Proceedings of the E-Learning and Smart Engineering Systems (ELSES 2023)

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The didactic transposition of probabilistic metric space concept

Authors
Youssef Achtoun1, 2, *, Mohammed Lamarti Sefian1, 2, Ismail Tahiri1, 2, Laakel Hemdanou Abderrafik1, 2, Mouali Sara1, 2
1LaSAD Laboratory, NormalHigherSchool, Abdelmalek Essaadi University, Tetouan, Morocco
2AMCS Team, NormalHigherSchool, Abdelmalek Essaadi University, Tetouan, Morocco
*Corresponding author. Email: achtoun44@outlook.fr
Corresponding Author
Youssef Achtoun
Available Online 5 February 2024.
DOI
10.2991/978-94-6463-360-3_21How to use a DOI?
Keywords
Probabilistic metric spaces; didactic transposition; thematisation
Abstract

A space is a set which in defined a structure. Many typologies of spaces are provided in Mathematics. Before studying a lesson, teachers may know the structure of a lesson and their knowledge scholar. Two related lessons, probability and statistics, are everywhere jointly thought, however they are completely separated in their knowledge origin. In this paper, we will present the metric spaces related to the statistics and we will introduce the didactic transposition of the probabilistic metric spaces which are a generalization of usual metric spaces, the idea is to replace the distance between two points by a distribution function, it means that we do not know exactly the distance between two points but we know the probabilities of possible values of the distance. We offer an approach by the didactic transposition for how to use this type of spaces in the scholarly knowledge. Through this paper, we give an epistemological analysis of this new concept with a thematization of knowledge about the concept of probabilistic metric spaces.

Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the E-Learning and Smart Engineering Systems (ELSES 2023)
Series
Atlantis Highlights in Social Sciences, Education and Humanities
Publication Date
5 February 2024
ISBN
10.2991/978-94-6463-360-3_21
ISSN
2667-128X
DOI
10.2991/978-94-6463-360-3_21How to use a DOI?
Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Youssef Achtoun
AU  - Mohammed Lamarti Sefian
AU  - Ismail Tahiri
AU  - Laakel Hemdanou Abderrafik
AU  - Mouali Sara
PY  - 2024
DA  - 2024/02/05
TI  - The didactic transposition of probabilistic metric space concept
BT  - Proceedings of the E-Learning and Smart Engineering Systems (ELSES 2023)
PB  - Atlantis Press
SP  - 196
EP  - 206
SN  - 2667-128X
UR  - https://doi.org/10.2991/978-94-6463-360-3_21
DO  - 10.2991/978-94-6463-360-3_21
ID  - Achtoun2024
ER  -