Based on the properties of a Primitive Pythagorean Triple (PPT), a computer program was written to generate, print, and count all PPTs greater than or equal to I[subscript x], where I[subscript x] is an arbitrarily chosen integer. The Density of Primitive Pythagorean Triples may be defined as the ratio of the number of PPTs whose hypotenuse is…

The design of technology tools has the potential to dramatically influence how students interact with tools, and these interactions, in turn, may influence students' mathematical problem solving. To better understand these interactions, we analyzed eighth grade students' problem solving as they used a java applet designed to specifically accompany…

We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…

The "I CAN Learn[R] Mathematics Curriculum" is designed to help ethnically diverse, inner-city students in grades 7 through 10 achieve parity in mathematics and problem-solving skills. It uses an interactive software program to teach pre-algebra and algebra. The "I CAN Learn[R] Algebra 1" course, which was used in all of the…

In the fall of 2005 the Maui Educational Consortium began a project that was funded through the Math Science Partnership program to implement the "Cognitive Tutor[R]" (CT) program, published by Carnegie Learning, in some of the Algebra 1 classes in the Maui School District and at the Maui Community College. At that time, Empirical…

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…

In Technology Enhanced Learning Environments, self-regulated learning (SRL) partly relies on the features of the technological tools. The authors present two environments they designed in order to facilitate SRL: the first one (e-Dalgo) is a website dedicated to the learning of algorithms and computer programming. It is structured as a classical…

This article discusses our teaching approach in graduate level Engineering Statistics. It is based on the use of modern technology, learning groups, contextual projects, simulation models, and statistical and simulation software to entice student motivation. The use of technology to facilitate group projects and presentations, and to generate,…

These proceedings contain the papers of the International Conference on Educational Technologies 2013 (ICEduTech 2013), which has been organised by the International Association for Development of the Information Society and co-organised by the Faculty of Computer Science & Information Technology, Universiti Putra Malaysia, Kuala Lumpur,…

Having students draw and investigate geometric shapes in a Logo environment is advocated as an excellent way to have them constructively learn geometric concepts. This document illustrates the potential of Logo for getting high school students involved in mathematical explorations by presenting a sequence of seven activities. The activities…

The chapters in this book were written by teachers to share strategies they have found effective in the mathematics classroom. Most describe a teaching idea or activity in sufficient detail for other teachers in elementary, middle, and secondary schools to be able to use it. The chapters concern: manipulative materials, developing a mathematics…

This manual is used with MATHBOXES, a computer program written for Apple II microcomputers to help children relate formal mathematical symbols for representing simple word problems to the informal strategies using physical objects that they naturally use to solve them. There is a substantial body of research that documents that young children are…

An outgrowth of a conference of developmental faculty and administrators interested in exploring computer-based education, this monograph presents 26 papers devoted to microcomputer applications in college basic skills programs. Included are 5 papers on general topics, 13 on language teaching, 7 on mathematics, and 1 dissent paper. Articles range…

The author presents two examples of lattice multiplication followed by a computer algorithm to perform this multiplication. The algorithm is given in psuedocode but could easily be given in Pascal. (PK)

Programs (using Logo) developed by children to produce multiples, the Fibonacci series, and square numbers are presented, with graphical representations of functions introduced. Another investigation involves drawing a circle using turtle graphics. (MNS)