Begun in the mid-90s, computers have long been a staple in teaching mathematics to engineering students. In recent years, with the effects of the COVID-19 pandemic and the arrival of Generation Z in tertiary education, the role of blended learning has increased. This paper highlights some of the greater challenges and successes of the transition…

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…

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.…

In this contribution, we show the practical use of the computer to visualise simple computational simulations to show phenomena that occur in everyday life, or require an abstract understanding for being unintuitive phenomena. The relationship of the mathematics to different scientific disciplines motivates us to devise different treatments to…

This paper provides a set of five indicators of CAS use, which provide a means to analyse a student's written solution to determine whether they used CAS for solving a given problem. These indicators provide a way for researchers and teachers to determine CAS use without requiring classroom observation or the explicit recording of extra…

The emphasis in several courses at technical faculties is on using a computer to perform numerical methods. Instead of focusing on mathematical rigorousness such courses usually concentrate on demonstrating the practical usage of numerical mathematical methods to the students. The practical usage of numerical methods is best learned by exposing…

CATO is a new user interface, developed by the author as a response to the significant difficulties faced by scientists, engineers, and students in their usage of computer algebra (CA) systems. Their tendency to use CA systems only occasionally means that they are unfamiliar with requisite grammar and syntax these systems require. The author…

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…

Using Mathematical Modelling has become a useful tool in teaching-learning mathematics at all levels. This is so because mathematical objects are seen from their very applications, giving them meaning from the beginning. In this paper we present some details on the development of a teacher's training course called Modelling in the Teaching of…

This paper offers a framework, an extension of Valsiner's "zone theory", for the analysis of joint student-teacher development over a series of technology-based mathematics lessons. The framework is suitable for developing research studies over a moderately long period of time and considers interrelated student-teacher development as…

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…

In this work we will present the ScilabUMA environment we have developed as an alternative to Matlab. This environment connects Scilab (for numerical analysis) and Maxima (for symbolic computations). Furthermore, the developed interface is, in our opinion at least, as powerful as the interface of Matlab. (Contains 3 figures.)

This article explains the didactical design of M@th Desktop (MD), a teaching and learning software application for high schools and universities. The use of two types of MD resources is illustrated: notebooks and palettes, focusing on the topic of exponential functions. The handling of MD in a blended learning approach and the impact on the…

This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

Two kinds of software, CAS and DGS, are starting to work towards mutual integration. This paper envisages common grounds for such integration based on principles of computer theorem proving (CTP). Presently, the CTP community seems to lack awareness as to which of their products' features might serve mathematics education from high-school to…