Mathematical Creativity in Problem Solving Situations

Document Type

Presentation Abstract

Presentation Date

12-20-2001

Abstract

The process of generalization is an important component of mathematical ability, and to develop this ability is an objective of mathematics teaching and learning (NCTM, 2000). The research study documented how high school freshmen in an accelerated algebra class developed generalization strategies in combinatorial problem-solving situations. Students were asked to solve five non-routine combinatorial problems in their journals, assigned at increasing level of complexity. The generality that characterized the solutions of the five problems was the pigeonhole (Dirichlet) principle.

The researcher documented the evolving strategies of the students. Data gathered through journal writings, open-ended interviews and classroom observations was analyzed using techniques from grounded theory. In particular the constant comparative method of Glaser & Strauss (1977) was used. The researcher expected that student strategies would evolve with the complexity of the problem and with time. Four students were successful in discovering, verbalizing, and in one case successfully applying the generality that characterized the solutions of the five problems, whereas five students were unable to discover the hidden generality.

The research categorized and described student behaviors that led to successful generalizations and those that led to unsuccessful generalizations, as well as identified the variables necessary for students to successfully arrive at mathematical generalizations. The research study resulted in a modification of Lester's (1985) problem-solving model, for the purpose of understanding the generalization process in problem-solving situations. The modified model was an adaptation and extension of Lester's (1985) model and elucidated the properties of the categories in terms of student behaviors. It included an explicit task component and an affective component. The modified model could serve as a pedagogical tool in a mathematics classroom.

Additional Details

Thursday, 20 December 2001
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. Math 104 (Lounge)

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