Abstract
A Test of Arithmetic Problem Posing was developed by the authors to examine the arithmetic problem-posing behaviours of sixty-three prospective elementary school teachers. Results of analysis were then used to examine task format (i.e., the presence or absence of specific numerical information) on subjects’ problem posing and the relationship between subjects’ problem posing and their mathematics knowledge and verbal creativity. The major findings were that the test effectively evaluated arithmetic problem posing, and that most subjects were able to pose solvable and complex problems. In addition, problem-posing performance was better when the task contained specific numerical information than when it did not, and that problem-posing performance was significantly related to mathematical knowledge but not to verbal creativity.
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References
Brown, S. I., & Walter, M. I. (1990).The art of problem posing (2nd edition). Hillsdale, NJ: Lawrence Erlbaum Associates.
Butts, T. (1980). Posing problems properly. In S. Krulik & R. E. Reys (Eds.),Problem solving in school mathematics (pp. 23–33). Reston, VA: National Council of Teachers of Mathematics.
Educational Testing Service (1986).The PPST guide. Princeton, NJ: Author.
Ellertoft, N. F. (1986). Children’s made up mathematics problems— A new perspective on talented mathematicians.Educational Studies in Mathematics, 17, 261–271.
Freudenthal, H. (1973).Mathematics as an educational task. Dordrecht: D. Reidel Publishing.
Getzels, J. W., & Jackson, P. W. (1962).Creativity and intelligence: Exploration with gifted students. New York: John Wiley.
Goldin, G. A., & McClintock, C. E. (1979).Task variables in mathematical problem solving. Columbus, OH: ERIC Clearinghouse for Science, Mathematics and Environmental Education.
Gonzales, N. A. (1996). Problem formulation: Insights from student generated questions.School Science and Mathematics, 96(3), 152–157.
Greer, B., & McCann, M. (1991). Children’s word problems matching multiplication and division calculations. In F. Furinghetti (Ed.),Proceedings of the Fifteen International Conference for the Psychology of Mathematics (pp. 80–87). Assisi, Italy: Author.
Guilford, J. P. (1967).The nature of human intelligence. New York: McGraw-Hill.
Hashimoto, Y. (1987). Classroom practice of problem solving in Japanese elementary schools. In J. Becker & T. Miwa (Eds.),Proceedings of the U.S.-Japan seminar on mathematical problem solving (pp. 94–119). Carbondale, IL: Southern Illinois University.
Haylock, D. W. (1987). A framework for assessing mathematical creativity in school children.Educational Studies in Mathematics, 18, 59–74.
Keil, G. E. (1965). Writing and solving original problems as a means of improving verbal arithmetic problem solving ability.Dissertation Abstracts, 25, 7109–7110. (University microfilms No. 65-2376).
Krutetskii, V. A. (1976).The psychology of mathematical abilities in school children. Chicago: University of Chicago Press.
Leung, S. S. (1993). The relation of mathematical knowledge and creative thinking to the mathematical problem posing of prospective elementary school teachers on tasks differing in numerical information content. Unpublished doctoral dissertation, University of Pittsburgh.
Leung, S. S. (1994). On analyzing problem-posing processes: A study of prospective elementary teachers differing in mathematics knowledge. In J. P. da Ponte & J. F. Matos (Eds.),Proceedings of the 18th International conference of the International Group for the Psychology of Mathematics Education, (pp. 168–175). Lisbon, Portugal: International Group for the Psychology of Mathematics Education.
Leung, S. S. (1995).A study on prospective and practising teachers’ problem posing behaviors. Technical report of research funded by National Science Council of Taiwan. (In Chinese).
Leung, S. S. (1996). Problem Posing as Assessments: Reflections and Re-constructions.The Mathematics Educators, 1 (2), 159–171.
Leung, S. S. (1997). On the role of creative thinking in problem posing.Zentralbatt fur Didaktik der Mathematik (ZDM), International Review on Mathematical Education, 97(2), 48–52.
National Council of Teachers of Mathematics (1989).Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (1991).Professional standards for teaching mathematics. Reston, VA: Author.
Newell, A., & Simon, H. A. (1972).Human problem solving. Englewood Cliffs, NJ: Prentice Hall.
Perez, J. A. (1985).Effects of student-generated problems on problem solving performance. Unpublished doctoral dissertation, Teachers College, Columbia University.
Polya, G. (1945).How to solve it (2nd ed.). New York: Doubleday.
Reusser, K. (1986).Problem solving beyond the logic of things: Textual and contextual effects on understanding and solving word problems. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA. (ERIC Document Reproduction Service No. ED 270327).
Silver, E. A. (1994). On mathematical problem posing.For the Learning of Mathematics, 14(1), 19–28.
Silver, E. A., Mamona, J., Leung, S. S., & Kenney, P. A. (1996). Posing mathematical problems: An exploratory study.Journal for Research in Mathematics Education, 27(3), 293–309.
Torrance, E. P. (1966).Torrance tests of creative thinking: Norms-technical manual. Englewood Cliffs, NJ: Personell Press.
Winograd, K. (1991).Writing, solving and sharing original math story problems: Case studies in the cognitive behavior of fifth grade children. Unpublished doctoral dissertation, University of Northern Colorado.
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Leung, S.S., Silver, E.A. The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Math Ed Res J 9, 5–24 (1997). https://doi.org/10.1007/BF03217299
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DOI: https://doi.org/10.1007/BF03217299