Describes some basic difficulties in early algebra and their causes and presents some strategies for overcoming them. Lists five areas as being essential foundations for learning algebra: (1) seeing the operation, not just the answer; (2) understanding the equals sign; (3) understanding the properties of numbers; (4) being able to use all numbers;…

Explains how number work in elementary school can be extended to prepare students for algebra. Suggests some practical strategies that focus on five aspects of number knowledge essential for algebra learning. (ASK)

Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Demonstrates a change in the goals of teaching the algebra of equation-solving in Victoria, Australia that requires a transition from a way of solving problems in arithmetic to a conceptually new algebraic way. Contains 20 references. (Author/ASK)

Discusses the benefits of new technologies, especially graphing calculators, in the teaching and learning of mathematics. Presents two activities for teaching algebra and regression using graphing calculators. (ASK)

Reports on a study in which three volunteer teachers helped design and then taught an experimental program of introductory differential calculus in which students had full access to calculators with a computer algebra system (CAS) in the classroom, at home, and during tests. Test scores indicated that the classes had learned similar amounts of…

Approximately 1,200 students in years 7 to 10 were tested on recognizing, using, and describing rules relating 2 variables. Fourteen interviewed students saw a variety of patterns, many of which were not helpful for algebra. Outlines critical steps in moving from a table to an algebraic rule. (MKR)

Investigates the cognitive and linguistic demands of learning algebra and explores students' understanding of algebraic notation. Findings indicate specific origins of misinterpretation that include intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in…

Investigates how different problem presentations promote the construction of different cognitive models in school students (N=268) aged 14 to 16. Concludes that the lack of correspondence between a cognitive model of the situation and an algebraic representation of relationships in a problem is a powerful obstacle to the use of algebraic methods.…

Data from students in grades 8-10 in suburban schools were presented to show that errors in formulating algebraic equations are not primarily the result of syntactic translation, as has been assumed in the literature. A theory of cognitive models is offered as an explanation for the errors. (Contains 37 references.) (MLN)