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

Referencias

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 Unpublished doctoral dissertation, University of North Carolina at Chapel Hill.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. (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. 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. 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, doi:10.1007/s10649011-9346-x. 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., 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. 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. 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. 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. 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. Lobato, J. Ellis, A, Charles, R., & Zbiek, R. (2010). Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning. Reston, VA: NCTM. Lamon, S. (2005). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum Associates. 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). 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. 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. Malloy, C. & Jones, G.M. (1998). An Investigation of African American students’ mathematical problem solving. Journal of Research in Mathematics Education, 29, 143-163. Meltzoff, J. (1998). Critical Thinking About Research: Psychology and Related Fields. Washington, DC. American Psychological Association. 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. 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: PrenticeHall. 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.