**ERIC Number:**ED525019

**Record Type:**Non-Journal

**Publication Date:**2009

**Pages:**172

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**ISBN-978-1-1241-0727-1

**ISSN:**N/A

A Cognitive Approach to Solving Systems of Linear Equations

Ramirez, Ariel A.

ProQuest LLC, Ph.D. Dissertation, Illinois State University

Systems of linear equations are used in a variety of fields. Exposure to the concept of systems of equations initially occurs at the high school level and continues through college. Attempts to unearth what students understand about the solutions of linear systems have been limited. Gaps exist in our knowledge of how students understand systems of equations and other topics typically studied in a linear algebra course. This study was designed after the conclusion of a prior study which described how students understand the solution of an equation. Data generated from this prior study revealed that full understanding of the solution of a system of linear equations may be composed of several components. One of those components investigated in this study is the characteristics of the ways that students come to understand the concept of solving a system of linear equations in the context of a linear algebra course. The research questions were guided by the APOS theory. Data were collected in the form of observations from a teaching sequence with a small Linear Algebra class and from written tasks presented during interviews with four students from the same class. An initial genetic decomposition was used to describe the concept. Analysis of the data led to the conclusion that understanding the concept of solving a system of linear equations is a part of the object conception of equivalent systems of linear equations. In order to understand the process of solving a system of linear equations, a student must realize the important role that equivalent systems play in the process. Analysis of the data also yielded enough evidence to modify the initial genetic decomposition to include the concept of equivalent systems and a detail description of the possible progression of a student's concept of solving a system of linear equations. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Descriptors: Equations (Mathematics), Algebra, Mathematics Instruction, College Mathematics, Secondary School Mathematics, Observation, Data Analysis, Problem Solving, Mathematical Concepts

ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site: http://www.proquest.com/en-US/products/dissertations/individuals.shtml

**Publication Type:**Dissertations/Theses - Doctoral Dissertations

**Education Level:**High Schools; Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A