History Of Mathematics Education Research Articles

Assessing the added value of a history-based activity for students with low mathematics skills

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pre-test and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students’ results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students’ disorientation is one of the purposes of history in mathematics education.

Book Review: Learning from the history of mathematics education. Alexander Karp (Ed.) (2022). Advances in the history of mathematics education

Book Review: Learning from the history of mathematics education. Alexander Karp (Ed.) (2022). Advances in the history of mathematics education

Geometric Constructions in the Current Math Teacher Training Courses at the Federal University of Mato Grosso do Sul

Background: Math teacher training in Brazil has been the subject of numerous studies under the most diverse approaches. From a historiographical perspective, we can highlight the performance of the Oral History and Mathematics Education Group and the History of Mathematics Education in the Research Group, both acting more directly with the narratives. Disciplines with the content of Geometric Constructions have historically been part of the training of Mathematics teachers. At issue in this text is the contribution of these disciplines to the formation of future teachers. Objective: This paper adds elements to mapping Mat teacher training and performance in the state of Mato Grosso do Sul and in Brazil, expanding discussions about the state and the possible role of geometric disciplines in undergraduate courses. Design: We present the normative documents of such courses and disciplines and the narratives, in the end, comparing the relevant literature for their analysis based on the researchers' questions. Environment and participants: Courses of Math Teacher Training at the Federal University of Mato Grosso do Sul – Brazil. The time frame of the research ranged from 2004 to 2019, the period in which the seven interviewees taught the subjects mentioned earlier. Data collection and analysis: The narratives of the interviewees, the teaching materials presented by them, and the normative documents are analyzed. Results: The narratives and pertinent literature allowed us a dispersive look, which turned outside the narratives themselves, having in them the triggering movement of reflections. Thus, we could produce questions and possible answers to such inquiries. Conclusions: Among the final notes, the following stand out: the importance of these disciplines, identified as “basic” in the course, to recover Geometry contents that students should have studied in Basic Education; the relevance of failure as a stimulus for the study; and the choice of materials that focus on other aspects of geometry. Such subjects are often intended for the substitute teacher, and there is no prior training to work in this discipline with a specific focus on teacher training.

New Objects, Questions, and Methods in the History of Mathematics

This article sums up recent developments in the history of mathematics. The range of mathematics considered has considerably broadened, expanding well beyond the traditional field of original research. As new topics have been brought under consideration, methodologies borrowed from neighboring academic fields have been fruitfully put into use. In the first section, we describe how well-known questions—about the concept of proof and the nature of algebra—have been reconsidered with new questions and analytical concepts. We then sketch up some of the new research topics, among others the history of mathematical education, the inclusion of actors previously neglected, and the prominent role of bureaucracies in the cultural development of mathematics. The last section briefly retraces the development of the Zilsel thesis as a case study illustrating the previous points. Introduced in the mid-20th century, the theory that early modern craftsmen once played a decisive role in the mathematization of nature has recently led to very diverse fruitful studies about the nature and development of mathematical knowledge.

Learning as a critical encounter with the other: prospective teachers conversing with the history of mathematics.

In this paper, drawing on the philosophy of dialectical materialism, we present an elaboration of two concepts that tend to remain backstage in debates in the field of history in mathematics education, namely, the concept of mathematics learning and the concept of classroom mathematics knowledge. The elaboration of these two concepts makes room to return to the longstanding question of the role of history in mathematics education. We argue that the history of mathematics in education is not a choice but a need—a central part of the process of understanding our human nature as essentially historical and cultural. We illustrate these ideas through the analysis of the encounter of a group of prospective teachers with a 14th century problem about motion. In this encounter the students engaged critically in conversations with voices of the past, while restoring the aesthetic, ethical, and historical dimensions of knowing and learning.

Three past mathematicians’ views on history in mathematics teaching and learning: Poincaré, Klein, and Freudenthal

In the HPM (History and Pedagogy of Mathematics) literature, the three mathematicians Henri Poincaré (1854–1912), Felix Klein (1849–1925), and Hans Freudenthal (1905–1990) are often mentioned in relation to having opinions about the role of the history of mathematics in the teaching and learning of mathematics. Such mentioning often appears without any further account of their viewpoints. In the paper, we seek to dig more deeply, asking the questions of what these three mathematicians’ views on history in mathematics education were, how they themselves expressed these, and what the similarities and differences might be. Our departure point was the known texts by the three mathematicians in which they touch upon aspects of the history of mathematics in relation to teaching and learning, or mathematics education in general. When possible, these written works were accompanied by secondary accounts. Finally, we draw perspectives concerning the issue of how the views of these three mathematicians may or may not align with some of the trends in modern day HPM research.

TOÁN HỌC MỚI, MỘT HIỆN TƯỢNG ĐẶC BIỆT TRONG LỊCH SỬ GIÁO DỤC TOÁN HỌC THẾ GIỚI

This article presents two theoretical research results regarding the “new math” movement, a special phenomenon in the history of mathematics education. Firstly, a brief history of that movement is clarified in a strictly logical manner: created by demands of the teaching of undergraduate mathematics degrees at university, the movement was activated by the special circumstances of the post-World War II period. Under the leadership of famous mathematicians, new math has changed the physiognomy of mathematics education at high schools since the 1960s. Despite receiving a lot of criticism and gradually entering a recession, the legacy of “new math” is undeniable. Furthermore, the systematization of certain lessons synthesized by researchers certainly preserves its full value for the reform of Vietnamese educational programs now in force.

Transcultural Networks and Connectivities: The Circulation of Mathematical Ideas between India and England in the Nineteenth Century

The nineteenth century has been characterised as a period in which mathematics proper acquired a disciplinary and institutional autonomy. This article explores the intertwining of three intersecting worlds of the history of mathematics inasmuch as it engages with historicising the pursuit of novel mathematics, the history of disciplines and, more specifically, that of the British Indological writings on Indian mathematics, and finally, the history of mathematics education in nineteenth century India. But, more importantly, the article is concerned with a class of science and mathematics teaching problems that are taken up by researchers—in other words, science and mathematics teaching problems that lead to scientific and mathematical research. The article argues that over a period of 50 years, a network of scholars crystallised around a discussion on mathematics proper, the history of mathematics and education. This discussion spanned not just nineteenth-century England but India as well, involving scholars from both worlds. This network included Scottish mathematicians, East India Company officials and administrators who went on to constitute the first generation of British Indologists, a group of mathematicians in England referred to as the Analytics, and traditional Indian scholars and mathematics teachers. The focus will be on the concerns and genealogies of investigation that forged this network and sustained it for over half a century.

On the Role of Imagination in the Use of History in Mathematics Education

Based on an experiment carried out with 10- to 11-year-old pupils, this paper questions the place of imagination in a class activity using the history of mathematics. The study focuses on three groups of pupils who were offered three variants of the same activity based on base-60 counting (our time measurement system inherited from the Babylonians). To identify differences and similarities between the three scenarios, a quantitative analysis, using a Principal Component Analysis (PCA), was carried out on the basis of the pupils’ productions and a questionnaire. The approach remains exploratory, but it seems to indicate that imagination plays a relevant role in sessions using history of mathematics.

History of Mathematics Education in China

China has a very long history of contributing to human civilisation, including its contribution to mathematics development. The Chinese had discovered many essential theories and concepts in mathematics long before the more famous Western mathematicians. Many of China's theories and concepts thousands of years ago have become references to many Western mathematicians. This paper traces the development of mathematics in China from all the dynasties in its history, including the development of mathematical theory, mathematical texts, and the famous mathematical figures of his time.

Uma história das mobilizações das medidas no contexto das finalidades de Desenho

Sob a perspectiva da história da educação matemática, este texto apresenta os resultados de um estudo que teve como questão norteadora discutir como as medidas podem ter sido mobilizadas no contexto das finalidades de ensino de Desenho para o curso primário paulista, no período de 1890-1950. Para isso, tomaram-se como base para análise os programas de ensino de São Paulo promulgados à época e os resultados apresentados pelas pesquisas de Guimarães (2017) e Trindade (2018). Nesse sentido, orientaram a análise os referenciais teórico-metodológicos da história cultural. Pelo exame, a mobilização das medidas ligada ao contexto das finalidades de ensino de Desenho, de modo a garantir a representação de desenhos geométricos e/ou do natural, se dava prioritariamente e implicitamente com ênfase numa medida intuitiva, conferida e associada ao desenvolvimento de habilidades manual e visual, seja ligada à reprodução de figuras geométricas, seja à cópia de modelos da natureza e/ou manufaturados.

Os jogos para o ensino de aritmética no manual ‘Didática da 1ª série’ de Amaral Fontoura

Tem-se por objetivo compreender o papel dos jogos para o ensino de aritmética no manual pedagógico ‘Didática da 1ª série’, de autoria de Amaral Fontoura, de 1958. As análises utilizam aportes da história cultural (CHARTIER, 2010), privilegiando os manuais como fonte de pesquisa (VALENTE, 2008), além dos demais aportes da história da educação matemática. Fontoura foi um autor importante, principalmente na divulgação dos pressupostos da Escola Nova, através dos seus manuais. Fontoura cita, recorrentemente, os testes ABC de Lourenço Filho, os centros de interesse, a importância da motivação e da competição. E todos estes aspectos podem ser alcançados, de acordo com o autor, com o uso dos jogos.

Análise textual com IRaMuTeQ de pesquisas recentes em História da educação matemática no Brasil: um exemplo de Humanidades Digitais

El objetivo de este trabajo es analizar la producción de conocimiento en historia de la educación matemática (HEM) bajo la óptica de las Humanidades Digitales, a partir de tesis de maestría y doctorado realizadas en 2012 y 2017 en Brasil. La muestra está compuesta por 52 tesis y se utilizó el software IRaMuTeQ para el análisis multidimensional de sus resúmenes. El análisis de frecuencia de palabras posibilitó la identificación de temáticas y metodologías; mientras que el análisis factorial de correspondencia posibilitó 1) la contextualización semántica y 2) visualizar las distancias entre los corpus textuales (resúmenes de tesis). En Brasil, la evolución de HEM muestra aumento del número de tesis, diversificación de temáticas y metodologías. En los años analizados la formación de profesores es el principal tema de interés. La hermenéutica de profundidad es el principal referente teórico-metodológico en las tesis de 2017. Los hallazgos evidencian la influencia de los grupos de investigación en las agendas de investigación de las universidades. Los resultados confirman la utilidad de las herramientas de las Humanidades Digitales, específicamente las relativas a la minería de texto, para analizar la evolución de la producción de conocimiento en HEM

Theoretical-methodological Approach of Research on the Production of New Mathematical Knowledge by Education Experts

This paper aims at making theoretical-methodological contributions to investigations that analyze the production and systematization of knowledge about teacher training and teaching by experts in education. To do so, we consider studies in the fields of History of Education and History of Mathematics Education. Our research work is justified, in the historiographical field, through the nature of the knowledge we intend to analyze, that is, the knowledge systematized by experts in regulations, decrees, teaching manuals, textbooks, school notebooks, etc. The study of such knowledge is interested in 1) enabling the understanding of the processes and dynamics of the constitution of knowledge in training and in teaching from a historical perspective; and in 2) highlight on the education expert`s role in the production process of such knowledge, which are considered here as “mathematics to teach” and “mathematics for teaching”, which are, respectively, a teacher’s object of work and working tools. Our investigation supports the hypothesis that “the different types of mathematics” change over time, and that education experts are the bringers of such change.

O Ginásio Nª Sª da Conceição de São Leopoldo e a Produção de Livros Didáticos de Aritmética

O artigo analisa os livros didáticos de Aritmética produzidos por padres Jesuítas, para o Ginásio Nª. Sª. da Conceição, de São Leopoldo, de 1904 a 1912, divididos em parte teórica e prática. As obras abordam diferentes temas, desde cálculos com números inteiros, frações, potenciação, radiciação, medidas, razões proporções, progressões e logaritmos. Como o tema se insere na História da Educação Matemática no Rio Grande do Sul, este estudo qualitativo e documental ampara-se na história cultural para análise dos assuntos abordados. O público-alvo eram alunos do 1º e do 2º ano ginasial. A ideia defendida pelos autores consistia em algo que contemplasse um ensino mais prático e contextualizado a partir de uma relação contínua da teoria com situações práticas. As atividades desenvolvidas, em sua maioria, eram a partir de situações-problema. Constatou-se que a metodologia utilizada pelos professores visava contribuir para despertar e aguçar no aluno o desejo de alcançar o conhecimento matemático.

Guidelines-on-the-use-of-teaching-materials-for-teaching-fractions-in-the-brazilian-primary-course-1930-1970

The present study, conducted from the perspective of cultural history (Certeau, 1982; Chartier, 1990; Chervel, 1990; Julia 2001)), aims to investigate guidelines for the use of teaching materials to teach fractions in the primary school, present in pedagogical manuals of the period from 1930 to 1970. The research is based in references such as Hofstetter and Schneuwly (2017) - professional knowledge; Valente (2016, 2019) - history of mathematical education; Carrillo Gallego and Sanchez Jimenez (2012) - teaching materials. The analysis of these references revealed that the authors of the selected manuals, Campos (1933), Albuquerque (1958), and Porto (1967, 1968), excelled in working with professional knowledge to teach fractions, when using didactic materials before reaching abstraction. When providing guidelines for the use of teaching materials for the teaching of fractions, in tune with the principles of the New Renovated School, the examined manuals make use of training and teaching knowledge linked to children interests and understanding. Thus, the research concluded that in this sense, the analyses show that the transformation of knowledge to teach fractions occurs when the use of manipulative didactic materials decreases and the use of graphs, diagrams, equivalence tables arises from Scientific Pedagogy, in the field of Psychology, in the field of Psychology Experimental, as indicated by the pedagogical manuals of Irene de Albuquerque and Rizza de Araujo Porto.

Arithmetic Textbooks of the Nª Sª da Conceição College, São Leopoldo, from 1885 to 1903

The article analyzes the arithmetic textbooks produced by the teachers of Colegio Sao Jose, used at Colegio Na Sa da Conceicao, in the city of Sao Leopoldo, from 1885 to 1903. The textbooks address different themes, starting with basic operations, decimals, fractions, ratios and proportions, rule of three (simple and compound), interest, discount rule, company, mixture and alloy, power, root and geometry. Since the theme is part of the History of Mathematical Education in Rio Grande do Sul, this qualitative and documentary study is supported by cultural history and historical research to analyze the approached subjects. The target audience was schoolgirls from Colegio Sao Jose and in a second moment the schoolboys from Colegio Conceicao dos Jesuitas, in their respective courses. The idea defended by the authors consisted of something practical and necessary that aimed to facilitate the schoolgirls of the College the knowledge of a science which was not always attractive to them. Therefore, the aim was to teach Arithmetic in a practical and contextualized way from a continuous relationship of guided theory with practical situations. Most of the activities were developed through problem situations, developed orally and in writing, centered on the process of repetition. It was found that the methodology used by the teachers aimed to contribute to arouse in the students the desire to achieve mathematical knowledge and its applicability.

Book Review: Digging into the memory of mathematics education. Fulvia Furinghetti, Alexander Karp (Eds.) (2018). Researching the history of mathematics education. An international overview

Book Review: Digging into the memory of mathematics education. Fulvia Furinghetti, Alexander Karp (Eds.) (2018). Researching the history of mathematics education. An international overview

Manchas de tinta no papel

Este artigo discute o uso da literatura como fonte para as pesquisas em História da Educação Matemática. Em um primeiro momento, trazendo brevemente referenciais teóricos que incorporam a literatura à historiografia, o texto advoga acerca do uso deste tipo de fonte, discutindo suas potencialidades e limitações; em seguida, faz considerações sobre a narrativa ficcional e apresenta dezesseis categorias de análise que podem ser utilizadas pelo pesquisador para interrogar a fonte literária no fazer da pesquisa historiográfica. Por fim, lançando mão de duas dessas categorias, apresentamos um exercício interpretativo a partir do livro “Planolândia”, de Edwin A. Abbott, cuja história tem, como personagens, entes geométricos. Tomada como fonte histórica, tal obra permite compreender ainda melhor várias tensões da sociedade vitoriana e, dentre essas, nosso estudo foca no modo como Abbott ressignifica os entes geométricos para representar a mulher da sociedade inglesa.

The Discipline of Special Didactics and the History of Mathematics Education: supporting the studies on the Mathematics Teachers Training at the College of Philosophy of Minas Gerais (Belo Horizonte, 1941-1954)

The aim of this paper is to discuss the contributions of the Special Didactics study, particularly of the Special Didactics of Mathematics subject, to research in the History of Mathematics Education that focus on the training of teachers from Philosophy, Science and Language University in the first half of the 20th century. The considerations presented derive from an investigation of the Philosophy course, of a university of Minas Gerais, in Brazil, between the years of 1941 and 1954. The study of “Special Didactics of Mathematics” subject offered by the Didactics course of this same institution, allowed the highlight of the role designed by this subject in the affirmation or differentiation of teacher training models in that period and its relations with the emergence of a subjective position in the Brazilian scientific-academic field, creating professionals dedicated to thinking, discussing and producing knowledge about the relationship among teaching, education and mathematics in order to prepare mathematics teachers for secondary education.