Students’ Use of “Look Back” Strategies in Multiple Solution Methods
The purpose of this study was to investigate the relationship between both 9th-grade and 1st-year undergraduate students’ use of “look back” strategies and problem solving performance in multiple solution methods, the difference in their use of look back strategies and problem solving performance in multiple solution methods, and the role of look back strategies in problem solving in multiple solution methods. Data for this study were comprised of 30 9th-grade and 30 1st-year undergraduate students’ problem solving scores in multiple solution methods and their think-aloud protocols. Based on and expanded from Polya’s (1973) ideas, “look back” in the present study means “examination of what was done or learned previously.” The results of this study indicated that both the 9th-grade and 1st-year undergraduate students who looked back more frequently tended to perform better in multiple solution methods, the 1st-year undergraduate students tended to look back more frequently and perform better than the 9th-grade students in multiple solution methods, and both the 9th-grade and 1st-year undergraduate students tended to review and to compare multiple solution methods in their use of look back strategies.
KeywordsLook back Multiple solution methods Problem solving
- Bloom, S. (1956). Taxonomy of educational objectives. Boston, MA: Allyn and Bacon.Google Scholar
- Cai, J. & Brook, M. (2006). Looking back in problem solving. Mathematics Teaching, 196, 42–45.Google Scholar
- Charles, R. I., Lester, F. & O’Daffer, P. (1987). How to evaluate progress in problem solving. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- Davis, E. J. & McKillip, W. D. (1980). Improving story-problem solving in elementary school mathematics. In S. Krulik & R. E. Reys (Eds.), Problem solving in school mathematics: 1980 Yearbook of the National Council of Teachers of Mathematics (pp. 80–91). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- DeGuire, L. J. (1980). Polya visits the classroom. In S. Krulik & R. E. Reys (Eds.), Problem solving in school mathematics: 1980 Yearbook of the National Council of Teachers of Mathematics (pp. 70–79). Reston, VA: NCTM.Google Scholar
- Fouche, K. K. (1993). Problem solving and creativity: Multiple solution methods in a cross-cultural study in middle level mathematics. (Doctoral dissertation). Retrieved from http://www.archive.org/details/problemsolvingcr00fouc. Accessed 6 Feb 2014.
- Heid, M. (1995). Algebra in a technological world (Addenda Series Grades 9–12). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- Jacobbe, T. (2007). Using Polya to overcome translation difficulties. Mathematics Teacher, 101(5), 390–393.Google Scholar
- Kersh, M. & McDonald, J. (1991). How do I solve thee? Let me count the ways. Arithmetic Teacher, 39(2), 38–41.Google Scholar
- Kilpatrick, J. (1967). Analyzing the solution of word problems in mathematics: An exploratory study. (Doctoral dissertation). Retrieved from http://eric.ed.gov/?id=ED027182. Accessed 30 Jan 2014.
- Krulik, S. & Rudnick, J. A. (1994). Reflect… for problem solving and reasoning. The Arithmetic Teacher, 41(6), 334–338.Google Scholar
- Leikin, R., Leikin, M., Waisman, I. & Shaul, S. (2013). Effect of the presence of external representations on accuracy and reaction time in solving mathematical double-choice problems by students of different levels of instruction. International Journal of Science and Mathematics Education, 11(5), 1049–1066.CrossRefGoogle Scholar
- National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
- Oehmke, T. (1979). The development and validation of a testing instrument to measure problem solving skills of children in grades five through eight. Doctoral dissertation: University of Lowa. http://pqdd.sinica.edu.tw/cgi-bin2/Libo.cgi?searchString=http%3A%2F%2Fpqdd.sinica.edu.tw%2Fcgi-bin2%2FLibo.cgi%3Frequest%3DLA_GET_HTML%26template%3Dresults_single%26user%3Dcnjppmejkooaihbondbcmcighckhpnieeodfedifjiadgkegehnkpekbklfmekbp%26client_type%3Dsearch%26lang%3Dddc.tw%26urlID%3D1418616853388%26app%3D13%26db%3D%26expr%3DCICHHEGIGFCHCAGBGOGECACHGEGFHGGFGMGPHAGNGFGOHECHCAGBGOGECACHGBGOGECHCAGBGOGECACHHGGBGMGJGEGBHEGJGPGOCHCAGBGOGECACHGPGGCHCAGBGOGECACHGBCHCAGBGOGECACHHEGFHDHEGJGOGHCHCAGBGOGECACHGJGOHDHEHCHFGNGFGOHECHCAGBGOGECACHHEGPCHCAGBGOGECACHGNGFGBHDHFHCGFCHCAGBGOGECACHHAHCGPGCGMGFGNCHCAGBGOGECACHHDGPGMHGGJGOGHCHCJ%26option%3DFLHDGPHCHEDNDBCOHEGJHEGMGFCOEJFNFLHDHJGOGPGOHJGNDNDBFN%26start%3D0%26number%3D30%26result_type%3Dsimple%26doi%3D8012402%3A8012402%26page_type%3Dhtm%26record_browse%3D1%26result_book_id%3D46150476%26ori_db%3D%26%26uID%3Dfdpahagdfoclhlmefjchflhi. Accessed 18 Dec 2013.
- Polya, G. (1973). How to solve it. Princeton, NJ: Princeton University Press.Google Scholar
- Schoen, H. L. & Oehmke, T. (1980). A new approach to the measurement of problem solving skills. In S. Krulik & R. E. Reys (Eds.), Problem solving in school mathematics: 1980 Yearbook of the National Council of Teachers of Mathematics (pp. 216–227). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- Schoenfeld, A. H. (1983). Problem solving in the mathematics curriculum: A report, recommendations, and an annotated bibliography. Washington, DC: Mathematical Association of America.Google Scholar
- Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic.Google Scholar
- Schoenfeld, A. H. (2009). Cognitive science and mathematics education: An overview. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 1–31). New York, NY: Routledge.Google Scholar
- Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C. & Strawhun, B. T. F. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24, 287–301.CrossRefGoogle Scholar
- Sowder, L. (1986). The looking-back step in problem solving. The Arithmetic Teacher, 79, 511–513.Google Scholar
- Tabachneck, H. J. M., Koedinger, K. R. & Nathan, M. J. (1994). Toward a theoretical account of strategy use and sense-making in mathematics problem solving. In A. Ram & K. Eiselt (Eds.), Proceedings of the sixteenth annual conference of the cognitive science society (pp. 836–841). Hillsdale, NJ: Erlbaum.Google Scholar
- Taback, S. (1988). The wonder and creativity in “looking-back” at problem solutions. The Arithmetic Teacher, 81(6), 429–435.Google Scholar
- Zahner, D. & Corter, J. E. (2010). The process of probability problem solving: Use of external visual representations. Mathematical Thinking and Learning, 12(2), 177–204.Google Scholar