This research addresses the issue of how to support students' representational fluency--the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is…

Middle-school students are expected to understand key components of graphs, such as slope and y-intercept. However, constructing graphs is a skill that has received relatively little research attention. This study examined students' construction of graphs of linear functions, focusing specifically on the relative difficulties of graphing slope and…

In a classroom environment in which continual access to graphing calculators is assumed, items that have been used to assess students' understanding of functions often are no longer appropriate. Describes strategies for modifying such items including requiring students to explain their reasoning, using calculator-active items, analyzing graphs and…

Presents a secondary classroom investigation into mathematical modeling techniques with the graphing calculator using a match stick puzzle. Geometric models, through their corresponding area formulas, are constructed, tested, and analyzed graphically to fit specified problem conditions. (Author/MKR)

Shows how five points determine the formula of a conic section and uses the determinant as a computational device to find the coefficients in the formula. Uses symbolic, numerical, and graphical techniques. (Author/MKR)

An alternative application of logarithms in the high school algebra curriculum that is not undermined by the existence and widespread availability of calculators is presented. The importance and use of linear relationships are underscored in the proposed lessons. (MP)

Introduces a strategy for writing equations of graphs to help students and teachers build strong conceptual connections between the symbolic representations of algebra and the spatial representations of geometry. (Author/MKR)

Describes how the computer algebra system Mathematica can be used to enhance the teaching of the topics of sequences and series. Examines its capabilities to find exact, approximate, and graphically generated approximate solutions to problems from these topics and to understand proofs about sequences. (MDH)

Describes how prospective elementary teachers examined, analyzed, and evaluated four students' written responses on a graphing task for an end-of-course performance assessment in a mathematics methods course. Provides evidence of the prospective teachers' pedagogical content knowledge. Indicates the importance of process and correct answers and…

The design of a "percent computer" that uses the concept of similar triangles is presented. The device can be easily made by elementary and secondary pupils out of graph paper and string. Sample student problems are included. (MP)

Illustrated is the problem of solving equations and some different strategies students might employ when using available technology. Gives illustrations for: exact solutions, approximate solutions, and approximate solutions which are graphically generated. (RT)

The Triple Representation Model of problem solving is presented. The use of microcomputers in this problem-solving environment is discussed, and examples are provided. The integration of this method into the mathematics curriculum is described. (CW)

Integrates mathematics and science by investigating the scientific application of the Polynomial Difference Theorem using data points from an experiment. Utilizes the different capabilities of the graphing calculator to investigate a problem whose solution is a second degree equation and makes connections between the mathematical concepts involved…

Promotes the use of computers in teaching not only to solve problems but also to help students be better at analyzing problems and developing procedures for their solution. Outlines several problems where a computer-assisted analysis can help give students a thorough understanding of the topic. (TW)

Provides an example of the integration of science and mathematics learning of one high school physics student in a constructivist classroom. Discusses the student's integration of mathematical and nonmathematical representations and of different mathematical representations in a nonuniform acceleration experiment. Describes a model for integrating…