Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and…

Discusses terminology used by teachers for the symbol "-x" which cause students to become confused. Suggested methods of avoiding this confusion are presented. (JP)

After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…

See EJ 030 376 and also TM 500 284 in this issue. (CK)

The reason for the inability of students to master the solving of word problems in algebra is identified as the failure to organize and analyse the problems. The author's approach to the solution of these problems, involving writing symbols for the unknown(s), generating equations, solving the unknown(s) and interpretation is presented through…

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…

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

Describes Fermat's last theorem and shows the proof for the case when the exponent is four. Outlines other works for the proof of the theorem, including Kummer's. Twelve references are listed. (YP)

This paper considers the problem of variables, in particular parameters, analyzes how these concepts are presented in textbooks, comments on paradigms of exercises in which parameters intervene, and points out difficulties encountered by students. Discusses results of teacher interviews concerning their dealing with parameters in class.…

Investigates whether three cognitive components of language proficiency--metalinguistic awareness of symbol, syntax, and ambiguity--are associated with students' success in learning algebraic notation. Reports that very few students with low metalinguistic awareness scores achieved high algebra scores in a total sample of more than 1500 students.…

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…