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Analecta: Studies and Materials for the History of Science

Analecta: Studies and Materials for the History of Science

Description
Analecta: Studies and Materials for the History of Science is a peer-reviewed scientific journal, supported and published biannually by the Institute for the History of Science, Polish Academy of Sciences since 1992. Drawing on the rich tradition of the publishing series Studia i Materiały z Dziejów Nauki Polskiej [Studies and Materials from the History of Polish Science], initiated in 1953 by Bogdan Suchodolski, the journal covers all areas of the history of science. It features extensive research papers, shorter studies, critical editions of source texts, as well as conference reports and book reviews. Occasionally, Analecta publishes themed issues on topics of particular interest within the history of scientific thought, edited in cooperation with prominent scholars.
ISSN
ISSN: 1509-0957
Publishers
Institute for the History of Science, Polish Academy of Sciences
Analecta: Studies and Materials for the History of Science is a peer-reviewed scientific journal, supported and published biannually by the Institute for the History of Science, Polish Academy of Sciences since 1992. Drawing on the rich tradition of the publishing series Studia i Materiały z Dziejów Nauki Polskiej [Studies and Materials from the History of Polish Science], initiated in 1953 by Bogdan Suchodolski, the journal covers all areas of the history of science. It features extensive research papers, shorter studies, critical editions of source texts, as well as conference reports and book reviews. Occasionally, Analecta publishes themed issues on topics of particular interest within the history of scientific thought, edited in cooperation with prominent scholars.

The editorial board accepts proposals in Polish and English on a rolling basis. Issues are published at the end of June and at the end of December each year. Editors neither charge fees for accepting articles for publication nor pay fees to authors.

Submissions are evaluated by the editorial board (internal review) and independent experts in the double-blind peer review process which means that the identity of both the author and the reviewer is concealed (external review). Reviewers are requested to disclose any conflict of interest and assess each publication impartially on the basis of eight objective criteria.

In the last ranking of the Polish Ministry of Education and Science (17.07.2023) Analecta: Studies and Materials for the History of Science received 70 points.

Editorial office

Jerzy Kaliszuk (editor-in-chief), jerzykaliszuk@gmail.com, ORCID: https://orcid.org/0000-0002-2049-5659 

Alicja Urbanik-Kopeć (Assistant Editor-in-chief), alicja.urbanik@gmail.com, ORCID: 0000-0002-1121-4309

Michał Siermiński (Editorial Assistant), m.siermiński@gmail.com, ORCID: 0000-0002-8355-5006

Karolina Karpińska (book review editor), karolinakarpinska001@gmail.com, ORCID: 0000-0002-1477-6622

Jakub Bajer, jakub_bajer@wp.pl, ORCID: 0000-0002-8845-7472

Jarosław Kurkowski, jkurkowski@poczta.onet.pl, ORCID: 0000-0002-7895-6438

Dorota Kozłowska, dorotapeczlewicz@gmail.com, ORCID: 0000-0001-5826-4381

Sławomir Szyller, s.szyller@gmail.com, ORCID: 0000-0002-1556-6395

 

Editorial board

Rūta Čapaitė (Lithuanian Institute of History, Vilnius)

Magdolna Hargittai (Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics)

Ernst Homburg (Department of History, University of Maastricht)

Brian Krostenko (Department of Classics, University of Notre Dame)

Halina Lichocka (Instytut Historii Nauki Polskiej Akademii Nauk, Warszawa)

Jacek Soszyński (Instytut Historii Nauki Polskiej Akademii Nauk, Warszawa)

Soňa Štrbáňová (Institute of Contemporary History, Czech Academy of Sciences, Prague)

Ignacio Suay-Matallana (Department of Public Health, History of Science and Gynaecology, Miguel Hernández University of Elche)

Józef Szudy (Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Toruń)

Jarosław Włodarczyk (Instytut Historii Nauki Polskiej Akademii Nauk, Warszawa)

Zbigniew Wójcik (Museum of the Earth, Polish Academy of Sciences, Warszawa)

Leszek Zasztowt (Faculty of Oriental Studies, University of Warsaw)

Contact

Institute for the History of Science, Polish Academy of Sciences

ul. Nowy Świat 72, pok. A 16

00-330 Warsaw, Poland

Telefon: (+48 22) 657 27 30, (+48 22) 657 27 46

E-mail: czasopismo.analecta@gmail.com

Articles are licensed under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.en), which means that anyone may download and redistribute the material for free.

All content is freely accessible on the publisher’s website and in the Science Library. The journal is abstracted and indexed by BazHum, Central European Journal of Social Sciences and Humanities, European Reference Index for the Humanities and Social Sciences, Federation of Digital Libraries and Index Copernicus.

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Content

Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2

1 Inter-Balkanic Connections: International Cooperation Among Mathematicians and Education Reform in Greece During the 1930s
Dionisis Baltzis
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 11-27 | DOI: 10.24425/asmdn.2025.158147
Keywords: history of mathematics education Hellenic Mathematical Society (HMS) Association of Secondary Education Mathematics Teachers (ASEMT) Inter-Balkanic Conference of Mathematicians
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Abstract

This study explores the interplay between Greek secondary mathematics education reform and international mathematical collaboration in the 1930s, focusing on the 1934 Inter-Balkanic Conference of Mathematicians in Athens. It examines the role of the Hellenic Mathematical Society (HMS) in shaping education, highlighting internal conflicts, particularly between university professors and secondary school teachers. These tensions led to the formation of the Association of Secondary Education Mathematics Teachers (ASEMT), which organized the landmark conference. The event, shaped by political, scientific, and educational aims, coincided with the Balkan Pact and emphasized regional cooperation. Despite initial HMS resistance, the conference gained international recognition. The study also addresses textbook authorship and publishing, showing how commercial competition and state control influenced education. The findings reveal broader implications of political and scientific developments for educational reform in Greece and the Balkans.
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Authors and Affiliations

Dionisis Baltzis
2 The Icelandic Learned School as a Secondary School in 19th-Century Europe
Kristín Bjarnadóttir
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 29-42 | DOI: 10.24425/asmdn.2025.158148
Keywords: Iceland mathematics education secondary school gymnasium Björn Gunnlaugsson
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Abstract

Iceland, inhabited by Norse people since the 9th c., had a population of fewer than 70,000 until the 1870s. Christianity, adopted in 1000 CE, brought literacy and cathedral schools, later reinforced by Lutheran Protestantism in 1550 and special privileges for Icelandic students at the University of Copenhagen. European secondary schools in the early 1800s placed increased emphasis on mathematics, sciences, and modern languages, modelled on the French lycée and Prussian gymnasium. In Iceland, the sole Icelandic secondary school could adapt to these changes due to the mathematician B. Gunnlaugsson, educated at the University of Copenhagen and trained in geodesy. By the 1870s, schools in the Danish school system were divided into a languages-and-history stream and a mathematics-and-science stream. However, the Iceland’s school was too small to split, there was no strong person to defend the study of mathematics, and a proposal to run a combined stream was rejected. A mathematics stream was only established in 1919.
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Authors and Affiliations

Kristín Bjarnadóttir
1
ORCID: ORCID
  1. School of Education, University of Iceland, Iceland
3 The Circulation of Wolff’s Elements of Mathematics Through Its Compendia
Davide Crippa
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 43-60 | DOI: 10.24425/asmdn.2025.158149
Keywords: Wolff history of mathematics education circulation of mathematical knowledge textbooks elementary geometry 18th century
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Abstract

Christian Wolff’s Der Anfangs-Gründe Aller Mathematischen Wissenschaften, published in Halle in 1710, gained popularity in the 18th c. through various editions, translations, and compendia. These were prepared by Wolff and other university educators for classroom use and included materials selected from German or Latin editions. This article explores its dissemination across Europe by analyzing two Vienna compendia from the late 18th c., which illustrate Wolff’s educational impact.
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Authors and Affiliations

Davide Crippa
1
ORCID: ORCID
  1. Institute of Philosophy, Czech Academy of Sciences, Prague, Czech Republic
4 The Belgian Subcommission of the International Commission on Mathematical Instruction
Dirk De Bock
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 61-79 | DOI: 10.24425/asmdn.2025.158150
Keywords: Belgian subcommission Guy Noël ICMI Joseph Neuberg Pol Burniat Willy Servais 20th century
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Abstract

In 1908, the International Commission on Mathematical Instruction (ICMI) was founded. Participating countries were represented by national delegates. To assist national delegates in preparing surveys and reports for ICMI, national subcommissions were established, at least in the most active countries within ICMI. Belgium was a member of ICMI from the beginning. In this paper, we discuss the activities of the Belgian delegates and the Belgian subcommission, with a focus on the period 1908—1920 and the period after ICMI’s reconstitution in 1952 (in 1920, the Commission was dissolved, but was able to resume its activities at the end of the 1920s, albeit much more modestly than before). For a relatively small country, Belgium was quite active in the first-mentioned period. Even in the Interwar period, the Belgians’ activity in ICMI did not stop. In the post-WWII era, activity was modest; however, the contributions of Pol Burniat, Willy Servais, and Guy Noël are noteworthy.
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Authors and Affiliations

Dirk De Bock
1
ORCID: ORCID
  1. KU Leuven, Leuven, Belgium
5 The Secret of Séguin’s Rods: Ratio as a Capstone in Maria Montessori’s Integration of Arithmetic and Geometry in Childhood.
Isabella Fascitiello , Ana Millán Gasca
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 81-100 | DOI: 10.24425/asmdn.2025.158151
Keywords: history of mathematics education Montessori ratio Séguin’s rods
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Abstract

Maria Montessori built an integrated approach to arithmetic and geometry in childhood, in the two stages of infant school (presented in The method of scientific pedagogy applied to infant education (1909)) and primary school (presented in the twin books Psycho Geometry and Psycho Arithmetic (1934)). The crucial role of the concept of ratio is discussed, as embedded in the educational materials designed by her, especially in the bicoloured rods inspired by her reading of Édouard Séguin. The rods were a materialization of the conceptual network connecting measure, rational numbers, and arithmetical/geometrical ratio and proportion.
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Authors and Affiliations

Isabella Fascitiello
1
ORCID: ORCID
Ana Millán Gasca
1
ORCID: ORCID
  1. Università Roma Tre, Italy
6 International Initiatives in Children’s Mathematics Education in the Early 20th Century Through the Testimony of Margarita Comas Camps
Elena Gil Clemente , Ana Millán Gasca
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 101-122 | DOI: 10.24425/asmdn.2025.158152
Keywords: 20th century history of mathematics education children’s mathematics education New Education Margarita Comas Camps
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Abstract

Margarita Comas Camps’ (1892—1972) contributions in the years 1915—1934 to children’s mathematics education offer a remarkable perspective on the international panorama of these studies and proposals in the early decades of the 20th c. Like many other young Spanish scholars, in the 1920s, she had the opportunity to travel as a graduate student to Great Britain and France thanks to scholarships from the council of the Junta de Ampliación de Estudios (JAE), a state institution inspired by the political-cultural program of the Europeanization of Spain. What were the research and action prospects that were offered to a young scholar between the two World Wars? Comas Camps developed a methodical body of documentation, supported by her study abroad, which constitutes a valuable historiographical source. Through her testimony, we can examine the intersection of proposals and studies from various national contexts, the varied contributions made by mathematical and pedagogical circles, and the attention to different aspects such as teaching methodology, the psychology of learning, and the nature of mathematical knowledge and its role in modern life.
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Authors and Affiliations

Elena Gil Clemente
1
ORCID: ORCID
Ana Millán Gasca
2
ORCID: ORCID
  1. Universidad de Zaragoza, Spain
  2. Università Roma Tre, Italy
7 The Introduction of Number Sets in Modern Mathematics in Belgium
Wendy Goemans
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 123-142 | DOI: 10.24425/asmdn.2025.158153
Keywords: history of mathematics education Modern Mathematics New Math number sets cardinal Peano axioms
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Abstract

During the 1960s and 1970s, a major curriculum change took place in mathematics education. In this so-called Modern Mathematics era, emphasis was placed on mathematical structures, and set theory was seen as the best basis for mathematics education. These beliefs also influenced the way in which number sets were introduced. Some extreme proposals were made, such as defining cardinals in primary education and introducing the Peano axioms in secondary education. In this paper, we examine the extent to which extreme ways of introducing number sets were actually implemented in the classroom. We analyse four textbook series for secondary education in the Flemish part of Belgium. We conclude that the Peano axioms were not introduced, but a formal definition of cardinals was. The four textbook series show several differences in the methods used to introduce the set of rational numbers and the set of real numbers, and in the order in which they are introduced. Limiting the current research to Flemish textbook series allows for more detailed work, but also shows the need to continue this research for the French-speaking part of Belgium. The same applies to extending the current research from the secondary level to the primary education level.
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Authors and Affiliations

Wendy Goemans
1
ORCID: ORCID
  1. Faculty of Economics and Business, KU Leuven, Brussels, Belgium
8 New Math at Primary Schools in West Germany
Tanja Hamann
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 143-157 | DOI: 10.24425/asmdn.2025.158154
Keywords: history of mathematics education New Math Modern Mathematics textbook analysis
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Abstract

This paper seeks to analyse the influences on the emergence and development of the New Math, respectively Modern Mathematics, movement in primary schools in West Germany by examining a sample of exemplary textbooks and comparing their content and methods with the original reform ideas. It is expected that transfer and implementation into classroom concepts lead to adaptations, socalled recontextualizations, and that parts of the original ideas are lost in this way. Indeed, the results of a previous study show that this happened in this specific national case. However, the reasons for and influences on this development differed. The paper identifies the relevant actors who influenced the reform and brings the process in line with political and social circumstances that seem to have played a crucial role in the reform of primary mathematics education.
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Authors and Affiliations

Tanja Hamann
1
ORCID: ORCID
  1. University of Hildesheim, Germany
9 A Fighter for Red Integrals (On L.A. Leifert)
Alexander Karp
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 159-176 | DOI: 10.24425/asmdn.2025.158155
Keywords: mathematics education Russia mathematical front Leningrad University
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Abstract

The title of this paper refers to reminiscences about Leningrad University professor Leonid Leifert, who explained to his students that even in seemingly the most abstract mathematical disciplines, the struggle between the revolutionary and the White Guard elements continued, and there were, therefore, red integrals and white integrals. After the revolution of 1917, Leifert became a member of the Communist Party and one of the most zealous implementers of what the party demanded. In this capacity, he had to fight with Leningrad’s (St. Petersburg’s) most prominent mathematicians and write about the methodology of mathematics instruction — one of the first Soviet textbooks on the subject was edited by him. But although he himself did not waver in implementing the party’s decisions, the party line itself wavered, and already in 1932 he had to repent for pernicious ideas that he had deviously promoted just a year earlier. This did not help him, and in 1938 he was executed. The present study contains an investigation of Leifert’s biography and his works, never undertaken before and useful for a better understanding of what went on at the time. It draws on archival materials and published works from the period under investigation.
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Authors and Affiliations

Alexander Karp
1
ORCID: ORCID
  1. Teachers College, Columbia University, New York, USA
10 Geometric Constructions in Secondary Schools in Prussian Poland
Karolina Karpińska
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 177-204 | DOI: 10.24425/asmdn.2025.158156
Keywords: Prussian Poland geometric constructions secondary education mathematics curriculum West Prussia Province of Posen
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Abstract

In this article, the status, pedagogical functions, and evolution of compass-and-straightedge constructions in the secondary schools of Prussian Poland are examined. Focusing on the provinces of West Prussia and the Province of Posen, it traces the early and sustained integration of synthetic tasks into final examinations — from Elbing’s 1799 locus-asymptote problem to 20th c. exercises, such as Bromberg’s 1904 task of constructing a parallelogram given the sum of the squares of two adjacent sides, the included angle and the length of the opposite diagonal. In West Prussia, teacher-authors F. Buchner, F. Strehlke, W.A. Förstemann, O. Reichel, K. Güßlaff, O. Herweg, and F. Kronke shaped classroom practice and examinations through graded problem collections and the fusion of planimetry with descriptive geometry. In the Province of Posen, synthetic tasks appeared with some regularity in final examinations from the late 1860s onward, supported, among other factors, by J. Schacht’s Raumlehre programme and methodological contributions by W. Jaehnike, R. Heffter, and H. Kiehl. Compliance with ministerial decrees and those of the Provinzialschulkollegium ensured that Abitur papers faithfully mirrored classroom instruction. By 1914, candidates in both provinces were expected to execute and justify constructions of triangles, quadrilaterals, selected loci and conics, illustrating how grassroots innovation and examination-driven feedback harmonised curricular standards across regions.
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Authors and Affiliations

Karolina Karpińska
1
ORCID: ORCID
  1. L. & A. Birkenmajer Institute for the History of Science, Polish Academy of Sciences, Warsaw, Poland
11 The Dawn of Mathematics Education for Girls at the Höhere Mädchenschule in Prussia in the Early 20th Century
Katja Krüger
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 205-221 | DOI: 10.24425/asmdn.2025.158157
Keywords: history of mathematics education female education secondary girls’ schools Meran Reform
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Abstract

This paper examines a famous reform of girls’ secondary schools in Prussia in 1908 regarding mathematics education. The historical analysis focuses on the aims, new objectives, and methods of teaching algebra and geometry to girls in comparison with a comprehensive reform of mathematics education for boys, the Meran Reform (Ger. Meraner Reform) of 1905. Contemporary didactic approaches to the methodological design of mathematics education for girls are outlined and illustrated by examples.
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Authors and Affiliations

Katja Krüger
1
ORCID: ORCID
  1. Department of Mathematics, Technical University of Darmstadt, Germany
12 Mathematics and the Language of Instruction in Morocco: Alternating Between French and Arabic During the Last 60 Years
Ezzaim Laabid
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 223-237 | DOI: 10.24425/asmdn.2025.158158
Keywords: Arabization language of instruction linguistic alternation mathematics teaching
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Abstract

Since the late 1950s, the language of instruction in mathematics in Morocco has undergone four major shifts between French and Arabic. Roughly every decade, a change occurred, and each shift faced significant challenges, including pedagogical issues, teacher training, textbook development, and sometimes political and ideological tensions. The most recent change, introduced in 2015, led to the creation of international baccalaureate tracks and marked the beginning of a new policy known as ‘linguistic alternation’. This policy allows certain subjects, particularly in the sciences, to be taught in foreign languages, namely French, English, and Spanish. Its adoption has sparked widespread debate in Moroccan society, drawing particularly strong criticism from conservative groups. This article first offers an overview of the various language policy changes in mathematics education, outlining their implementation strategies and the arguments behind them. It then explores the emergence of linguistic alternation and examines the controversies and public responses that have accompanied its introduction.
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Authors and Affiliations

Ezzaim Laabid
1
ORCID: ORCID
  1. Cadi Ayyad University, Morocco
13 Charles Méray’s Geometry Tested in the Classrooms
Frédéric Métin
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 239-258 | DOI: 10.24425/asmdn.2025.158159
Keywords: history of mathematics fusion of space and plane geometry mathematicians Paris Congress in 1900 geometry education French educational reform in 1902
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Abstract

When he published his Nouveaux Éléments de Géométrie in 1874, Charles Méray had already written the book that made him the first mathematician to propose a coherent theory of irrational numbers. Had he continued on this path, he would be more famous than Cantor today.

A professor of advanced mathematics at the University of Dijon, he turned to elementary mathematics and focused on teaching geometry to beginners. According to him, plane geometry ‘does not belong to the reality of things, as nature only offers space figures’. His view on old-fashioned geometry was cruel: ‘[geometry]... Finding it silent on three-dimensional space, the geometry believer willingly believes that it does not exist’.

So, the Nouveaux Éléments show another way of introducing and thinking about geometry, which can be linked to the fusion movement in Europe, including the use of algebra, especially for locus problems and conic sections. In 1874, classroom experiments had been rejected by academic authorities, but new attempts at the beginning of the 20th c. would give satisfaction to many teachers who were keen to test the new methods: starting with three-dimensional geometry dealing with everyday objects, use of visual intuition instead of abstract axioms, use of movement and geometric transformations, etc. Enthusiastic reports with many mentions of success were published in 1901, first in Burgundy, then in national academic newspapers.

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Authors and Affiliations

Frédéric Métin
1
ORCID: ORCID
  1. University of Burgundy-Europe in Dijon, France
14 Exploring the Presence of Mathematics in the Spanish Weekly Magazine “Alrededor del Mundo” (1899-1930)
Antonio M. Oller-Marcén
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 259-277 | DOI: 10.24425/asmdn.2025.158160
Keywords: mathematics recreational mathematics press Spain early 20th century
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Abstract

The presence of recreational problems in mathematics texts is as old as the discipline itself. Recreational mathematics can be useful in education in several ways. This idea was exploited beyond the formal educational contexts already during the 18th c. in Spain, where it was sometimes possible to find mathematical problems in daily journals that fostered interactions between readers. This was not a local phenomenon, since we know of the presence of recreational mathematics columns in American newspapers from the end of the 19th c. In this paper, we present a first exploratory approach to the analysis of the presence of mathematics in the Spanish weekly magazine Alrededor del Mundo [Around the World], which was published between 1899 and 1930. In this magazine, we find works of scientific dissemination, questions and answers sections, travel articles, letters to the editor, etc. The last pages were always dedicated to a fixed section called Recetas y Recreos [Recipes and Recreations], which contained medicinal and gastronomic recipes, chess problems, and also riddles and enigmas that sometimes were of mathematical content. This research aims to analyze the presence of mathematics not only in this recreational section, but also in the entire magazine. Our work illustrates the interest of studying the presence of mathematics in non-formal contexts and environments, and it places this Spanish particular case in what seems to have been a wider international trend.
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Authors and Affiliations

Antonio M. Oller-Marcén
1
ORCID: ORCID
  1. Departamento de Matemáticas — IUMA, Universidad de Zaragoza, Spain
15 The Production of Textbooks in Mathematics in Norway: 1930-1986
Hilde Opsal , Bjørn Smestad
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 279-296 | DOI: 10.24425/asmdn.2025.158161
Keywords: textbooks mathematics mathematics education
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Abstract

To provide an overview of Norwegian mathematics textbook production 1930—1986, we replicated Johan Prytz’ study of Swedish textbook production. Such a replication also facilitates comparisons between Norway and Sweden, two countries that have often had almost parallel developments in the school system and in mathematics curricula, with Sweden often a few years ahead. Our method includes systematic searches of the National Library of Norway catalogue, supplemented by searches in other sources, including lists of government approved textbooks, to create a database as complete as possible. We find that, as in Sweden, textbook production increases after curriculum reforms, but also that textbook production was more active in the period 1960—1987 than in 1930—1960. New publishers and authors were active from the 1960s. Also, foreign textbooks published in Norwegian editions played an increasing role from 1960. The theory that the abolition of textbook review in Sweden stimulated textbook production is not supported by our study, as Norway had a similar increase in production without the abolition of textbook review.
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Authors and Affiliations

Hilde Opsal
1
ORCID: ORCID
Bjørn Smestad
2
ORCID: ORCID
  1. Faculty of Humanities and Education, Volda University College, Norway
  2. Faculty of Humanities and Education, Volda University College, Norway; Faculty of Teacher Education and International Studies, OsloMet — Oslo Metropolitan University, Norway
16 Genesis of Applied Mathematics: A Specific Case Study by Reflecting Early Modern Scholar Treatises
Toni Reimers
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 297-317 | DOI: 10.24425/asmdn.2025.158162
Keywords: applied mathematics mining surveying early modern sciences mathematisation scientific treatises knowledge classification
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Abstract

The emergence of applied mathematics as a distinct field is closely linked to the mathematisation of practical disciplines. This article investigates the development of scholarly textbooks on mine surveying as an early case of applied mathematics by analysing early modern scholarly treatises. It traces how mathematical methods were gradually incorporated into the literature on surveying, illustrating the evolving relationship between theoretical knowledge and practical applications. The study also considers the broader historical and institutional context, including shifts in academic classification and the role of philosophy in structuring scientific disciplines. By examining these aspects, the paper sheds light on the epistemological foundations of applied mathematics in the early modern period.
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Authors and Affiliations

Toni Reimers
1
ORCID: ORCID
  1. Institute for Mathematics, Martin Luther University Halle-Wittenberg, Halle/Saale, Germany
17 Teaching Geometry in the Preparatory Cycle of Technical Education in Portugal (1947—1967).
Alexandra Sofia Rodrigues
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 319-337 | DOI: 10.24425/asmdn.2025.158163
Keywords: technical education geometry textbooks preparatory cycle history of mathematics education
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Abstract

Between 1947 and 1967, students in Portugal received technical training through the Ciclo Preparatório do Ensino Técnico. This research undertakes a documentary analysis of two curricular dimensions: the ‘prescribed’ and ‘presented’ mathematics curricula during this period. To achieve this, two methodological frameworks were combined — one proposed by Okeeffe and the other by Krüger. Almeida and Rodrigues previously employed this combination to analyse chapters on integers in textbooks from secondary schools and technical schools in Portugal during the Modern Mathematics Movement, and Rodrigues used it to analyse a chapter on integers from an industrial school’s textbook. The mathematics programme remained stable throughout this period. This text examines the textbook Matemática: ensino técnico profissional: segundo ano do ciclo preparatório, for the second year, published in 1954, focusing on the geometry chapters. The information gathered from the textbook analysis enables us to reflect on the importance of the textbook in student learning at a time when mathematics teaching underwent significant transformations. The textbook’s author endeavoured to incorporate his teaching experience into its preparation, focusing on the importance of preparatory training for life in society.
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Authors and Affiliations

Alexandra Sofia Rodrigues
1
ORCID: ORCID
  1. EDUNOVA.ISPA — Centro de Investigação Interdisciplinar em Educação, Faculdade de Ciências e Tecnologia da Universidade NOVA de Lisboa, CICS.NOVA, UIED, Portugal
18 The Evolution of the Structural Elements of Mathematics Teacher Training — Controversies About the Case of Brazil
Gert Schubring
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 339-360 | DOI: 10.24425/asmdn.2025.158164
Keywords: mathematics teacher training teacher licence degree role of the bachelor’s degree founding Faculties of Philosophy
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Abstract

Training for future secondary school teachers was established eventually in the early 19th c. Since then, the training has included two major constituents: knowledge of the subject matter to be taught and pedagogical-didactic competencies for teaching. These constituents became institutionalised in quite different manners among countries that created public education systems.

Based on studies about the emergence and evolution of teacher training in various European education systems, the development of mathematics teacher training in Brazil is analysed here for further structural insight. Having established no teacher education during the 19th c., following the French practice after the Revolution, teacher education became the key intention of the first universities founded in the 1930s. The paper analyses archival findings and discusses the meanings of the conferred diploma, as well as why recent Brazilian publications about teacher training misrepresent the aims and realisations of teacher education.

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Authors and Affiliations

Gert Schubring
1 2
ORCID: ORCID
  1. Fakultät für Mathematik, University of Bielefeld, Germany
  2. Departamento de Matemática, Universidade Federal do Rio de Janeiro (UFRJ), Brazil
19 Sefer Over la-Soher — A Commercial Arithmetic Book in Hebrew Printed in Venice at the Beginning of the 17th Century
Stela Segev
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 361-376 | DOI: 10.24425/asmdn.2025.158165
Keywords: history of mathematics commercial math books 17th century Italy mathematics education Hebrew mathematical book
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Abstract

In 1627, an arithmetic book in Hebrew was published in Venice. The name of the book was Sefer Over la-Soher [Money current among merchants], and it was printed by one of the students of the mathematician-astronomer Menahem Zion (Emanuel) Port (Porto) Kohen Rappa. Printing books in Hebrew in northern Italy, and particularly in Venice, was not unusual at that time. Beginning in the mid-15th c., many Hebrew printing houses were established in Italy in various places, and even Christian-owned printing houses printed books in Hebrew. However, the number of Hebrew books dealing with mathematics was minimal (a few percent).

Menachem Zion’s book is the first arithmetic book printed in Italy and the second overall. It was preceded only by Eliyahu Mizrahi’s books, which were printed in Constantinople and Basel at the beginning of the 16th c.

Currently, this is the only known arithmetic book printed in northern Italy during the 16th and 17th c., making it a rare piece of evidence of the Jewish community ‘s interest in this subject in the region. Consequently, research on this topic is essential.

This paper will present the author’s goals for writing the book, its mathematical content, its sources, and comparisons with other texts on the same subject in Hebrew and other languages. Moreover, it will attempt to answer why Hebrew arithmetic books were so rare in this period while describing the cultural environment of the Jews of Northern Italy.

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Authors and Affiliations

Stela Segev
1
ORCID: ORCID
  1. Herzog College, Israel
20 Frances Arnold and the Mathematical Education of Girls in Her Time
Yana Shvartsberg
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 377-393 | DOI: 10.24425/asmdn.2025.158166
Keywords: Brearley School girls-only school female education Frances Arnold female mathematics education mathematics education Progressive Era
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Abstract

This work explores the life and career of Frances Arnold, a mathematics teacher at the Brearley School from 1898 to 1930. Brearley, a girls-only school established in New York at the end of the 19th c., set out to offer a rigorous education for girls, equal to that of boys in similar institutions. Frances Arnold’s connection to Brearley began as a student, and later, she returned to the school as a teacher and headmistress. Throughout her life, Arnold remained a dedicated advocate for women’s rights, and this commitment was evident during and after her tenure at Brearley. The goal of this work is to examine Arnold’s contributions to mathematics education at Brearley, focusing not only on her merits as a teacher but also on her lasting impact on the educational principles of girls’ mathematics education.
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Yana Shvartsberg
1
ORCID: ORCID
  1. Pace University, New York, NY, USA
21 Diesterweg’s Concept of Anschauung and Its Implementation in His Praktisches Rechenbuch
Susanne Spies
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 395-414 | DOI: 10.24425/asmdn.2025.158167
Keywords: Adolph Diesterweg Anschauung visualization intuition teaching arithmetic in 19th-century Prussia arithmetic textbook for elementary schools number-images
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Abstract

The German pedagogue Friedrich Adolph Wilhelm Diesterweg (1790—1866) is well-known for his political and philosophical contributions to the so-called Volksbildung (public education). However, his influence on the teaching of mathematics in his time — particularly through his textbook Praktisches Rechenbuch für Elementar- und höhere Bürgerschulen [Practical Arithmetic Book for Elementary and Higher Civic Schools], written in collaboration with Peter Heuser — has so far received relatively little attention. In the three exercise books and accompanying teacher commentaries, Diesterweg emphasizes his two key pedagogical principles, derived from the ideas of Pestalozzi and Schopenhauer as well as his own pedagogical philosophy: Anschauung and self-activity. This article examines Diesterweg’s concept of Anschauung within the framework of his approach to teaching and learning arithmetic, arguing for his significance as an influential figure in the history of mathematics education in the 19th c. Accordingly, the article elaborates on his concept of Anschauung and investigates how it was practically implemented in both his textbooks and the accompanying teacher guidelines.
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Authors and Affiliations

Susanne Spies
1
ORCID: ORCID
  1. Department Mathematik, Universität Siegen, Germany
22 About the Time When Calculus Was Banned in Prussian Gymnasia
Peter Ullrich
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 415-434 | DOI: 10.24425/asmdn.2025.158168
Keywords: Prussian gymnasium Humboldtian reform infinitesimal calculus at secondary schools Karl Heinrich Schellbach schools preparing for polytechnical schools
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Abstract

The Meran Reform of 1905 is often credited with bringing infinitesimal calculus to the Prussian gymnasia and also to the secondary schools preparing for technical studies. Evidence for this comes from comparing the document on the final examination of the gymnasium from 1788 and the description of the curricula for secondary schools from 1882. A closer study shows, however, that the story is not that simple and that interesting things happened during the almost century between these years: The Humboldtian reform in the first decades of the 19th c. raised mathematics to the status of a main subject of the Prussian gymnasia. During the following years, however, other school subjects like Latin claimed their supremacy. In particular, in 1829 the Prussian authorities issued an order banning infinitesimal calculus from the gymnasia since it was considered too difficult for the pupils — which implies that it had been taught at some schools before! Furthermore, many teachers did not want to abandon the tasks dealing with the determination of local extrema and tried to get around the ban. The most prominent example was the Berlin mathematics educator Karl Heinrich Schellbach (1804—1892) who published a method that avoided the open use of infinitesimal ideas. Both Schellbach’s and others’ texts, even official documents, from this time also show that the term ‘function’ was standard for Prussian mathematics teachers in the mid-19th c.
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Authors and Affiliations

Peter Ullrich
1
ORCID: ORCID
  1. Fachbereich 3, Mathematisches Institut, Universität Koblenz, Koblenz, Germany
23 The Geometry of Motions in the Context of West German and East German New Math
Ysette Weiss
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 435-459 | DOI: 10.24425/asmdn.2025.158169
Keywords: New Math geometry education curriculum reform Federal Republic of Germany (FRG) German Democratic Republic (GDR) Cold War
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Abstract

Reforms in education are particularly interesting moments in the history of education, as educational goals are formulated, educational ideals and pedagogical paradigms are negotiated, and reformers take critical looks at the past to justify their reform efforts. The various developments of the International New Math, or Modern Math, Reform reveal the importance of cultural-historical conditions, underlying economic systems and ideological frames, together with institutional differences that led to numerous variants of the New Math movement in various countries. This paper focuses on differences between East German and West German reform efforts in the post-war period, especially on the introduction of modern ideas of geometric transformations in the teaching of geometry in the 1960s and 1970s. Since West Germany, later the Federal Republic of Germany (FRG), was formed from the three occupation zones of the victorious powers the USA, the United Kingdom and France, and East Germany, later the German Democratic Republic (GDR), was in the sphere of influence of the Soviet Union, the study of East and West German reform efforts allows us to relate opposing educational ideologies linked to these contexts, albeit only indirectly and implicitly.
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Authors and Affiliations

Ysette Weiss
1
  1. University of Mainz, Germany
24 Ideology and Public Opposition to the ‘New Math’ Reform Movement in the United States (1960 to 1980)
Sian Zelbo
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 461-476 | DOI: 10.24425/asmdn.2025.158170
Keywords: New Math Modern Mathematics history of curriculum reform sociology of science science communication discourse theory
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Abstract

This study explores public opposition to the American New Math reform movement through an analysis of readers’ letters published in major American newspapers from 1960 to 1980. The findings identify key themes in the public debate about the New Math curriculum, revealing that opposition extended beyond specific pedagogical criticisms to reflect broader ideological dispositions, including distrust of academic elites and nostalgia for traditional notions of authority. The study demonstrates that these ideological themes in letters critical of New Math aligned with the central messaging of the rising conservative movement of the late 1960s and early 1970s. This investigation of ideology in the public response to New Math suggests that educational reforms, regardless of their merits, may fail to gain lasting public support when they conflict with dominant cultural and political values.
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Authors and Affiliations

Sian Zelbo
1
ORCID: ORCID
  1. Teachers College, Columbia University, New York, USA
25 Pierre Van Hiele: A Dutch Didactician of Mathematics with Global Renown
Bert Zwaneveld , Dirk De Bock
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 477-496 | DOI: 10.24425/asmdn.2025.158171
Keywords: Dina van Hiele-Geldof geometry education Hans Freudenthal Pierre van Hiele Tatiana Afanassjewa
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Abstract

Pierre van Hiele, a Dutch secondary school mathematics teacher who developed textbooks and published quite extensively on the didactics of mathematics, received worldwide recognition for his theory of levels of mathematical thinking. We describe Van Hiele’s life and work, in particular his ‘level theory’, and then take a closer look at his most important sources of inspiration: the doctoral research of his wife Dina van Hiele-Geldof, on whose experiments he based his level theory; the ideas of Tatiana Afanassjewa, who proposed a three-step approach to geometry education as early as the 1920s; and Hans Freudenthal, the supervisor of his thesis. Finally, we discuss some existing responses to Van Hiele’s theory, both nationally and internationally.
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Authors and Affiliations

Bert Zwaneveld
1
ORCID: ORCID
Dirk De Bock
2
ORCID: ORCID
  1. Faculty of Science, Open University of the Netherlands, Heerlen, Netherlands
  2. Faculty of Economics and Business, KU Leuven, Leuven, Belgium
26 Archaeo-Genealogical Approach for Research in the History of Mathematics Education
Claudia Regina Flores , Débora Regina Wagner , Rosilene Beatriz Machado , Paula Cristina Bacca
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 499-501 | DOI: 10.24425/asmdn.2025.158172
Keywords: power discourse biopower subject knowledge
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Abstract

This study presents a Foucauldian approach to research in the history of mathematics education, emphasizing the concepts of archaeology and genealogy of knowledge. By focusing on provenance and emergence, it analyzes how discursive objects and educational practices take shape through power and knowledge relations. Drawing on studies of drawing and financial education, it highlights the discontinuities and contingencies that mark the formation of school knowledge. This perspective offers innovative methodological tools for historical writing and contributes to critical reflections on mathematics education, teaching, and teacher training.
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Authors and Affiliations

Claudia Regina Flores
1
ORCID: ORCID
Débora Regina Wagner
1
ORCID: ORCID
Rosilene Beatriz Machado
1
ORCID: ORCID
Paula Cristina Bacca
2
ORCID: ORCID
  1. Federal University of Santa Catarina, Brazil
  2. Federal Institute of Santa Catarina, Brazil
27 Anany Levitin’s Collection of Algorithmic Puzzles as Mathematical Recreations
Pawel Perekietka
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 503-505 | DOI: 10.24425/asmdn.2025.158173
Keywords: mathematical recreations algorithms
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Abstract

Anany Levitin (1947—2021) is the author of the textbook Introduction to the Design and Analysis of Algorithms and a co-author (with Maria Levitin) of Algorithmic Puzzles. This paper outlines how Levitin collected and classified ‘algorithmic puzzles’ as mathematical recreations and how these puzzles were promoted as a teaching tool in algorithm courses, inspiring educators to incorporate puzzle-like problems into computer science pedagogy.
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Authors and Affiliations

Pawel Perekietka
1
  1. The Kórnik Foundation, Poland
28 Tamas Varga’s Reform and Complex Mathematics Education (CME) as a Possible Field of Education for Democracy — From the Mid-20th Century to the Present
Gergely Szmerka , Ödön Vancsó
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 507-510 | DOI: 10.24425/asmdn.2025.158174
Keywords: education for democracy Hungarian tradition CME Tamás Varga
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Abstract

In our research, we investigated how the idea of mathematics as a possible field for democracy education is present in the CME-inspired tradition of mathematics education in Hungary. 13 interviews were conducted with Tamás Varga’s direct collaborators, his students, and practising teachers who teach in the spirit of CME. In this paper, we give a short overview.
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Authors and Affiliations

Gergely Szmerka
1
ORCID: ORCID
Ödön Vancsó
2
ORCID: ORCID
  1. Békásmegyeri Veres Péter High School, Hungary
  2. Eötvös Loránd University Faculty of Science, Hungary
29 In Memoriam: Bert Zwaneveld (1946-2025)
Dirk De Bock
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 513-516 | DOI: 10.24425/asmdn.2025.158175
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Authors and Affiliations

Dirk De Bock
1
ORCID: ORCID
  1. KU Leuven, Leuven, Belgium
30 Book Review: Mastering the History of Pure and Applied Mathematics. Essays in Honor of Jesper Liitzen, ed. by Toke Knudsen, Jessica Carter, De Gruyter, Berlin—Boston 2024
Davide Crippa
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 519-525 | DOI: 10.24425/asmdn.2025.158176
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Authors and Affiliations

Davide Crippa
1
ORCID: ORCID
  1. Institute of Philosophy, Czech Academy of Sciences, Prague, Czech Republic
31 On the Series International Studies in the History of Mathematics and Its Teaching
Alexander Karp , Gert Schubring
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 527-530 | DOI: 10.24425/asmdn.2025.158177
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Authors and Affiliations

Alexander Karp
1
ORCID: ORCID
Gert Schubring
2 3
ORCID: ORCID
  1. Teachers College, Columbia University, New York, USA
  2. Fakultät für Mathematik, University of Bielefeld, Germany
  3. Departamento de Matemática, Universidade Federal do Rio de Janeiro (UFRJ), Brazil
32 Bibliography of the History of Science and Technology for 2024 (Selection)
Dorota Kozlowska
Analecta: Studies and Materials for the History of Science | 2025 | vol. 34 | Nr 2 | 531-566 | DOI: 10.24425/asmdn.2025.158178
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Authors and Affiliations

Dorota Kozlowska
1
ORCID: ORCID
  1. L. & A. Birkenmajer Institute for the History of Science, Polish Academy of Sciences, Warsaw, Poland

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