In this paper "Derive" functions are provided for the computation of the Moore-Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore-Penrose inverse. Making it possible to compute the Moore-Penrose inverse easily with one of the most commonly used Computer Algebra Systems--and to have the blueprint…

Electronic communication is a powerful tool teachers can leverage to improve learning. In this article, the authors explain how they used chat and discussion forums to improve their mathematics classes, and how others can adapt their strategies across the curriculum.

In a previous article in this journal, simple constructions were considered to study the reflective property of a parabola and of a paraboloid. The purpose was to help middle school students understand the importance of the parabola shape and its ability to focus parallel rays. The examples demonstrated a use of the two "Cabri" products to study a…

The nature of mathematical reference fields has substantially evolved with the advent of new types of digital technologies enabling students greater access to understanding the use and application of mathematical ideas and procedures. We analyze the evolution of symbolic thinking over time, from static notations to dynamic inscriptions in new…

Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his "big ideas" as he lived through the most amazing innovations in technology that have changed our lives…

Teacher played an important role in ascertaining effective teaching of mathematics. The objective of this paper was to investigate the pedagogical usability of a digital module prototype that integrated a dynamic geometry software, Geometer's Sketchpad (GSP) in mathematics teaching. The prototype was developed based on Reiser's and Dick's…

After carrying out a project over several years in eight upper secondary schools in Thuringia on the effects the use of a handheld CAS (Computer Algebra System) has on the students' skills in mathematics, the former ban on the use of such technology in mathematics education was revoked. Late in the project (2002) a survey of all students in the…

The authors explore the teaching of trigonometry using a method developed by Jeremy Burke of Kings College. A series of lessons was planned using an approach which looks at moving from a mathematical description of the topic, to a sequence plan, to a set of activities, which students can use to help them come to understand the topic. This is…

The National Council of Teachers of Mathematics identified technology as a feature of high-quality mathematics education. One way that teachers can use technology to facilitate their pupils' mathematical understanding is through the generating and exploring multiple representations of mathematical ideas. The purposes of this study are to: (1)…

In this paper, the development of an innovative Virtual Manipulatives and Whiteboard (VMW) system is described. The VMW system allowed users to manipulate virtual objects in 3D space and find clues to solve geometry problems. To assist with multi-representation transformation, translucent multimedia whiteboards were used to provide a virtual 3D…

This study provides empirical evidence of a highly specific use of games in education--the assessment of the learner. Linear regressions were used to examine the predictive and convergent validity of a math game as assessment of mathematical understanding. Results indicate that prior knowledge significantly predicts game performance. Results also…

The purpose of this study was to investigate the impact of the mathematics anxiety treatment messages in a computer-based environment on ninth-grade students' mathematics anxiety and mathematics learning. The study also examined whether the impact of the treatment messages would be differentiated by learner's gender and by learner's prior…

This research seeks to (1) establish a feasible development and implementation model for an inquiry-based learning environment with e-mentoring using videoconference, and (2) apply the model to examine its impact on rural students' learning. To achieve these goals, we developed a model of inquiry-based learning with e-mentoring (IBLE) based on…

New methodologies in science (or mathematics) learning process and scientific thinking in the classroom activity of engineer students with ICT (information and communication technology), including graphic calculator are presented: visual modelling with ICT, action research with graphic calculator, insight in classroom and communications and…

A grounded theory approach was employed to explore the variation in strategies used by students when solving mental multiplication problems. Metacognitive prompts, externally generated stimuli that activate thoughtful cognition, were automatically generated via computer during the solving of mental multiplication problems to elicit awareness,…