School algebra and the computer

How are we to use the computer in the teaching and learning of algebra? In the longterm the new technology is introducing new possibilities that may radically change the algebra curriculum. However, in the short-term we already have the National Curriculum placing its template on the development of algebra in school. The recent regrouping of topics into five attainment targets has integrated number pattern with the development of algebraic symbolism. It seems natural to build from expressing patterns in words to expressing them in a shorthand algebraic notation, but, although this proves a sound tactic for the more able, there are subtle difficulties for the majority of children. Instead I shall advocate introducing algebraic symbolism by using it as a language of communication with the computer, through programming in a suitable computer language. This has two distinct benefits – it develops a meaningful algebraic language which can be used to describe number patterns, and it gives a foundation for traditional algebra and its manipulation

Casimir forces for inhomogeneous planar media

Casimir forces arise from vacuum uctuations. They are fully understood only for simple models, and are important in nano- and microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases condence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green's functions is at the boundary of current computer algebra technology. We further demonstrate that Lifshitz theory of electromagnetic vacuum energy can not be directly applied to calculate the Casimir stress for models of this type, and produce results that have led to alternative regularisations. Using a combination of our new computational framework and the new theory based on our results, we provide specic calculations of Casimir forces for planar dielectrics having permittivity that declines exponentially. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and describe a combined numerical and symbolic computational framework for calculating Casimir forces for arbitrary planar models.Publisher PD

Technology’s edge: the educational benefits of computer-aided instruction

Because a significant portion of U.S. students lacks critical mathematic skills, schools across the country are investing heavily in computerized curriculums as a way to enhance education output, even though there is surprisingly little evidence that they actually improve student achievement. In this paper we present results from a randomized study in three urban school districts of a well- defined use of computers in schools: a popular instructional computer program which is designed to teach pre-algebra and algebra. We assess the impact of the program using statewide tests that cover a range of math skills and tests designed specifically to target pre- algebra and algebra skills. We find that students randomly assigned to computer-aided instruction score at least 0.17 of a standard deviation higher on a pre- algebra/algebra test than students randomly assigned to traditional instruction. We hypothesize that the effectiveness arises from increased individualized instruction as the effects appear larger for students in larger classes and those in classes in which students are frequently absent.Computer-assisted instruction ; Technology

Algebra skills and traps and diagnostic teaching for the future

Explores on some research about teaching and learning algebra and related classroom issues. Diagnostic instruments that may be used by senior secondary teachers in teaching algebra to senior classes; Strategies for remediating algebraic difficulties and misconceptions; Impact of technology on the algebra curriculum; Usefulness of copying algebraic expressions while using Computer Algebra Systems or mathematics processing software in a calculus class.<br /

Development of Multimedia Application for Learning Algebra

New technology and advancement in computer technology has attracted educators and researchers to develop educational computer applications. These learning applications help to enrich learning materials with the utilization of multimedia presentation. The objective of this study is to assess the undergraduate engineering students’ understanding of algebra and to develop a multimedia application for learning algebra. The study was carried out in three stages. In the first stage, a set of questionnaire was distributed to 113 students and a set of test was given to 60 students. The second stage was the development of the application and the third stage, the evaluation of the developed application. The survey and test result show that most of the students have difficulties in understanding algebra especially in the subtopic of factorization. In turn, an Algebra Tutor was developed based on the survey information and the students’ test result. Keywords: Algebra, Multimedia Application, Factorizatio

Algebra, matrices, and computers

What part does algebra play in representing the real world abstractly? How can algebra be used to solve hard mathematical problems with the aid of modern computing technology? We provide answers to these questions that rely on the theory of matrix groups and new methods for handling matrix groups in a computer

Algebra, matrices, and computers

What part does algebra play in representing the real world abstractly? How can algebra be used to solve hard mathematical problems with the aid of modern computing technology? We provide answers to these questions that rely on the theory of matrix groups and new methods for handling matrix groups in a computer

SOLVING PROBLEMS ON THE TEACHING METHODS OF LINEAR ALGEBRA THROUGH TECHNOLOGY PLATFORM DOT.NET

This article will be considered when solving problems on linear algebra. It present a method in solving this problem with the use of computer technology, and also presents a list of tasks to be solved with various applications that was created on platform DOT.NET. This application is quick and easy to understand and will help everyone to understand linear algebra