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Education Sciences
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Fermi Problems in Mathematics and Science Education
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Fermi Problems in Mathematics and Science Education

A special issue of Education Sciences (ISSN 2227-7102).

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 12389

Special Issue Editors

Dr. Irene Ferrando Palomares

E-Mail Website
Guest Editor
Department of Didactics of Mathematics, Universitat de València, Av. de Tarongers, 4, 46010 València, Valencia, Spain
Interests: mathematical education; teacher training; mathematical modelling; affectivity and talent
Dr. Lluís Albarracín

E-Mail Website
Guest Editor
Department de Didàctica de la Matemática I les Ciències Experimentals, Universitat Autónoma de Barcelona, 08193 Barcelona, Spain
Interests: mathematics education; secondary school; modelling; Fermi problems; teacher knowledge

Special Issue Information

Dear Colleagues,

Fermi problems (also known as Fermi questions or back-of-envelope problems) have been used since the mid-20th century at all levels of education (from primary school to university) for a number of different pedagogical purposes in various fields of knowledge. Enrico Fermi used them in his physics classes to show to students the potential of estimation in promoting efficient laboratory work. They have also been used, however, in other scientific disciplines (chemistry or biology), as well as mathematics, engineering, computer science, and economics.

Subsequently, they have been used as activities to promote mathematical modeling, to develop number sense in different scientific disciplines, to promote critical thinking, to support the decision-making and planning phases in engineering processes, to identify good problem solvers in professional selection processes, or as a way of dealing with the first stages of product development when entrepreneurs evaluate the commercial viability of new commodities to teach how to identify

However, despite this variety of pedagogical uses, research on Fermi problems is scarce, since in the literature, one can find multiple recommendations for their use but few studies, and they are disconnected from each other, without any construction of knowledge based on previous research.

Against this background, this Special Issue calls for all kinds of research articles, both empirical and theoretical, as well as examples of novel uses that highlight the potential of Fermi problems in different disciplines and educational levels.

Dr. Irene Ferrando Palomares
Dr. Lluís Albarracín
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a double-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Education Sciences is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fermi problem
  • estimation
  • mathematics education
  • science education
  • engineering
  • modeling

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Published Papers (4 papers)

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Research

14 pages, 7513 KiB  
Article
Analysis of the Relationship between Creativity in Fermi Problems Measured by Applying Information Theory, Creativity in Psychology, and Mathematical Creativity
by Hidemichi Okamoto, Mutfried Hartmann and Tetsushi Kawasaki
Educ. Sci. 2023, 13(3), 315; https://doi.org/10.3390/educsci13030315 - 18 Mar 2023
Cited by 1 | Viewed by 2409
Abstract
Many educational institutions demand the development of creativity. However, it is still insufficient for encouraging creative work or thinking. One reason is the lack of simple tools to measure creativity in schools. This study focused on Fermi problems to solve the reason for [...] Read more.
Many educational institutions demand the development of creativity. However, it is still insufficient for encouraging creative work or thinking. One reason is the lack of simple tools to measure creativity in schools. This study focused on Fermi problems to solve the reason for this issue. Fermi problems have been suggested to be deeply related to creativity. However, few empirical studies have been conducted on their relationship. Therefore, this study conducted a survey and analyzed them by structural equation modeling. The results showed a moderate correlation between creativity in Fermi problems and creativity in psychology (r = 0.47, p < 0.01). Additionally, it was shown that there is a strong correlation between creativity in Fermi problems and mathematical creativity (r = 0.76, p < 0.01). Furthermore, regression analysis showed that creativity in Fermi problems is an important factor for measuring creativity in psychology and mathematical creativity. Full article
(This article belongs to the Special Issue Fermi Problems in Mathematics and Science Education)
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18 pages, 2678 KiB  
Article
In-Service and Pre-Service Science Teachers’ Enacted Pedagogical Content Knowledge about the Particulate Nature of Matter
by Anastasia Buma and Doras Sibanda
Educ. Sci. 2022, 12(9), 576; https://doi.org/10.3390/educsci12090576 - 24 Aug 2022
Cited by 1 | Viewed by 2413
Abstract
The particulate nature of matter is a fundamental concept in science that students in lower grades find difficult to understand. Pedagogical content knowledge (PCK) has been identified as germane for addressing difficult topics and it enhances effective learning. The purpose of this study [...] Read more.
The particulate nature of matter is a fundamental concept in science that students in lower grades find difficult to understand. Pedagogical content knowledge (PCK) has been identified as germane for addressing difficult topics and it enhances effective learning. The purpose of this study was to capture the quality of the enacted PCK that practising and pre-service teachers activate during planning. Data were collected through a validated PCK questionnaire which was completed by both practising and pre-service teachers. A rubric was used to code their responses. A Rasch analysis model was used to analyse the five components of the topic-specific PCK construct. Data from an item analysis show that pre-service teachers found the test items to be less difficult than did the practising teachers. We found that there was a statistically significant difference between the two groups of teachers in terms of knowledge activated during planning. These findings show that, in transforming the topic content and concepts of the particulate nature of matter, the pre-service teachers integrated more components of enacted PCK compared to practising teachers. Discussions around the curriculum for both groups of teachers might provide insight into the design of future teacher development programmes. Full article
(This article belongs to the Special Issue Fermi Problems in Mathematics and Science Education)
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19 pages, 540 KiB  
Article
MAD+. Introducing Misconceptions in the Temporal Analysis of the Mathematical Modelling Process of a Fermi Problem
by Marta Pla-Castells, Carmen Melchor and Gisela Chaparro
Educ. Sci. 2021, 11(11), 747; https://doi.org/10.3390/educsci11110747 - 18 Nov 2021
Cited by 2 | Viewed by 2730
Abstract
This work describes how the combination of the mistakes committed by a group of pre-service teachers when solving a Fermi problem, with the representation of the temporal analysis of their resolutions, can offer more in-depth information about their conceptual misconceptions regarding mathematical and [...] Read more.
This work describes how the combination of the mistakes committed by a group of pre-service teachers when solving a Fermi problem, with the representation of the temporal analysis of their resolutions, can offer more in-depth information about their conceptual misconceptions regarding mathematical and modelling concepts. The combined representation allows knowing when mistakes occur and provides a powerful tool for instructors to adapt the teaching–learning processes of mathematics at all levels of education. Our study is based on a recent categorisation of students’ mistakes, together with the creation of a new representation tool, called MAD+, that can combine all this information. The macroscopic view provided by the MAD+ diagrams gives insight into the context in which the mistakes take place and makes the analysis of the resolution of a Fermi problem more efficient. Full article
(This article belongs to the Special Issue Fermi Problems in Mathematics and Science Education)
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19 pages, 1266 KiB  
Article
Classification and Analysis of Pre-Service Teachers’ Errors in Solving Fermi Problems
by Carlos Segura and Irene Ferrando
Educ. Sci. 2021, 11(8), 451; https://doi.org/10.3390/educsci11080451 - 23 Aug 2021
Cited by 6 | Viewed by 2825
Abstract
Fermi problems are useful for introducing modelling in primary school classrooms, although teachers’ difficulties in problem solving may hinder their successful implementation. These difficulties are associated with the modelling process, but also with the estimation and measurement skills required by Fermi problems. In [...] Read more.
Fermi problems are useful for introducing modelling in primary school classrooms, although teachers’ difficulties in problem solving may hinder their successful implementation. These difficulties are associated with the modelling process, but also with the estimation and measurement skills required by Fermi problems. In this work, a specific categorization of errors for Fermi problems was established, and it allowed us to analyse the errors of N = 224 pre-service primary school teachers. The results showed that prospective teachers make a large number of errors when solving this type of task, especially conceptual ones, which are associated with the process of simplifying/structuring the real situation and the mathematization process. They also showed that there is a significant relationship between the characteristics of the problem context and the error categories. Knowing the types of errors that prospective teachers make and designing task sequences that make them emerge so that prospective teachers learn from them could be an effective way to improve initial teacher education in modelling and estimation problem solving. Full article
(This article belongs to the Special Issue Fermi Problems in Mathematics and Science Education)
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