Following a line of inquiry regarding the exact number of real roots of a real polynomial, this investigation considers: Descartes' Rule of Signs, the Budan-Fourier Theorem, and versions of Sturm's Method in contrast with the approximate root count gleaned from graphing utilities. Online applets are provided to allow the reader to freely…

Learning content in mathematics, such as vector geometry, is still predominantly taught in an abstract manner, as the visualization and interaction of three-dimensional problems are limited with classical forms of teaching such as blackboard lessons or exercise sheets. This research article proposes the use of augmented reality (AR) in mathematics…

An important and interesting area in the study of triangle geometry is the related issue of extrema problems and inequalities. These problems play a significant role in the mathematics study program in high school. In tasks such as these, the difficulty level is high when one does not know in advance what the expected answer is. When one knows…

An iPad® can be used to teach students to graph parabolas with ease and grasp vocabulary quickly. Parabolas come to life for students in this easily implemented activity described in this article. Teachers can use this tool in a fun and interactive way to not only address these graphing and vocabulary concepts but also introduce and explore…

This paper reports on a qualitative investigation into the use of Show and Tell tablet technology in mathematics classrooms. A Show and Tell application (app) allows the user to capture voice and writing or text in real time. Described here are the perceptions of 11 teachers during and after their exploration into the use of Show and Tell in their…

The integration of digital technology confronts teachers, educators and researchers with many questions. What is the potential of ICT for learning and teaching, and which factors are decisive in making it work in the mathematics classroom? To investigate these questions, six cases from leading studies in the field are described, and decisive…

To determine the effect of learning computer programming and the use of a computer on mathematical achievement of eleventh grade students, for each of two years, average and above average students were randomly assigned to an experimental and control group. The experimental group wrote computer programs and used the output from the computer in…

Reasons other than utility are needed to justify the place of algebra in the mathematics curriculum for all children. The possibility of considering generalized arithmetic and computer algebra are each discussed. (MNS)

How 125 seventh graders had three days of hands-on computer experience is described in some detail. Computer programs are included. (MNS)

The suggested program is designed for mathematics teachers. It concerns the solution of systems of linear equations, but it does not complete the job on its own. The user is the solver while the computer is merely a computing assistant. (MNS)

A module built around programing the computer is described. It recognizes the need of many children to have algebra introduced in a practical way and to give some concrete meaning to it. (MNS)

Issues about computer use are addressed by a discussion activity designed to help students think about situations and understand various points of view. Four situations are given, each presented from the viewpoints of four persons. (MNS)

An intuitive approach to exponential functions is described. Microcomputers are used to aid discovery of derivatives. (MNS)

A first computer lesson in algebra is described, with illustrations of programing by students. Standard algebraic notation with BASIC are discussed, and further activities described. The purpose is to use the computer so that it develops a rational understanding of the mathematical concepts involved. (MNS)