We present an investigative activity that was set as part of a course of pre-service teachers of mathematics. The emphasis in the course was set on the importance of using the computerized technological tool for teaching the subject. The activity focused on investigating interesting geometrical conservation properties which are not known to the…

Taking as its point of departure, situations arising in classrooms exposed to a heavy use of CAS, exemplified by the Danish upper secondary school mathematics program, the paper discusses the use of "old" cognitive frameworks of mathematics education as an alternative to more recent theoretical developments in the field. The paper draws…

The article presents some examples of plane geometric variance of an area with the use of computer technology. These tools can offer teachers opportunities for adaptation and preparation of pedagogical presentations which will help students along the process of fruitful conjectures formation and eventually construction of formal deductive proofs.…

This article gives an example for using Dynamic Geometry Software to encourage making conjectures, reasoning, and experiencing mathematics as a process.

Eliciting student thinking is paramount to effective mathematics teaching and learning. Although one can use many strategies and techniques to promote student thinking, technology is one resource that is often underutilized. Whether it is the informed use of calculators or an interactive website, technology can be leveraged to promote mathematical…

To draw conclusions from data, we need to understand the context of the data and the measurement units. In 2007, Franklin and colleagues presented the "Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report" to provide teachers with a framework to assist in developing students' investigation of statistical…

Automated theorem proving (ATP) for Propositional Classical Logic is an algorithm to check the validity of a formula. It is a very well-known problem which is decidable but co-NP-complete. There are many algorithms for this problem. In this paper, an educationally oriented implementation of Semantic Tableaux method is described. The program has…

The subject of the article is usage of modern computer technologies through the example of interactive geometry environment Geogebra as an innovative technology of representing and studying of geometrical material which involves such didactical opportunities as vizualisation, simulation and dynamics. There is shown a classification of geometric…

The availability of sophisticated computer programs such as "Wolfram Alpha" has made many problems found in the secondary mathematics curriculum somewhat obsolete for they can be easily solved by the software. Against this background, an interplay between the power of a modern tool of technology and educational constraints it presents is…

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a…

Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…

Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

Students' use of technology allows them to generate and manipulate multiple representations of a concept, compute numbers with relative ease, and focus more on mathematical concepts and higher-order thinking skills. In elementary school mathematics classrooms, students develop higher-order thinking skills by completing complex tasks that require…

A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)

A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…