An analysis of U.S. pre-service teachers’ modeling and explaining 0.14㎡
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This investigation engaged elementary and middle school pre-service teachers in a task of modeling and explaining the magnitude of 0.14 and examined their responses. The study analyzed both successful and unsuccessful responses in order to reflect on the patterns of misconceptions relative to pre-service teachers’ prior knowledge. The findings suggest a need to promote opportunities for pre-service teachers to make connections between different domains through meaningful tasks, to reason abstractly and quantitatively, to use proper language, and to refine conceptual understanding. While mathematics teacher educators (MTEs) could use such mathematical tasks to identify the mathematical content needs of pre-service teachers, MTEs generally use instructional time to connect content and pedagogy. More importantly, an early and consistent exposure to a combined experience of mathematics and pedagogy that connects and deepens key concepts in the program’s curriculum is critical in defining the important content knowledge for K-8 mathematics teachers.
Abstract
This investigation engaged elementary and middle school pre-service teachers in a task of modeling and explaining the magnitude of 0.14 and examined their responses. The study analyzed both successful and unsuccessful responses in order to reflect on the patterns of misconceptions relative to pre-service teachers’ prior knowledge. The findings suggest a need to promote opportunities for pre-service teachers to make connections between different domains through meaningful tasks, to reason abstractly and quantitatively, to use proper language, and to refine conceptual understanding. While mathematics teacher educators (MTEs) could use such mathematical tasks to identify the mathematical content needs of pre-service teachers, MTEs generally use instructional time to connect content and pedagogy. More importantly, an early and consistent exposure to a combined experience of mathematics and pedagogy that connects and deepens key concepts in the program’s curriculum is critical in defining the important content knowledge for K-8 mathematics teachers.
참고문헌 (38)
- Barrett, J., "Children’s unit concepts in measurement : A teaching experiment spanning grades 2 through 5", ZDM Mathematics Education, 43, pp.637~650 (2011)
- Battista, M. T., "Understanding area and area formulas", Mathematics Teacher, 75(5), pp.362~387 (1982)
- Battista, M. T., "Learning and teaching measurement: 2003 yearbook", pp.122~142 (2003), NCTM
- Battista, M. T., "Applying cognition-based assessment to elementary school students' development of understanding of area and volume measurement", Mathematical Thinking and Learning, 6(2), pp.185~204 (2004)
- Battista, M. T., "Students’ spatial structuring of 2D arrays of squares", Journal for Research in Mathematics Education, 29, pp.503~532 (1998)
- Baturo, A., "Student teachers' subject matter knowledge within the domain of area measurement", Educational Studies in Mathematics, 31(3), pp.235~268 (1996)
- Clements, D. H., "Learning and teaching measurement: 2003 yearbook" (2003), National Council of Teachers of Mathematics
- "Common core state standards for mathematics" (2010)[URL]
- Cooney, T. J., "Didactics of mathematics as a scientific discipline", pp.103~116 (1994), Kluwer
- Curry, M., "Building connections: Theory, research and practice (Proceedings of the 27th MERGA conference)" (2005), MERGA
- Davydov, V. V., "Types of generalization in instruction: Logical and psychological problems in the structuring of school curricula, (Soviet studies in mathematics education, Vol. 2)" (1990), NCTM
- Davydov, V. V., "Mathematics: Class 1", Unpublished manuscript. State University, ~ (1999)
- Dorko, A., "Calculus students’understanding of area and volume units", Investigations in Mathematics Learning, 8(1), pp.23~46 (2015)
- Empson, S. H., "Fractions as the coordination of multiplicatively related quantities : A cross-sectional study of children’s thinking", Educational Studies in Mathematics, 63(1), pp.1~28 (2006)
- Fernández, C., "The development of students’use of additive and proportional methods along primary and secondary School", European Journal of Psychology of Education, 27, pp.421~438 (2012)
- Fernández, C., "Do students confuse dimensionality and “directionality”?", Journal of Mathematical Behavior, 36, pp.166~176 (2014)
- Grant, T. J., "Learning and teaching measurement: 2003 yearbook", pp.46~56 (2003), NCTM
- Kent, P., "Measurement in the workplace : The case of process improvement in manufacturing industry", ZDM Mathematics Education, 43, pp.747~758 (2011)
- 김정하, "평면도형의 넓이 측정 지도에 대한 고찰", 한국초등수학교육학회지, 15(3), pp.509~531 (2011), 한국초등수학교육학회
- Lee, J., "Teaching algebraic expressions to young students : The three-day journey of ‘a+2’", School Science and Mathematics, 106(2), pp.98~104 (2006)
- Lee, S., "Mathematics teachers’ reasoning about fractions and decimals using drawn representations", Mathematical Thinking and Learning : An International Journal, 13(3), pp.198~220 (2011)
- Lehrer, R., "A research companion to principles and standards for school mathematics" (2003), NCTM
- Lehrer, R., "Learning and teaching measurement: 2003 yearbook", pp.100~121 (2003), NCTM
- 임아름, "개방형 교수법에 따른 평면도형의 넓이 지도에 대한 연구1) -평행사변형, 삼각형, 사다리꼴, 마름모를 중심으로-", 한국초등수학교육학회지, 15(2), pp.361~383 (2011), 한국초등수학교육학회
- Menon, R., "Preservice teachers’ understanding of perimeter and area", School Science and Mathematics, 98, pp.361~367 (1998)
- Miles, M. B., "Qualitative data analysis: An expanded sourcebook" (1994), Sage
- 나귀수, "초등학교 학생들의 넓이 개념 이해도 조사- 초등학교 6학년 학생들을 중심으로-", 한국초등수학교육학회지, 16(3), pp.451~469 (2012), 한국초등수학교육학회
- National Council of Teachers of Mathematics, "Principles and standards for school mathematics" (2000), NCTM
- Outhred, L., "Learning and teaching measurement:2003 yearbook", pp.81~99 (2003), NCTM
- 박은률, "평면도형의 넓이 학습에서 나타나는 인식론적 장애", 수학교육학연구, 20(3), pp.305~322 (2010), 대한수학교육학회
- Ross, S., "Place value : Problem solving and written assessment", Teaching Children Mathematics, 8(7), pp.419~423 (2002)
- Simon, M., "Building and understanding multiplicative relationships : A study of prospective elementary school teachers", Journal for Research in Mathematics Education, 25, pp.472~494 (1994)
- Sisman, G., "A study on sixth grade students’ misconceptions and errors in spatial measurement : Length, area, and volume", International Journal of Science and Mathematics Education, 14, pp.1293~1319 (2016)
- Smith, J., "Assessing curricular contributions to poor measurement learning", Paper presented at Research Presession Symposium (2008), National Council of Teachers of Mathematics
- Smith, J., "Learning, teaching, and using measurement : Introduction to the issue", ZDM Mathematics Education, 43, pp.617~620 (2011)
- Strauss, A., "Basics of qualitative research: Techniques and procedures for developing grounded theory" (1998), Sage
- Yew, W. T., "Examining preservice teachers’ knowledge of area formulae", Procedia-Social and Behavioral Sciences, 8, pp.198~206 (2010)
- Zacharos, K., "Prevailing educational practices for area measurement and students’ failure in measuring areas", The Journal of Mathematical Behavior, 25(3), pp.224~239 (2006)