Beyond Corrections: Students Revise Their Math Solutions

 

 

Amy Wolpin

Amherst Public Schools

Amherst, MA 01002

 

 

Students from a fourth grade class (n= 21) were asked to individually solve a complex open-response math problem in a test situation. Student performance was evaluated using an analytical trait scoring rubric along the dimensions of conceptual understanding, mathematical accuracy, approach, and explanation. Most students had difficulty solving the problem with accuracy. The solutions were returned to the students with written prompts for revisions. The revised solutions showed only significant improvement in the area of conceptual understanding. Overall 66% of the students improved their original score after their revision. The students completed self-monitoring questionnaires, and they were individually interviewed about their revised solutions. Most students maintained or increased their confidence levels after their revisions; however, student attitudes and self-awareness about the task varied.

 

Selected Bibliography:

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Dacey, L.S. (2000, November). Fostering children’s representations of mathematical ideas. Paper presented at the Regional Conference of the National Council of Teachers of Mathematics, Springfield, MA.

 

Fortunato, I., Hecht, D., Tittle, C.K., & Alvaez, L. (1991). Metacognition and problem solving. Arithmetic Teacher, 39 (4), 38-40.

 

Goos, M., Gailbraith, P.,& Renshaw, P. (2000). A money problem: A source of insight into problem solving action. International Journal of Mathematics Education, April 2000. [Online]. Available http://www.ex.ac.uk/cimt/ijmt/ijmenu.htm.

 

Lester, F. K., Jr. (1994). Musing about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25  (6), 660-675.

 

National Council of Teachers of Mathematics. (1989, 2000). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

 

Polya, G. (1954). How to solve it. Garden City, NY: Doubleday & Company, Inc.

 

Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of research on mathematics and meaning, New York: Macmillan.