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Mathematics
Special Issues
New Advances in Mathematics Education and Mathematics History
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New Advances in Mathematics Education and Mathematics History

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 13594

Special Issue Editors

Prof. Dr. Alexander Maz Machado

E-Mail Website
Guest Editor
Departament of Mathematics, Facultad de Ciencias de la Educación, Universidad de Córdoba, San Alberto Magno s/n, 14071 Córdoba, Spain
Interests: mathematical education; history of mathematics; history of mathematics education; mathematics teacher training; attitudes toward mathematics; curriculum in higher education; bibliometrics, scientometrics
Dr. Maria Jose Madrid Martín

E-Mail Website
Guest Editor
Faculty of Education, Universidad Pontificia de Salamanca, Henry Collet, 52-70, 37007 Salamanca, Spain
Interests: didactics of mathematics; history of mathematics education; history of mathematics; mathematics teacher training; attitudes toward mathematics; bibliometrics

Special Issue Information

Dear Colleagues,

The MDPI journal Mathematics is launching a Special Issue on the history of mathematics and mathematics education.

The interest of research groups in the history of mathematics and mathematics education has increased in recent decades. Knowledge about how mathematics and its teaching have advanced and evolved allows researchers to understand mathematics problems of the past, to know how they were approached and overcome. This knowledge provides cognitive, philosophical, and epistemological tools to face different aspects of modern-day mathematics problems, in particular aspects related to its understanding, dissemination or teaching.

This Special Issue aims to discuss current trends in all dimensions of the history of mathematics and mathematics education. It is an opportunity to show different studies of researchers and research groups which are focused on powerful ideas with the potential to enrich this field. Therefore, it will become a global forum for research on various topics related to the history of mathematics and mathematics education.

Authors are invited to submit their original research manuscripts to this Special Issue, all of which will be peer-reviewed.

You are also welcome to disseminate this call to others whose research you think would be relevant to this Special Issue.

Prof. Alexander Maz Machado
Dr. Maria Jose Madrid Martín
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 single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • History of mathematics education
  • History of mathematics
  • Analysis of old mathematics books
  • History of mathematics in modern-day classroom
  • Historical evolution of mathematical concepts
  • New research perspectives on the history of mathematics and mathematics education

Published Papers (5 papers)

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Research

13 pages, 2455 KiB  
Article
Optimization Problems in Spanish Differential Calculus Books Published in the 18th Century
by José Carlos Casas-Rosal, Carmen León-Mantero, Noelia Jiménez-Fanjul and David Gutiérrez-Rubio
Mathematics 2022, 10(13), 2322; https://doi.org/10.3390/math10132322 - 2 Jul 2022
Viewed by 1353
Abstract
History of mathematics and mathematics education research allows us to know, among other issues: the influence that certain textbooks have had on the teaching of school mathematics, in academic or professional training, during a certain historical period; as well as the scientific advances [...] Read more.
History of mathematics and mathematics education research allows us to know, among other issues: the influence that certain textbooks have had on the teaching of school mathematics, in academic or professional training, during a certain historical period; as well as the scientific advances achieved in each historical period and their incorporation into the teaching of the subject matter. In this work, we focus our attention on the applications of the method of finding maxima and minima included in the textbooks published during the 18th century in Spain. Specifically, we identify the approach of the algorithm used, the shortcomings or deficiencies that the posing of the proposed problems may have, the verification of the nature of the optimal points obtained and the consideration—or not—of the negative solutions in the process of resolution. Full article
(This article belongs to the Special Issue New Advances in Mathematics Education and Mathematics History)
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11 pages, 401 KiB  
Article
Developing an Instrument for Analyzing Mathematics and Mathematics Education Ideas in the Spanish Press of the 18th Century
by María José Madrid, Alexander Maz-Machado, Astrid Cuida and Cristina Pedrosa-Jesús
Mathematics 2022, 10(13), 2308; https://doi.org/10.3390/math10132308 - 1 Jul 2022
Cited by 2 | Viewed by 1438
Abstract
Old mathematics books and textbooks have focused different researchers onto the history of mathematics and mathematics education. However, books are not the only information source for this field; for example, researchers can also study periodical-type publications from the past (such as diaries, weeklies, [...] Read more.
Old mathematics books and textbooks have focused different researchers onto the history of mathematics and mathematics education. However, books are not the only information source for this field; for example, researchers can also study periodical-type publications from the past (such as diaries, weeklies, newspapers, etc.). Considering this, this study developed an instrument to analyze publications about mathematics and mathematics education included in newspapers, weeklies, journals, etc., which were not exclusively devoted to science, from the perspective of the history of mathematics and mathematics education. In order to do so, a descriptive research focused on the analysis of historical texts was carried out using the content analysis technique. The different labels and categories of this instrument are here exemplified by the categorization of some entries included in several periodical publications published in the 18th century in Spain. Full article
(This article belongs to the Special Issue New Advances in Mathematics Education and Mathematics History)
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20 pages, 1072 KiB  
Article
The Values of Illustration in the Economic Society of Asturias and Its Reflection in Mathematics Education at the Royal Asturian Institute of Nautical Studies and Mineralogy during the Last Quarter of the 18th Century
by Carmen López-Esteban and Fernando Almaraz-Menéndez
Mathematics 2022, 10(10), 1747; https://doi.org/10.3390/math10101747 - 20 May 2022
Viewed by 1596
Abstract
The Economic Society of Friends of the Country of Asturias, Spain, was an instrument of enlightened reformism which operated in a region with serious economic backwardness. It was born in 1780 at the initiative of Campomanes and responds to the Matritense model, meaning [...] Read more.
The Economic Society of Friends of the Country of Asturias, Spain, was an instrument of enlightened reformism which operated in a region with serious economic backwardness. It was born in 1780 at the initiative of Campomanes and responds to the Matritense model, meaning that it focused on economic development and popular education. It is known that Jovellanos directly participated in the establishment of the Royal Institute of Nautical Studies and Mineralogy of Gijón. In this work, the historical method of research in education was used with the objective of determining the sociogenesis of the kind of technical mathematics that was taught in this Institute. The results show the role of the Asturian Economic Society in the creation of the Institute and we also analysed the teaching and curriculum of mathematics that was taught there, and if it was in line with the internal debates of the discipline in that historical moment. The limitations of the Jovellanista model of the Technical Training School for Sailors and Miners created in Gijón are made clear, although the attempt to start it up in such a peripheral place is no less remarkable. Full article
(This article belongs to the Special Issue New Advances in Mathematics Education and Mathematics History)
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19 pages, 1881 KiB  
Article
The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century
by Qiao-Ping Zhang and Ngai-Ying Wong
Mathematics 2021, 9(18), 2310; https://doi.org/10.3390/math9182310 - 18 Sep 2021
Cited by 3 | Viewed by 2743
Abstract
The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This [...] Read more.
The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This study identified the problems and characteristics regarding how similarity is treated in secondary mathematics textbooks in Hong Kong in the past half century. The content analysis method was used to analyze six secondary mathematics textbook series published in different periods. From the epistemological perspective of the textbook contents, our analysis shows the historical context and learning trajectories of how similarity was treated in school curriculum. The natural axiomatic geometry paradigm is not emphasized too much at different stages and most of the textbooks did not provide formal proofs of similarity. The intuitive idea was gradually consolidated into a formal definition of similarity. Furthermore, the way that rigorous geometric deduction can be performed from intuitive concepts and experimental geometry to the idea of proofs and formal proofs is also discussed. Full article
(This article belongs to the Special Issue New Advances in Mathematics Education and Mathematics History)
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21 pages, 12246 KiB  
Article
Mathematics Curriculum Reform and Its Implementation in Textbooks: Early Addition and Subtraction in Realistic Mathematics Education
by Marc Van Zanten and Marja Van den Heuvel-Panhuizen
Mathematics 2021, 9(7), 752; https://doi.org/10.3390/math9070752 - 31 Mar 2021
Cited by 6 | Viewed by 4955
Abstract
Since the late 1960s, a reform in mathematics education, which is currently known under the name Realistic Mathematics Education (RME), has been taking place in the Netherlands. Characteristic for this approach to mathematics education is that mathematics is not seen as ready-made knowledge [...] Read more.
Since the late 1960s, a reform in mathematics education, which is currently known under the name Realistic Mathematics Education (RME), has been taking place in the Netherlands. Characteristic for this approach to mathematics education is that mathematics is not seen as ready-made knowledge but as an activity of the learner. Although much has been written about the big ideas and intentions of RME, and multiple RME-oriented textbooks have been published, up to now the development of this approach to mathematics education has not been thoroughly investigated. In the research reported in this article, we traced how RME has evolved over the years. The focus in our study was on early addition and subtraction in primary school. For this, we studied RME core curriculum documents and analyzed RME-oriented textbooks that have been published between the onset of RME and the present. We found that the big ideas and teaching principles of RME were clearly reflected in the learning facilitators for learning early addition and subtraction and were steadily present in curriculum documents over the years, although some were made concrete in further detail. Furthermore, we found all RME learning facilitators also to be present in all RME-oriented textbooks, though in some cases in other ways than originally intended. Our research shows the complexity of a curriculum reform process and its implementation in textbooks. Full article
(This article belongs to the Special Issue New Advances in Mathematics Education and Mathematics History)
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