Suggests use of the quadratic formula to build understanding that connections between factors and solutions to equations work both ways. Making use of natural connections among concepts allows students to work more efficiently. Presents four sample problems showing the roots of equations. Messy quadratic equations with rational roots can be solved…

Explores quadratic functions using the graphing calculator. Discoveries are made graphically whereas hypotheses are proven algebraically. Includes traditional quadratics, other algebraic quadratics, nonpolynomial quadratics, transcendental quadratics, and proofs. (MKR)

Investigates secondary mathematics teachers' use of the graphing calculator in their classrooms. Examines whether algebra teachers are currently using this technology in their classrooms, their perceptions toward the technology, and any changes in the curriculum or instructional practices. Indicates that the use of the graphing calculator is still…

Active involvement and infusion of mathematics into familiar, everyday experiences are essential elements in challenging students to engage in true thinking. Presents an investigation on graphing that touches on all representations including tables of values, graphs, and verbal descriptions. (ASK)

Offers teaching suggestions for activities using the TI-73 graphing calculator in middle schools. Topics include the number line, data handling, and algebraic thinking. (MM)

Describes the use of the TI-73 calculator to support and enhance the teaching of mathematics with 9-11 year old students. Topics include equivalent fractions, algebra, and data handling. (MM)

Using Newton's method as an intermediate step, we introduce an iterative method that approximates numerically the solution of f(x) = 0. The method is essentially a leap-frog Newton's method. The order of convergence of the proposed method at a simple root is cubic and the computational efficiency in general is less, but close to that of Newton's…

This article illustrates the fact that unless tempered by algebraic reasoning, a graphing calculator can lead one to erroneous conclusions. It also demonstrates that some problems can be solved by combining technology with algebra.

Multi-line-multi-operation calculators such as the TI-80 provide eighth-grade prealgebra and algebra students with significantly better computational tools for basic order-of-operation problems involving integers and signed rational numbers than do calculators offering only last-entry-or-result displays. Effects are more apparent for weaker…

This paper presents the conceptualisation of infinity as a multi-faceted concept, discussing two examples. The first is from history and illustrates the work of Euler, when using infinity in an algebraic context. The second sketches an activity in a school context, namely students who approach the definite integral with symbolic-graphic…

As part of the Electrical Engineering program at the Univesity of Southern Maine, students are typically introduced to Two's Complement algebra and representation, a method to include negative numbers in the binary representation of integers that is widely used in microprocessors and related digital systems. The traditional, procedural method to…

Suggests and illustrates ways in which systematic consideration of selected unary operations can be facilitated by using electronic calculators. Emphasis is placed upon unary operations suitable for exploration and investigation at the pre-algebra level, using calculation algorithms as a basis for generating examples and non-examples to develop…

Describes an activity in which students are given a set of designs and are required to use their electronic grapher to reproduce the designs. The activity reinforces students' understanding of lines and of the formula for a linear function. (MKR)

Identifies big ideas for the informal study of algebra-related topics in the middle grades including notation, variable, function, and properties of number. Suggests meaningful ways to accomplish them. (YDS)

Presents the Fibonacci sequence in a format that is readily implemented using the table and list features of the Texas Instruments TI-82 graphing calculator or a spreadsheet. Includes questions and investigations that can be explored using these tables and lists. (MKR)