Why is the use of letters in algebraic expressions and equations--variables--the source of such uncertainty for students and teachers? The authors studied a sixth-grade classroom and observed that students hold many misconceptions about variables. Some students hold an algebraic view of the equal sign. For them, it indicates an equation and…

The authors teach a problem-solving course for preservice middle-grades education majors that includes concepts dealing with absolute-value computations, equations, and inequalities. Many of these students like mathematics and plan to teach it, so they are adept at symbolic manipulations. Getting them to think differently about a concept that they…

Mathematics is a language that is characterized by words and symbols that have precise definitions. Many opportunities exist for miscommunication in mathematics if the words and symbols are interpreted incorrectly or used in imprecise ways. In fact, it is found that imprecision is a common source of mathematical disagreements and misunderstandings…

Mathematics is rich in visual representations. Such visual representations are the means by which mathematical patterns "are recorded and analyzed." With respect to "vocabulary" and "symbols," numerous educators have focused on issues inherent in the language of mathematics that influence students' success with mathematics communication.…

The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that instructional programs at the middle grades should enable students to "represent and analyze mathematical situations and structures using algebraic symbols" (2000, p. 222). Guess and check is a powerful problem-solving strategy that can connect a conceptual…

Developing meaning for symbolic representations is an important part of the middle school mathematics experience for all students. Teachers must not see simply writing symbolic representations as the end goal, but focus on the internal meaning that students ascribe to these symbols. Too often, students lack a deep understanding of the algebraic…

The equal sign is perhaps the most prevalent symbol in school mathematics, and developing an understanding of it has typically been considered mathematically straightforward. In fact, after its initial introduction during students' early elementary school education, little, if any instructional time is explicitly spent on the concept in the later…

The abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical…

Describes some differences in representations of mathematical concepts and procedures of recent immigrants. Discusses considerations for success of recent immigrants. (YDS)

This article describes a variety of activities that ask students to identify, describe, compare, and classify symbol strings (algebraic expressions and equations). The activities use a collection of twelve symbol strings on cards. (Contains 2 figures.)

This article describes the implementation of an activity designed to confront a common misconception about variable. (Contains 1 table and 3 figures.)