최소 단어 이상 선택하여야 합니다.
최대 10 단어까지만 선택 가능합니다.
다음과 같은 기능을 한번의 로그인으로 사용 할 수 있습니다.
NTIS 바로가기Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.61 no.1, 2022년, pp.1 - 28
The purpose of this study is to explore how students' fractional knowledge is related to their solving of proportion problems. To this end, 28 clinical interviews with four middle-grade students, each lasting about 30~50 minutes, were carried out from May 2021 to August 2021. The present study focus...
Ahn, S. H., & Pang, J. S. (2008). A survey on the proportional reasoning ability of fifth, sixth, and seventh graders. Journal of Educational Research in Mathematics, 18(1), 103-121.
Behr, M., Harel, G., Post, T., & Lesh, R. (1993). Rational numbers: towards a semantic analysis emphasis on the operator construct. In T. P. Carpenter, E. Fennema & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 49-84). Lawrence Erlbaum.
Carney, M. B., Smith, E., Hughes, G. R., Brendefur, J. L., & Crawford, A. (2016). Influence of proportional number relationships on item accessibility and students' strategies. Mathematics Education Research Journal, 28, 503-522. https://doi.org/10.1007/s13394-016-0177-z
Chong, Y. O. (2015). Teaching proportional reasoning in elementary school mathematics. Journal of Educational Research in Mathematics, 25(1), 21-58.
Clement, J. (2000). Analysis of clinical interview: Foundations and model viability. In Lesh, R. and Kelly, A., Handbook of research methodologies of science and mathematics education (pp. 341-385). Lawrence Erlbaum.
Corbin, J., & Strauss, A. (2015). Basics of qualitative research (4th ed.). Sage Publications.
Ezzy, D. (2002). Qualitative analysis: Practice and innovation. Routledge.
Hackenberg, A. J. (2010). Students' reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383-432. https://doi.org/10.1080/07370008.2010.511565
Hackenberg, A. J. (2013). The fractional knowledge and algebraic reasoning of students with the first multiplicative concept. Journal of Mathematical Behavior, 32(3), 538-563. https://doi.org/10.1016/j.jmathb.2013.06.007
Hackenberg, A. J., & Lee, M. Y. (2015). Relationships between students' fractional knowledge and equation writing. Journal for Research in Mathematics Education, 46(2), 196-243. https://doi.org/10.5951/jresematheduc.46.2.0196
Hackenberg, A. J., & Tillema, E. S. (2009). Students' whole number multiplicative concepts: A critical constructive resource for fraction composition schemes. Journal of Mathematical Behavior, 28(1), 1-18. https://doi.org/10.1016/j.jmathb.2009.04.004
Hong, G. J. (2013). A discussion on the terms related to ratio and rate from the revised 2007 curriculum textbook. Journal of Educational Research in Mathematics, 23(20), 285-295.
Hong, J. Y., & Kim, M. K. (2013). A study on children's proportional reasoning based on an ill-structured problem. School Mathematics, 15(4), 723-742.
Jeong, E. S. (2003a). An educational analysis on ratio concept. Journal of Educational Research in Mathematics, 13(3), 247-265.
Jeong, E. S. (2003b). A historical. mathematical, psychological analysis on ratio concept. School Mathematics, 5(4), 421-440.
Jeong, E. S. (2013). Study on proportional reasoning in elementary school mathematics. Journal of Educational Research in Mathematics, 23(4), 505-516.
Johnson, H. L. (2015). Secondary students' quantification of ratio and rate: A framework for reasoning about change in covarying quantities. Mathematical Thinking and Learning, 17(1), 64-90. https://doi.org/10.1080/10986065.2015.981946
Kaput, J., & West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235-287). State University of New York Press.
Kim, K. H., & Paik, H. S. (2010). Comparison of the curricula and the textbooks concerning the proportion and ratio area between Korea and Singapore. School Mathematics, 12(4), 473-491.
Kim, S. H., & Na, G. S. (2008). Teaching the concept of rate and ratio: Focused on using the reconstructed textbook. Journal of Educational Research in Mathematics, 18(3), 309-333.
Kim, S. H., Shin, J. H., & Lee, S. J. (2018). A theoretical analysis of students' solving equal sharing problems with the framework of Steffe's partitioning operations and its application. School Mathematics, 20(1), 17-42. https://doi.org/10.29275/sm.2018.03.20.1.17
Ko, E. S., & Lee, K. H. (2007). Analysis on elementary students' proportional thinking: A case study with two 6-graders. Journal of Educational Research in Mathematics, 17(4), 359-380.
Kwon, O. N., Park, J. S., & Park, J. H. (2007). An analysis on mathematical for proportional reasoning in the middle school mathematics curriculum. The Mathematical Education, 46(3), 315-329.
Lamon, S. J. (1993). Ratio and proportion: Connecting content and children's thinking. Journal for Research in Mathematics Education, 24(1), 41-61. https://doi.org/10.5951/jresematheduc.24.1.0041
Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). Information Age Publishing and the National Council of Teachers of Mathematics.
Lee, J. A., & Lee S. J. (2020). Secondary students' reasoning about covarying quantities in quadratic function problems. Journal of Educational Research in Mathematics, 30(4), 705-732. https://doi.org/10.29275/jerm.2020.11.30.4.705
Lee, J. Y. (2019). A study on introducing fractions in mathematics textbooks: Focused on stages of units coordination. Journal of Elementary Mathematics Education in Korea, 23(3), 323-345.
Lee, J. Y., & Pang, J. S. (2016). Reconsideration of teaching addition and subtraction of fractions with different denominators: Focused on quantitative reasoning with unit and recursive partitioning. School Mathematics, 18(3), 625-645.
Lee, S. J., & Shin, J. H. (2020). Students' proportion problem solving with different units coordination stages. Journal of Educational Research in Mathematics. 30(2), 245-279. https://doi.org/10.29275/jerm.2020.05.30.2.245.
Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number Concepts and Operations in the Middle Grades (pp. 93-118). National Council of Teachers of Mathematics.
Liss, D. R., II (2019). The development of distributive partitioning operations. The Journal of Mathematical Behavior, 56, Article 100775 https://doi.org/10.1016/j.jmathb.2019.04.004
Lobato, J., Ellis, A. B., Charles, R. I., & Zbiek, R. M. (2010). Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematicsin grades 6-8. The National Council of Teachers of Mathematics.
Lobato, J., Hohensee, C., Rhodehamel, B., & Diamond, J. (2012). Using student reasoning to inform the development of conceptual learning goals: The Case of Quadratic Functions. Mathematical Thinking and Learning, 14, 85-119. https://doi.org/10.1080/10986065.2012.656362
Ministry of Education (2015). Mathematics curriculum. Proclamation of the Ministry of Education No. 2015-74 [Vol. 8].
Nabors, W. K. (2003). From fractions to proportional reasoning: A cognitive schemes of operation approach. Journal of Mathematical Behavior, 22(2), 133-179. https://doi.org/10.1016/S0732-3123(03)00018-X
Norton, A., & Boyce, S. (2013). A cognitive core for common state standards. Journal of Mathematical Behavior, 32(2), 266-279. https://doi.org/10.1016/j.jmathb.2013.01.001
Norton, A., & Boyce, S. (2015). Provoking the construction of a structure for coordinating n+1 levels of units. Journal of Mathematical Behavior, 40, 211-232. https://doi.org/10.1016/j.jmathb.2015.10.006
Norton, A., Boyce, S., Ulrich, C., & Phillips, N. (2015). Students' units coordination activity: A cross-sectional analysis. Journal of Mathematical Behavior, 39, 51-66. https://doi.org/10.1016/j.jmathb.2015.05.001
Olive, J., & Steffe, L. P. (2002). The construction of an iterative fractional scheme: The case of Joe. Journal of Mathematical Behavior, 20, 413-437. https://doi.org/10.1016/S0732-3123(02)00086-X
Park, J. S. (2008). Characteristics of students' problem solving using additive strategy in ratio and proportion tasks. School Mathematics, 10(4), 605-626.
Park, K. S. (2010). A critical analysis on definitions of biyoul and value of bi in elementary mathematics in Korea. Journal of Educational Research in Mathematics, 20(3). 397-411.
Shin, J. H., Lee, S. J., & Steffe, L. P. (2020). Problem solving activities of two middle school students with distinct levels of units coordination. Journal of Mathematical Behavior, 59, 1-19. https://doi.org/10.1016/j.jmathb.2020.100793
Shin, J. H., & Lee, S. J. (2019). Conceptual analysis for solving a missing value problem using a proportional relationship. Journal of Educational Research in Mathematics, 29(2), 227-250. https://doi.org/10.29275/jerm.2019.5.29.2.227
Smith, J., & Thompson, P. W. (2007). Quantitative reasoning and the development of algebraic reasoning. In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades (pp. 95-132). Lawrence Erlbaum.
Steffe, L. P. (1992). Schemes of action and operation involving composite units. Learning and Individual Differences, 4(3), 259-309. https://doi.org/10.1016/1041-6080(92)90005-Y
Steffe, L. P. (2001). A new hypothesis concerning children's fractional knowledge. Journal of Mathematical Behavior, 20(3), 267-307. https://doi.org/10.1016/S0732-3123(02)00075-5
Steffe, L. P. (2003). Fractional commensurate, composition, and adding scheme. Learning trajectories of Jason and Laura: Grade 5. Journal of Mathematical Behavior, 22(3), 237-295. https://doi.org/10.1016/S0732-3123(03)00022-1
Steffe, L. P. (2010). Operations that produce numerical counting schemes. In L. P. Steffe & J. Olive (Eds.), Children's fractional knowledge (pp. 27-47). Springer.
Steffe, L. P. (2014). On children's construction of quantification. In R. Mayes, & L. Hatfield (Eds), Quantitative reasoning and mathematics and science education: Papers from an international STEM research symposium (Vol. 3, pp. 13-41). WISDOMe Monographs, University of Wyoming.
Steffe, L. P., Liss II, D. R., & Lee, H. Y. (2014). On the operations that generate intensive quantity. In K. C. Moore, L. P. Steffe, & L. L. Hatfield (Eds.), Epistemic algebra students: Emerging models of students' algebraic knowing (Vol. 4, pp. 49-80). WISDOMe Monographs, University of Wyoming.
Steffe, L. P., & Olive, J. (2010). Children's fractional knowledge. Springer.
Thompson, P. W. (1994). The development of the concept of speed and its relationship to concepts of rate. In G. Harel, & J. Confrey (Eds.), The Development of multiplicative reasoning in the learning of mathematics (pp. 181-234). SUNY Press.
Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain, & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education, WISDOMe Monographs (Vol. 1, pp. 33-57). University of Wyoming.
Thompson, P. W., & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to the principles and standards for school mathematics (pp. 95-113). National Council of Teachers of Mathematics.
Ulrich, C. (2012). The addition and subtraction of signed quantities. Invited chapter in R. Mayes, L. Hatfield, & M. Mackritis (Eds), Quantitative reasoning and mathematical modeling: A drive for STEM integrated education and teaching in context (pp. 127-141). University of Wyoming.
Ulrich, C. (2015). Stages in constructing and coordinating units additively and multiplicatively (part 1). For the Learning of Mathematics, 35(3), 2-7.
Ulrich, C. (2016). Stages in constructing and coordinating units additively and multiplicatively (part 2). For the Learning of Mathematics, 36(1), 34-39.
Yoo, J. Y., & Shin, J. H. (2021). Construction of recursive partitioning operation and fraction schemes with interiorized two levels of units. School Mathematics, 23(1), 1-31. https://doi.org/10.29275/sm.2021.03.23.1.1
Yoo, K. W., Jong, J. W., Kim, Y. S., & Kim, H. B. (2018). Understanding qualitative research methods (pp. 75-110). Park Young Story.
*원문 PDF 파일 및 링크정보가 존재하지 않을 경우 KISTI DDS 시스템에서 제공하는 원문복사서비스를 사용할 수 있습니다.
Free Access. 출판사/학술단체 등이 허락한 무료 공개 사이트를 통해 자유로운 이용이 가능한 논문
※ AI-Helper는 부적절한 답변을 할 수 있습니다.