Throughout the years of the history of the development of mathematics, starting with the ancient mathematicians, new things were discovered from time to time, which made it a central component of the computerized world, which serves us in many fields, with the young "swimming" in it, and the adults asking: how could we live without it!…

Learning-by-teaching has been identified as one of the more effective approaches to learning. Recently, educational researchers have investigated virtual environments in order to utilize the learning-by-teaching pedagogy. In a face-to-face learning-by-teaching situation, the role of the learners is to teach their peers or instructors. In virtual…

Two combined design cases examine historically significant projects in technology-assisted instruction developed at Stanford in the 1960's and 1970's: Computer Assisted Instruction (CAI) for elementary school students, and the Nicaraguan Radio Mathematics Project (NRMP). The combination of the cases allows for the exploration of the commonalities…

We report on the development of a "language of description" that facilitates an integrated analysis of classroom video data in terms of the quality of the teaching-learning process and the students' access to valued forms of mathematical knowledge. Our research setting is the introduction of software for teachers for improving the mathematical…

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Computer-aided assessment (CAA) has been used at a university with one of the largest mathematics and engineering undergraduate cohorts in the UK for more than ten years. Lecturers teaching mathematics to first year students were asked about their current use of CAA in a questionnaire and in interviews. This article presents the issues that these…

Three community colleges--El Paso Community College, Bunker Hill Community College, and Patrick Henry Community College--incorporated technology into the curriculum to support student progress in mathematics through developmental education. Each college took its own path: El Paso developed a self-accelerated emporium-style computer lab, Patrick…

An online testing system developed for entry-skills testing of first-year university students in algebra and calculus is described. The system combines the open-source computer algebra system "Maxima" with computer scripts to parse student answers, which are entered using standard mathematical notation and conventions. The answers can…

This paper describes the creation and early uses of Logo. It includes a brief summary of more recent work on Logo-derived languages and learning applications. It closes with a lament on the unrealized potential of student programming languages as empowering tools for knowledge construction and learning.

It has been recognised that the general lack of enjoyment of institutional mathematics learning at the secondary level is one of the basic reasons behind the bad reputation of mathematics in society. Increasing students' motivation to learn mathematics through enjoyment and playing, especially in their free time, might therefore be a relevant…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

Many colleges and universities today are faced with the problem of low student academic achievement in math. Some of them are trying to improve student academic achievement through the use of technology. Their proposed solution is to teach children how to use the technological tools available to them and integrate that technology into the…

There has been a recent call for the use of more systematic thought experiments when investigating learning. This paper presents a storyboarding method for capturing and sharing initial ideas and their evolution in the design of a mathematics learning task. The storyboards produced can be considered as "virtual data" created by thought experiments…

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to…

The projects Xmath (Bringslid and Canessa, 2002) and dMath (Bringslid, de la Villa and Rodriguez, 2007) were supported by the European Commission in the so called Minerva Action (Xmath) and The Leonardo da Vinci programme (dMath). The Xmath eBook (Bringslid, 2006) includes algorithms into a wide range of undergraduate mathematical issues embedded…