Geometrography, "alias the art of geometric constructions" was proposed by Emile Lemoine between the late 1800s and the early 1900s. It consisted originally of a system to measure the complexity of ruler-and-compass geometric constructions, capable of: designate every geometric construction by a pair of values that manifests its…

This paper concerns the design of a specific computer-based educational environment fostering students' shift from argumentation to proof in geometry. In particular, we focus on the language difficulties that such a shift might present and on the need for suitable interventions to overcome them. In this respect, we designed a specific device,…

There has been a large amount of research about the impact of dynamic geometry software (DGS) on the learning of mathematics mainly related to different representations of mathematical concepts and functional dependences. This paper goes beyond these investigations by suggesting meaningful connection and integration of DGS with physical resources…

This paper reports a study developed with twenty-six students from a 7th-grade class and was carried in the context of teaching experience in the school year of 2016/2017, using an applet, Equation Buster, on the learning of solving single-variable linear equations. The research objectives are to assess how this applet can help students to see the…

In this paper we analyse the role of the teacher in a Digital interactive Storytelling in Mathematics (DiST-M) activity. involved in the story as a character (the Guru, a math expert), the teacher acts as a mediator in students' problem-solving process. We analyse how the teacher may orchestrate the mathematical discussions to allow students…

Dynamic geometry environment allows us to investigate geometric relationships and problems more efficiently than the pencil-and-paper method. Continuous variation of geometric configurations shows the relationship from different points of view. This paper aims to provide some indications of how a dynamic geometry environment, especially GeoGebra…

Sometimes Computer Algebra Systems (CAS) offer an answer that is somewhat different from the answer that is probably expected by the student or teacher. These (somewhat unexpected) answers could serve as a catalyst for rich mathematical discussion. In this study, over 120 equations from school mathematics were solved using 8 different CAS. Many…

Solving systems of equations at school, at least in Argentina, is usually a task that students are given as a series of techniques that "allow" them to find a solution. How to overcome educational obstacles that are generated from a fragmented approach of knowledge? What can DGS do, in particular the CAS environment? What epistemic and…

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

This paper investigates the possible influence of attitude on seven Year 11 students' use of a Computer Algebra System (CAS) during a class activity where students could choose to use CAS or pen-and-paper in solving a range of problems. Investigation of anxiety, confidence, liking and usefulness through a survey and interview revealed that these…

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

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…

This article begins with a comparison of two groups of teachers, working on the same tasks in Analytic Geometry. One group has only basic experience in CAS-assisted problem solving, and the other group has extensive experience. The comparison is discussed in terms of the interplay between reflection, operative knowledge and execution. The findings…

As part of a module on mathematical problem solving in an Initial Teacher Education programme, the student teachers are encouraged to produce alternative solutions to the problems they tackle and, in particular, to consider whether ICT can help. In this paper we discuss a number of unusual solutions produced for some of the problems, specifically…

T-algebra is a project for creating an interactive learning environment for expression manipulation tasks of elementary algebra. Our main didactical principle has been that all the necessary decisions and calculations at each solution step should be made by the student, and the program should be able to understand the mistakes. This paper…