Date of Award

Summer 7-1-2022

Degree Type

Dissertation

Degree Name

Doctor of Education in Middle Grades Education

Department

Education

Committee Chair

David Glassmeyer

First Committee Member

Olga Koz

Second Committee Member

Kadian Callahan

Abstract

Developing mathematical and geometric thinking provides access to mathematics and promotes independent problem-solving skills, an essential life skill in the ever-changing job market. The process of building mathematical thinking and mathematical knowledge relies heavily on generalizations, which extend a range of knowledge or reasoning to a new situation. Promoting generalization among high school students helps develop problem-solving skills that allow for independent solving of non-routine problems or problems that students have not experienced before.

This research identified the generalizations of general principles of strategies, patterns, and rules high school geometry students exhibited during inquiry-based lessons and then applied those generalizations to solve non-routine problems. This qualitative case study identified the application of generalizations through a thematic analysis, a generalization taxonomy, and collecting data from sixteen students through observations, journaling, and interviews while covering the topics of geometric transformations and trigonometry. The findings of this research show students used general principle reflection generalizations to solve non-routine problems on both geometric transformations and trigonometry. Additionally, students used prior knowledge to solve the trigonometry non-routine problems. The findings showed how the generalization taxonomy can be used for lesson development and how the generalization taxonomy can be applied to communicate the demonstration of geometric habits of mind. This research is an example of how classroom educators can promote generalizations and solving non-routine problems.

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