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Debugging is a vital but challenging skill for beginner programmers to learn. It is also a difficult skill to teach. For secondary school teachers, who may lack time or programming experience, honing students' understanding of debugging can…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
This survey paper is an expanded version of an invited keynote at the ThEdu'22 workshop, August 2022, in Haifa (Israel). After a short introduction on the developments of CAS, DGS and other useful technologies, we show implications in…
The motivation for this paper comes out of our experience with teaching natural deduction (ND) and with the way this formal system is implemented by the \textsc{Coq} proof assistant, namely by means of so-called tactics, which are…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
Trimming is a core technique in geometric modeling. Unfortunately, the resulting objects do not take the requirements of numerical simulations into account and yield various problems. This paper outlines principal issues of trimmed models…
In this paper, we are concerned with geometric constraint solvers, i.e., with programs that find one or more solutions of a geometric constraint problem. If no solution exists, the solver is expected to announce that no solution has been…
Holography as a subject is neglected largely in current physics lessons and in school books. Even though this topic might be complex, it is applicable and viable in the world that we live in. Holography lends itself to further develop…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
The study of decimal numbers in secondary education is often approached from algorithmic perspectives, which limits students' understanding of their structure. This paper presents the task Footprints of the Walking of Numbers, a dynamic…
Illustrations are widely used in education, and sometimes, alternatives are not available for visually impaired students. Therefore, those students would benefit greatly from an automatic illustration description system, but only if those…
We survey theoretical, algorithmic, and computational results at the intersection of distance geometry problems and mathematical programming, both with and without adjacencies as part of the input. While mathematical programming methods can…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Several tools have been developed to enhance automation of theorem proving in the 2D plane. However, in 3D, only a few approaches have been studied, and to our knowledge, nothing has been done in higher dimensions. In this paper, we present…
We provide a theoretical framework for analysing and comparing different forms of organizing introductions to mathematical analysis at the secondary level, then illustrate it by two characteristic examples from certain periods of change in…
Understanding geometric relationships with little mathematical knowledge can be challenging for today's students and teachers. A new toolset is introduced that is able to create a proof without words by combining the benefits of the…
In this work, I present an automatic system for the evaluation of closed-type exercises in physics at the high school level or in the first year of a degree where physics is a mandatory course. It is expected that this will allow students…