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…

Reports on the responses of students using a computer algebra system (CAS) called DERIVE in an introductory calculus course at undergraduate level. Indicates that the use of this technology was a catalyst for students to use three types of learning strategies: (1) regularly using multiple representations, (2) discussing meaning with peers and…

There are many perceived benefits of using technology, such as computer algebra systems, in undergraduate mathematics courses. However, attaining these benefits sometimes proves elusive. Some of the key variables are the teaching approach and the student instrumentation of the technology. This paper considers the instrumentation of computer-based…

For the last three years the author of this paper has been teaching mathematics to a group of students at Year 9 level who have rarely had success in mathematics, particularly in the area of algebra. Most of these students struggle with algebraic concepts and processes and generally have poor retention of any acquired knowledge. For the two years…

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

A model with fixed relations between manifest and latent variables is presented for investigating choice reaction time data. The numbers for fixation originate from the polynomial function. Two options are considered: the component-based (1 latent variable for each component of the polynomial function) and composite-based options (1 latent…

Cognitive load theorists have frequently used subjective measures of cognitive load to test the effectiveness of instructional procedures. This study sought to broaden the applications of subjective measures by testing their ability to detect variations in intrinsic cognitive load within tasks. In two experiments students were asked to complete…