**ERIC Number:**ED550301

**Record Type:**Non-Journal

**Publication Date:**2011

**Pages:**269

**Abstractor:**As Provided

**Reference Count:**N/A

**ISBN:**978-1-2677-9357-7

**ISSN:**N/A

Grade 4-6 Student Conceptions and Utilization of Informal and Formal Variable Representations across Mathematically Equivalent Tasks

Switzer, Matt

ProQuest LLC, Ph.D. Dissertation, University of Missouri - Columbia

This study reports how 24 grade 4-6 students in one elementary and middle school interpreted formal and informal representations of variables. While interpretations for variables represented as letters (e.g., x and y) have been well established for students in algebra classes and beyond, little research into elementary school students' initial interpretations of variables exists. This study examined student interpretations of formal (e.g., x + y = 12) and informal representations of variables (e.g., [white triangle up] + [white square] = 12). The students in this study were consistent in their meaning of various representations of variables presented in equations, but did not parallel normative algebraic solutions. For example, students treated the representation of the variables as different variables even if they were the same (e.g., y + y = 12). Student also consistently produced multiple solutions for each variable. For example, they supplied the ordered pair solutions such as (6,6), (5,7), (4,8), regardless of the representation of the variable (e.g., y + y = 12; a + b = 12; and [white triangle] + [white square] = 12). Further, these students did not exhibit many of the misconceptions exhibited by students in algebra classes and beyond. For example, the common misconception that different variables can only take on different values was not a typical response for these students (Fujii, 2003). However, when these same tasks were presented as word problems, students treated variables in an algebraically normative way. In other words, the students were more "successful" solving the word problems (Koedinger & Nathan, 2004). Students attended to the syntactic and semantic structure of the word problems to determine meanings for the variables that were not evident in the 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: Elementary School Mathematics, Elementary School Students, Middle School Students, Student Attitudes, Mathematical Concepts, Algebra, Misconceptions, Task Analysis, Word Problems (Mathematics), Problem Solving, Syntax, Semantics, Concept Formation, Grade 4, Grade 5, Grade 6

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

**Education Level:**Elementary Education; Middle Schools; Secondary Education; Junior High Schools; Grade 4; Intermediate Grades; Grade 5; Grade 6

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A