It is agreed that algebra has an important role in physics, particularly through handling symbols. A lot of previous research has focused on how mathematics is used in physics from perspectives where mathematics is taken for granted, and not addressing potential differences of mathematics in the physics classroom and in the mathematics classroom.…

Symbols are a cornerstone of the written language of physics and mathematics but inconsistencies in their use pose a challenge to students. This article reports on interviews held with first-year undergraduate physics students, focused on their early experiences with symbols in university physics. Students reported being confused by the symbolic…

This paper presents an analysis of the different types of meanings that an individual may assign to a collection of algebraic symbols depending on the mathematical context in which the symbols are presented and the mathematical knowledge possessed by that individual. Four contexts for the Quadratic Theorem are used to illustrate the ways in which…

Discusses algebra teaching by looking back into the history of algebra and the work of George Peacock, who considered algebra from two points of view: symbolic and instrumental. Claims that, to be meaningful, algebra must be linked to real-world problems. (18 references) (MKR)

Presents a study using a module of work based on a graphing calculator that provided an environment where students could experience some aspects of variables and begin to build an understanding of them. Graphing calculators proved to be an instrument for achieving significant improvement in student understanding, which had often proved difficult…

Attempts to describe a notion parallel to number sense, called symbol sense, incorporating the following components: making friends with symbols, reading through symbols, engineering symbolic expressions, equivalent expressions for non-equivalent meanings, choice of symbols, flexible manipulation skills, symbols in retrospect, and symbols in…

Provides a brief historical explanation of the multiplication sign in mathematics. (ASK)

Presents and discusses examples that can be used to develop the concept of slope as a rate of change through three modes of learning: (1) visualization, (2) verbalization, and (3) symbolization. (ASK)

Algebra, an important skill, provides a way to represent situations so they can be analyzed carefully. In the new algebra classroom, students will listen and talk to one another while learning to understand problems and devise solutions. Teachers will organize tasks (involving graphing, rating, and ranking techniques) to help students discover the…

Sensitizes high school and college teachers to challenges that students often have with mathematical symbols and suggests instructional strategies that can reduce such difficulties. Discusses various uses of symbols and identifies common difficulties encountered as students verbalize, read, and write symbols. Offers teaching strategies that can…

Explores how students interpret algebraic notation and what teachers can do to support appropriate interpretations. Presents two research-based strategies and concludes that in the face of reform and technological advances, finding a definition for symbol sense takes on added significance. Contains 22 references. (ASK)

Considers some of the implications of replacing, for the purposes of physics instruction, algebraic notation with programming language. Introduces a framework based on two theoretical constructs. Concludes that algebra-physics can be characterized as the physics of balance and equilibrium and programming-physics as the physics of processes and…

Explains that the use of symbols in some textbooks to represent both physical quantitites and numerical measures is illogical and confusing. (GA)

Describes a student's work on a word problem after which she was very comfortable with her answer but her work was not correct. Discusses symbol sense, goals for students, and how tasks can be used to help meet those goals. (KHR)

Introduces a strategy for writing equations of graphs to help students and teachers build strong conceptual connections between the symbolic representations of algebra and the spatial representations of geometry. (Author/MKR)