Related papers: L'algorithme : pourquoi et comment le d{\'e}finir …
The school choice problem concerns the design and implementation of matching mechanisms that produce school assignments for students within a given public school district. In this note we define a simple student-optimal criterion that is…
In this paper we try to organize machine teaching as a coherent set of ideas. Each idea is presented as varying along a dimension. The collection of dimensions then form the problem space of machine teaching, such that existing teaching…
In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra in the variety has a decidable word problem. It has a uniformly decidable word problem if…
While the field of algorithmic fairness has brought forth many ways to measure and improve the fairness of machine learning models, these findings are still not widely used in practice. We suspect that one reason for this is that the field…
Innovations in AI have focused primarily on the questions of "what" and "how"-algorithms for finding patterns in web searches, for instance-without adequate attention to the possible harms (such as privacy, bias, or manipulation) and…
Curriculum design is a fundamental component of education. For example, when we learn mathematics at school, we build upon our knowledge of addition to learn multiplication. These and other concepts must be mastered before our first algebra…
Algorithms learned from data are increasingly used for deciding many aspects in our life: from movies we see, to prices we pay, or medicine we get. Yet there is growing evidence that decision making by inappropriately trained algorithms may…
Knowledge about programming is part of the knowledge matrix that will be required of the professionals of the future. Based on this, this work aims to report the development of a teaching tool developed during the monitoring program of the…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
We argue that explanations for "algorithmic decision-making" (ADM) systems can profit by adopting practices that are already used in the learning sciences. We shortly introduce the importance of explaining ADM systems, give a brief overview…
The introductory programming sequence has been the focus of much research in computing education. The recent advent of several viable and freely-available AI-driven code generation tools present several immediate opportunities and…
This chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
The desire to make applications and machines more intelligent and the aspiration to enable their operation without human interaction have been driving innovations in neural networks, deep learning, and other machine learning techniques.…
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…
While Machine learning gives rise to astonishing results in automated systems, it is usually at the cost of large data requirements. This makes many successful algorithms from machine learning unsuitable for human-machine interaction, where…
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
Engineering needs mathematics, but the converse is also increasingly evident. Indeed, mathematics is still recovering from the drawbacks of several "reforms". Encouraging is the revived interest in proofs indicated by various recent…
We argue how AI can assist mathematics in three ways: theorem-proving, conjecture formulation, and language processing. Inspired by initial experiments in geometry and theoretical physics in 2017, we summarize how this emerging field has…