Date of Award

Spring 1-1-2018

Document Type

Thesis

Degree Name

Master of Arts (MA)

First Advisor

Eric Stade

Second Advisor

Katherine E. Stange

Third Advisor

David Grant

Abstract

We define sequencing of mathematical processes (SMP) to encompass all scenarios where changing the order in which operations or processes are applied to a math problem affects the result. Student errors in secondary and post-secondary mathematics courses frequently stem from SMP misconceptions. In this paper we explore SMP issues in a middle school Pre-Algebra class. Data is drawn from student assessments, including homework assignments, tests, and semester examinations throughout a year-long course. We find in a largely qualitative analysis that students are most successful when they incorporate a step- by-step process understanding with a big-picture object understanding of mathematical ideas. By working to attain this duality, students can be efficient both storing and recalling information. We make use of learning theories of Dubinsky, Gray and Tall, and Sfard to inform our analysis and conclusions.

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