Describes the experimental intelligent computer algebra system STRAMS which can solve problems using a set of methods and techniques traditionally taught, learn new mathematical problem solving methods, and generate different kinds of explanations. Analyzes these features of STRAMS to give reasons for its potential applicability in building…

Presents ways of using theories of knowing and learning to inform use of computer algebra systems (CAS) in school and early college mathematics. Describes the role of macroprocedures and microprocedures, process-object distinctions, and the movement towards more formal ways of expressing mathematical ideas. Discusses how these theories along with…

Describes the different ways in which two pioneering Australian teachers adapted their teaching to use computer algebra systems (CAS). One teacher used CAS with the primary goal of increasing understanding but restricted student use. The other teacher adopted CAS as an extra technique for solving standard problems, emphasizing time saving routines…

Draws on previously published cases of six secondary school mathematics teachers as they began to use computer algebra systems (CAS) in their classrooms. Urges movement towards a model of effective teaching with CAS that allows for the various manifestations and degrees of success encountered in the literature. (Author/MM)

Describes an approach to the design of learning environments around a computer algebra kernel. Presents two environments to help students learn precalculus. Provides students with symbolic, graphic, and numeric tools as well as functionalities to help them build proofs. (Author/KHR)

Investigates whether computer algebra systems (CAS) are suitable environments for implementing mathematical microworlds. Recalls what constitutes a microworld and explores how CAS can be used for implementation, stating potentials as well as limitations. Provides as an example the microworld "Formula 1", implemented in Maple Software. (Author/KHR)

Investigates how animation is used to improve students' comprehension of the limit concept in an experimental course in which the main topics are approximation and interpolation by Taylor polynomials. Uses Mathematica software to generate the dynamic graphics, visualize the process of convergence, and give meaning to the definitions. Analyzes…

Presents examples to illustrate that iteration and recursion are useful pedagogical tools that can be used in many areas of mathematics, make models traditionally taught in upper levels accessible in grades 9-14, and provide alternative problem solving approaches less dependent upon ready-made formulas. (Author/MM)

Stresses the links between the technical work and the conceptual reflection in the learning of mathematics and argues that the potential of Computer Algebra Systems (CAS) is to be found in the more varied and richer techniques that CAS can offer. Reports on an experiment with DERIVE as well as findings of research on graphical calculators, and…

Provides a qualitative description of what happened to 10th grade students' attitudes and cognitive development when learning algebra using Computer Algebra Systems (CAS). Chronicles the frustrations, changes in attitude, motivation, determination, and improvements in cognitive development of algebraic concepts over the course of the six-week…

Reviews what is happening in examination systems that have begun to allow the use of Computer Algebra Systems (CAS) in externally set 'high stakes' assessment regimes. Discusses possible options for the future with the intention of developing a dialogue on how assessment with a CAS can help develop the mathematical literacy of students. (Author/MM)

Discusses the notion of variables in computer algebra, mathematics, and science. Central are the questions of how variables are actually used in mathematics and science, how computer algebra supports the various uses of variables, what conceptual differences exist, and what consequences follow from this for teaching, learning, and doing…

Demonstrates a less utilized feature of the TI-92+: its natural and powerful programming language. Shows how to implement several linear algebra related algorithms including the Gram-Schmidt process, Least Squares Approximations, Wronskians, Cholesky Decompositions, and Generalized Linear Least Square Approximations with QR Decompositions.…

Shows how teachers can often use unexpected outputs from Computer Algebra Systems (CAS) to reinforce concepts and to show students the importance of thinking about how they use the software and reflecting on their results. Presents different examples where DERIVE, MAPLE, or Mathematica does not work as expected and suggests how to use them as a…

Illustrates two ways of exploring the properties of cubic polynomials. The first exploration uses a Computer Algebra System (CAS) to help students understand an important part of mathematical history, the discovery of an algorithm to find the roots of a cubic equation. The second exploration states some conditions required for a curve and finds a…