974)
- Karplus, R., "Intellectual development beyond elementary school ?: Proportional, Probabilistic, and correlational reasoning", School Science and Mathematics, 80(8), pp.673~683 (1980)
- Khoury, H., "Classroom challenge in Making sense offrations, ratios, and proportions: 2002 Yearbook", pp.100~102 (2002), National Council of Teachers of Mathematics
- Kim, M., "The effects of proportional reasoning program on the development of the middle school students' logical thinking and cognitive level", 석사, pp.1999
- Kwon, Y. J., "Linking prefrontal lobe functions with reasoning and conceptual change", 박사, pp.1997
- Lawson, A, E., "A neurological model of sensory-motor problem solving with possible implications for higher-order cognition and instruction", Journal of Research in Science Teaching, 23(6), pp.503~522 (1986)
- Lee, Y., "An analysis of strategies and errors in solving proportion problems - based on the 5 th & 6 th -grades in elementary school", 석사, pp.1998
- Lenneberg, E. H., "The biological foundations of language" (1967), Wiley
- Lovett, S., "The development of children's understanding of probability: Perceptual and quantitative concepts", the biennial meeting of the Society for Research in Child Development (1991)
- Michel, G. F., "Developmental psychology: An interdisciplinary science" (1995), The MIT Press
- Michel, G. F., "ritical period: A history of the transition from questions of when, to what, to how", Developmental Psychology, 46, pp.156~162 (2005), Ministry of Education & Human Resources
- Development, "Mathematics 6-A: Teacher's manual", ~ (2002)
- 남정희, "변인통제 문제해결 활동에서 학생들의 인지수준에 따른 상호작용 분석", 한국과학교육학회지, 22(1), pp.110~121 (2002), 한국과학교육학회
- National Council of Teachers of Mathematics (NCTM), "Understanding rational numbers and proportions" (1994), Author
- Parllrand, G. J., "The transition to formal though", Journal of Research in Science Teaching, 16(5), pp.445~451 (1979)
- Tourniaire, F., "Proportional reasoning: A review of the literature", Educational Studies in Mathematics, 16, pp.181~204 (1985)
- Vernaud, G., "Multiplicative structures in Acquisition of mathematics concepts and processes" (1983), Academic Press
- Werker, J. F., "Speech perception as a window for understanding plasticity and commitment in language systems of the brain", Developmental Psychobiology, 46(3), pp.233~251 (2005)
