#### Year of Award

2020

#### Document Type

Thesis

#### Degree Type

Master of Arts (MA)

#### Degree Name

Education

#### Department or School/College

Teaching and Learning

#### Committee Chair

David Erickson

#### Commitee Members

David Erickson, Chair, Teaching and Learning, Frederick Peck, Department of Mathematical Sciences, Matthew Roscoe, Department of Mathematical Sciences

#### Publisher

University of Montana

#### Subject Categories

Science and Mathematics Education

#### Abstract

Many mathematical problems can only be solved in routine ways. But when students see that problems can be solved in innovative, original, or novel ways, unexpected benefits arise such as development in one’s mathematical creativity. The general mathematics classroom must be reformed into a more perceptive atmosphere that challenges all students, where student mathematical creativity is fostered, and creative insights are encouraged. Mathematical creativity encourages the full development of the learner, all students on the spectrum from underchallenged to traditional. Mathematical creativity is the ability of "divergent production in mathematical situations, and the ability to overcome fixations in mathematical problem solving” (Haylock, 1987, p. 69). Mathematical creativity can be broken down into three dimensions of divergent thinking – fluency, flexibility, and originality. Educators must provide tasks that promote divergent thinking and creativity, such as challenging mathematical problems that give students opportunities to problem solve/pose and showcase their talents. But because of fixations, it is difficult for students to showcase originality on their own. Therefore, the goal of this study is to improve mathematical creativity in secondary mathematics students using good problem-‐solving tasks and finding best methods for promoting and rewarding divergent thinking. High school students in an Intermediate Algebra class partook in pre-‐intervention-‐ post cycles over the course of five weeks. Students took a pre-‐ Math Creativity Test, comprised of four open-‐ended, multiple solution tasks, designed for students to provide multiple solutions, distinct from what their peers would provide. Students were given scores for fluency, flexibility, originality, and total mathematical creativity. Students completed an intervention process of developing divergent thinking iii and utilizing problem-‐solving settings as a venue for expressing mathematical creativity. After the intervention, the students took the post-‐ Math Creativity Test, comparing the scores in fluency, flexibility, originality, and total math creativity between the pre-‐ and posttests. Results informed effective ways to develop mathematical creativity.

#### Recommended Citation

Gruntowicz, Brooke, "Mathematical Creativity and Problem Solving" (2020). *Graduate Student Theses, Dissertations, & Professional Papers*. 11562.

https://scholarworks.umt.edu/etd/11562

#### Included in

© Copyright 2020 Brooke Gruntowicz