Uses articles on children's thinking to find out and improve student teachers' thinking about algebra and proof. (ASK)

Cooperative student work often fails to generate individual understanding of abstract algebra materials. Suggests techniques that enable abstract algebra students to master proofs and enhance cooperative work. (Author/ASK)

Presents problems from the Mathematics in Context (MiC) project with a central theme concerning the construction of a variety of formulas by students. (AIM)

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…

Describes what may be called the next step in making the most effective use of real-life problems in collaborative learning exercises for the classroom. Proceeds from two premises: real-life problems should be used to introduce concepts, and students need to experience mathematics as a process. Illustrates a series of group projects that develop…

Students can learn to make algebra, trigonometry, and geometry work for them by using matrices to rotate figures on the graphics screen of a graphing calculator. Includes a software program, TRNSFORM, for the TI-81 graphing calculator which can draw and rotate a triangle. (MKR)

Describes the Treisman model which involves supplemental workshops in which college students solve problems in collaborative learning groups. Reports on the effectiveness of Math Excel, an implementation of the Treisman model for introductory mathematics courses at Oregon State University over five academic terms. Reveals a significant effect on…

Describes a study that was conducted to determine whether the use of the integrated learning system Learning Logic by high school students in Algebra I had a significant effect on their performance in a traditionally-taught algebra II course. Results showed no significant differences, but teachers using Learning Logic noted some benefits in…

Describes a classroom experiment using hand-held computer algebra systems (CAS) for the learning of algebra with the aim of developing the conception of a parameter as a means for generalization. The idea of the instrumentation of information and communications technology tools turned out to be fruitful in the interpretation of the students'…

Quantitative algebraic and qualitative topological models can be used in the quest for simple explanations in the field of teaching and learning. The examples described cover such diverse topics as teacher anxiety and classroom control, process-product studies, aptitude-treatment interactions, the pace of instruction, the size of classes, and…

Outlines efforts to create mathematics-related activities for freshman/sophomore level college algebra and statistics classes at Shippensburg (Pennsylvania) University. Shares some of the ways in which these activities were created and adapted. (ASK)

Uses the chicken problem for sixth grade students to scratch the surface of systems of equations using intuitive approaches. Provides students responses to the problem and suggests similar problems for extensions. (ASK)

Examines an algebraic model for projecting how many newly hired teachers will be needed in both public and private schools from 1998-99 to 2008-09. Discusses results based on the model, including several alternative projections. (Author)

Adapts Stanic and McKillip's ideas for the use of developmental algorithms to propose that the present emphasis on symbolic manipulation should be tempered with an emphasis on the conceptual understanding of the mathematics underlying the algorithm. Uses examples from the areas of numeric computation, algebraic manipulation, and equation solving…

Describes a study on secondary school students' ways of thinking about linear, quadratic, rational, and square-root inequalities. Indicates that using graphic representations of parabolas when solving rational and quadratic inequalities usually yielded correct solutions and difficulties arose when students failed to reject the excluded values or…