# Symbolic Representation

## Using Schemas to Develop Algebraic Thinking

This article describes how students generalize and formalize patterns using student developed schemas including subtracting out and building up. The article includes samples of student work including students explanations for each schema. This article could supplement readings from section II and IV.

## Strategies Used by Second-Year Algebra Students to Solve Problems

This article is a brief overview of the results of a research project focusing on solution strategies algebra students used to solve non-linear function problems. The article focuses on the variety of strategies, the relationship to achievement and using multiple representations. Examples of the constructed response items and student solutions are given. This reading could be used to supplement readings from section II and IV.

## Middle School Students' Understanding of Core Algebraic Concepts: Equivalence + Variable

This article describes the results of a multi-year research project on algebraic reasoning in middle school students. The article describes middle school studentsí understandings and/or misunderstandings of two core algebraic ideas ñ equivalence and variables. The article gives student response examples and discusses implications for instruction. This article could be used to supplement the readings from sections II and IV.

## Developing Students' Understanding of Variable

This article describes the implementation of an activity designed to confront a common misconception about variable. The article describes common misconceptions held by middle level students and describes a problem situation designed to uncover studentsí misconceptions. This article could be used to supplement the readings from sections II and IV.

## Building a Foundation for Learning Algebra in the Elementary Grades

The research summarized in this Volume of In Brief focuses on the ability of elementary students to reason algebraically. The articles can be used with CTS Section IV.

## Balancing Act: The Truth behind the Equals Sign

This article illustrates the misconceptions that students have when using the equals sign and describes an activity used with students to develop the foundation for an accurate conception of equivalency. The author states that developing an accurate understanding of the equal sign is the basis for comprehending equations and inequalities. This article could be used to supplement the readings from sections II and IV.

## Algebra In Simplest Terms

Video instructional series consisting of 26 programs designed to be used by students or as a review of content matter for teachers. Illustrations and examples are used to solve real-world problems. This series could be used to supplement the readings from section I.