An investigation into sixth grade students’ understanding of ratio and proportion

Autores

Palavras-chave:

Proportional Reasoning, Problem Solving Strategies, African American Students, Conceptual Understanding, Middle School

Resumo

Drawing on written assessments collected from 58 sixth grade students, this article discusses the results of a study that examined patterns in middle-grade boy’s and girl’s written problem solving strategies for a mathematical task involving proportional reasoning and their level of understanding of ratios and proportions. This work is a part of a larger, longitudinal project, Mathematics Identity Development and Learning (MIDDLE), that focused on the impact of mathematics reform on students’ development as mathematics knowers and learners and identifying processes the explains changes in students’ mathematical learning and selfconceptions. Findings the current work speaks to student strategy use, errors, and levels of understanding.

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Referências

Author. (2008). Making the Invisible Visible: An Examination of African American Students’ Strategy Use During Mathematical Problem Solving. Unpublished doctoral dissertation, University of North Carolina at Chapel Hill.

Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational Number, Ration, and Proportion. In D. Grouws (e.), Handbook of Research on Mathematics Teaching and Learning (pp. 296-333). Macmillan, New York.

Cai, J. (1997). Beyond Computation and Correctness: Contributions of Open-Ended Tasks in Examining U.S. and Chinese Students’ Mathematical Performance. Educational Measurement: Issues and Practices, Spring, 5-11.

Cai, J. (2000). Mathematical Thinking Involved in U.S. and Chinese Students’ Solving of Process-Constrained and Process-Open Problems. Mathematical Thinking and Learning, 2(4), 309-340.

Carpenter, T., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), Classrooms that Promote Mathematical Understanding (pp. 19-32). Mahwah, NJ: Erlbaum.

Carr, M., & Hettinger, H. (2002). Perspectives on Mathematics Strategy Development. In J. Royer (Ed.), Mathematical Cognition (pp. 33-68). Greenwich, CT: Information Age Publishing.

Carr, M., & Jessup, D. L. (1997). Gender differences in first-grade mathematics strategy use: Social and metacognitive influences. Journal of Educational Psychology, 89(2), 318-328.

Che, M., Wiegert, E., & Threlkeld, K. (2011). Problem solving strategies of girls and boys in single-sex mathematics classrooms. Educational Studies in Mathematics.

Cramer, K., & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404–407.

Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. Owens (Ed.), Research ideas for the classroom (pp. 159–178). New York: Macmillian.

English, L. (1993). Children's Strategies for Solving Two- and Three-Dimensional Combinatorial Problems. Journal for Research in Mathematics Education, 24(3), 255- 273.

Fennema, E., & Peterson, P. (1985). Autonomous Learning Behavior: A Possible Explanation of Gender-Related Differences in Mathematics. In L.Wilkinson & C. Marrett (Eds.), Gender Influences in Classroom Interaction (pp.17-35). Orlando, FL: Academic Press.

Fennema, E., Carpenter, T., Jacobs, V., Franke, M., & Levi, L. (1998). A Longitudinal Study of Gender Differences in Young Children’s Mathematical Thinking. Educational Researcher, 27, 6-11.

Gallagher, A. M., & De Lisi, R. (1994). Gender differences in Scholastic Aptitude Test – Mathematics Problem Solving Among High-Ability Students. Journal of Educational Psychology, 86(2), 204-211.

Gallagher, A., De Lisi, R., Holst, P., McGillicuddy-De-Lisi, A., Morely, M. & Chalan, C. (2000). Gender Differences in Advanced Mathematical Problem Solving. Journal of Experimental Child Psychology, 75, 165-190.

Gick, M. (1986). Problem-Solving Strategies. Educational Psychologists, 21(1 &2), 99-120.

Hembree, R. (1992). Experiments and Relational Studies in Problem Solving: A Meta-Analysis. Journal for Research in Mathematics Education, 23(3), 242-273.

Hibert, J., & Lefevre, P. (1986). Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis. In James Hibert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics (pp. 1-27). Hillsdale, NJ: L. Erlbaum Associates, 1986.

Kroll, D.L., & Miller, T. (1993). Insights from Research on Mathematical Problem solving in middle grades. In D. Owens (Ed.), Research ideas for the classroom: Middle grades Mathematics (pp. 58-77).. New York: MacMillan Publishing Company.

Lamon, S. (1993). Ratio and Proportions: Children’s Cognitive and Metacognitive Processes. In T. Carpenter, E. Fennema, & T. Romberg (Eds.), Rational Numbers: An Integration of Research (131-156).

Lamon, S. (2005). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum Associates.

Leder, G. C. (1992). Mathematics and Gender: Changing Perspectives. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 597-622).. New York, NY: Macmillan.

Liamputtong, P., Ezzy, Douglas (2005). Qualitative Research Methods (2nd ed.). Oxford; New York, N.Y.: Oxford University Press.

Lobato, J. Ellis, A, Charles, R., & Zbiek, R. (2010). Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning. Reston, VA: NCTM.

Malloy, C. & Jones, G.M. (1998). An Investigation of African American students’ mathematical problem solving. Journal of Research in Mathematics Education, 29, 143-163.

Malloy, C. E. (April 2004). National Council of Teachers of Mathematics Research Pre-Session, Symposium Leader: Students’ Perception of and Engagement with Mathematics Reform Practices, Philadelphia, Pa.

McGraw, R., & Lubienski, S. T. (2007). 2003 NAEP mathematics findings regarding gender. In P. Kloosterman & F. Lester (Eds.), Results from the ninth mathematics assessment of NAEP (pp. 261–287). Reston: NCTM.

Meltzoff, J. (1998). Critical Thinking About Research: Psychology and Related Fields. Washington, DC. American Psychological Association.

Moskal, B. M. & Magone, M. E. (2000). Making Sense of What Students Know: Examining the Referents, Relationships, and Modes Students Displayed in Response to a Decimal Task. Educational Studies in Mathematics, 43, 313-335.

National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (2000). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.

National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

Polya, G. (1981). Mathematical Discovery: On Understanding , Learning, and Teaching Problem Solving (Combined Edition). New York, NY: John Wiley & Sons.

Pugalee, D. (2004). A Comparison of Verbal and Written Descriptions of Students’ Problem Solving Processes. Educational Studies in Mathematics, 55, 27-47.

Schoenfeld, A. (1985). Mathematical Problem Solving. Orlando, Florida: Academic Press.

Siegler, R. (1998). Children’s Thinking (3rd. Ed.). Upper Saddle River, New Jersey: Prentice-Hall.

Silver, E., Shapiro, L., & Deutsch, A. (1993). Sense Making and the Solution of Division Problems Involving Remainders: An Examination of Middle Students’ Solution Processes and Their Interpretations of Solutions. Journal for Research in Mathematics Education, 24(2), 117-135.

Sowder, J., & Philipp, R. (1999). Promoting Learning in Middle –Grades Mathematics. In E. Fennema & T. A. Romberg (Eds.), Classrooms that Promote Mathematical Understanding (pp. 89-108). Mahwah, NJ: Erlbaum.

Steinthorsdottir, O. (2003). Making Meaning of Proportion: A Study of Girls in Two Icelandic Classrooms. Unpublished doctoral dissertation, University of Wisconsin-Madison.

Tourniaire, F., & Pulos, S. (1985). Proportional Reasoning: A Review of the Literature. Educational Studies in Mathematics, 16, 181-204.

Publicado

2014-01-01

Como Citar

MORTON, C. H. An investigation into sixth grade students’ understanding of ratio and proportion. Revista Internacional de Pesquisa em Educação Matemática, v. 4, n. 1, p. 68-80, 1 jan. 2014.

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