Academician Jonas Kubilius: works dedicated to the history of Lithuanian mathematics

The rise of the Lithuanian mathematical school in the second half of the 20th century is associated with the development of probability theory and its application, and the foundations of that school were insightfully laid by the famous Lithuanian mathematician Jonas Kubilius. However, the academician also had a second vocation – the history of mathematics. At the end of the 20th century, he purposefully researched the mathematical legacy of the poet, bishop A. Baranauskas, recognizing him as the first Lithuanian mathematician researcher of the second half of the 19th century. At the beginning of the 21st century, J. Kubilius undertook a detailed implementation of the idea of a work in the history of Lithuanian mathematics. For this purpose, an informal group of specialists was convened, the content of the work was planned, and the research-based book series ``From the History of Lithuanian Mathematics'' was published. The fourth book in this series, Mathematics in Lithuanian Higher Education Institutions in 1921–1944, presents the research of an academic who reveals the situation of mathematics in universities in Kaunas and Vilnius. In addition, the memoirs of mathematics history by J. Kubilius, dedicated to mathematicians Z. Žemaitis, G. Žilinskas and V. Statulevičius, should be mentioned. The article, at the end of which fragments of the author's memories are presented, is dedicated to the centenary of the birth of Academician J. Kubilius.

Degrees of Freedom: Is Good Philosophy Bad Science?

The lecture starts by considering analytic philosophy as a tradition, and its global spread over recent years, of which Disputatio’s success is itself evidence. The costs and benefits of the role of English as the international language of analytic philosophy are briefly assessed. The spread of analytic philosophy is welcomed as the best hope for scientific philosophy, in a sense of ‘science’ on which mathematics, history, and philosophy can all count as sciences, though not as natural sciences. Arguably, experimental philosophy provides no plausible alternative methodology for philosophy, only a way of psychologizing it. However, it serves a useful purpose by highlighting the inadequacy of current methods for detecting errors in judgments on possible cases, which may result from reliance on possibly universal but imperfectly reliable cognitive heuristics. The problem is exacerbated by analytic philosophers’ tendency to regard increased flexibility in a theoretical framework as progress, where natural scientists would treat it as methodologically vicious profligacy with degrees of freedom. The result is a familiar type of bad science, overfitting theory to uncritically accepted data. The recent ‘hyperintensional revolution’ may be an example of such overfitting, it is suggested. The lecture ends with a call for a more miserly attitude to degrees of freedom.

INTEGRASI “RAHMAT” DALAM PEMBELAJARAN MATEMATIKA

This research aimed at describing the improvement of the students’ attitude towards mathematics lesson after following the lesson using mathematics history. This was a best practice research implemented in two phases: preparation and implementation. The subjects of this research were the students of class XII MIA 2 of SMA N 1 Kubu in the first semester of academic year 2019/2020. There were 25 students consisting of 10 male students and 15 female students. The data of students’ attitude were collected through attitude questionnaires. The collected data were then analyzed descriptively. This research showed that the students’ attitude of class XII MIA 2 of SMA N 1 Kubu in the first semester of academic year 2019/2020 towards mathematics lesson after following the lesson using mathematics history improved. The students’ attitude improved from pre-learning to post-learning using mathematics history. The average of students’ attitude was 48.21 before learning and in the fair category, meanwhile after learning, the average of students’ attitude towards mathematics lesson improved to 74.00 with good category. The improving students’ attitude had positive effect towards the improvement of mathematics learning achievement. The average of students’ daily test improved from 75.48 with learning mastery 92% at the first daily test to 78.72 with learning mastery 100% at the second daily test.

Um Mapeamento de Estudos Históricos da Matemática nos Periódicos Nacionais de Qualis A1, A2 e B1 em Ensino no Período de 2013 a 2018

ResumoO trabalho tem por objetivo apresentar um mapeamento dos artigos envolvendo estudos históricos da Matemática publicados nos periódicos nacionais de qualis A1, A2 e B1 em ensino, no período de 2013 a 2018. Os dados foram coletados a partir da leitura dos títulos, resumos e palavras-chave dos artigos, que foram classificados entre os campos temáticos: História da Matemática, História da Educação Matemática e História na Educação Matemática. De um total de 13 revistas com 212 edições e 2516 publicações, foram categorizados 255 artigos, sendo 91 no campo História da Matemática, 123 no campo História da Educação Matemática e 41 no campo História na Educação Matemática. Dentre os periódicos analisados, a Revista Brasileira de História da Matemática (RBHM), que tem como foco a publicação de trabalhos acadêmicos originais sobre História da Matemática em geral e sobre suas relações com outros campos, como a Educação Matemática e a Filosofia da Matemática, foi o periódico com maior número de artigos identificados na análise, 72 ao todo. Com relação a quantidade de trabalhos classificados em História da Matemática, apesar de serem computados 91 artigos, desses, 59 se encontram na Revista Brasileira de História da Matemática (RBHM), restando 32 artigos identificados em 12 periódicos. Todos os outros periódicos tiveram um volume maior de artigos classificados no campo História da Educação Matemática, 113 ao todo, incluindo duas edições temáticas em dois periódicos. O campo História na Educação Matemática, foi o que teve menos trabalhos classificados, 41 ao todo. Os dados refletem uma mudança no panorama das produções de estudos históricos da Matemática, que inicialmente eram voltados principalmente para a História da Matemática e que, no decorrer do tempo passou-se a ter o crescimento de um movimento em torno da História da Educação Matemática. Palavras-chave: Publicações em Periódicos. História da Matemática. História da Educação Matemática. História na Educação Matemática. AbstractThe work aims to present a mapping of articles involving historical studies of Mathematics published in national journals of qualis A1, A2 and B1 in teaching, from 2013 to 2018. Data were collected from the reading of titles, abstracts and words -key of the articles, which were classified among the thematic fields: History of Mathematics, History of Mathematics Education and History in Mathematics Education. From a total of 13 magazines with 212 editions and 2516 publications, 255 articles were categorized, 91 in the History of Mathematics field, 123 in the History of Mathematics Education field and 41 in the History in Mathematics Education field. Among the journals analyzed, the Revista Brasileira de História da Matemática (RBHM), which focuses on the publication of original academic works on the History of Mathematics in general and on their relations with other fields, such as Mathematics Education and the Philosophy of Mathematics, was the journal with the largest number of articles identified in the analysis, 72 in all. Regarding the number of papers classified in the History of Mathematics, although 91 articles are computed, of these, 59 are in the Revista Brasileira de História da Matemática (RBHM), leaving 32 articles identified in 12 journals. All other journals had a higher volume of articles classified in the History of Mathematical Education field, 113 in all, including two thematic editions in two journals. The History in Mathematics Education field had the least classified jobs, 41 in all. The data reflect a change in the panorama of the production of historical studies of Mathematics, which initially were mainly focused on the History of Mathematics and which, over time, began to have the growth of a movement around the History of Mathematics Education. Keywords: Publications in Journals. History of Mathematics. History of Mathematics Education. History in Mathematics Education.

Epistemological beliefs in relation to the Content, teaching and learning of mathematics teachers

One result of the research is the paper "integral intervention of mathematics' teaching and learning processes" developed in a public university in Colombia, Latin America. The analysis of the epistemological beliefs of a group of academics from the Mathematics Department, who teach subjects to engineer and technology students is presented. We performed descriptive and quantitative cohort research. The objective was to identify the beliefs regarding mathematics' content, learning, and teaching. The 56 participants were included from a voluntary sample, in which the majority were engineers. A questionnaire adapted from Vizcaíno, with a specific domain of mathematical beliefs, approached from the multidimensional model de Schommer was used as a measuring instrument. The results showed that, in general, the teachers' system beliefs are naive or simple and in some specific topics sophisticated. It was observed a percentage of teachers who didn't assume a precise position in their beliefs when responding neutrally to the questionnaire, which could be interpreted as a lack of reflection on their teaching practice, which revealed the need to generate discussion spaces for promoting reflective practices that improve the mathematics' learning. Likewise, the need for training in mathematics' history, epistemological knowledge, and didactics was evidenced, which promotes better mathematics teaching practices.

Investigation of the Elements of the History of Mathematics in Secondary School Mathematics Coursebooks

This study investigates the use of the history of mathematics in secondary school mathematics coursebooks designed according to the new curriculum prepared in 2018 and to make alternative suggestions in which mathematics history can be used. For this purpose, four mathematics coursebooks, which were decided to be taught in schools affiliated to the Turkish Ministry of National Education for four years as of 2018, were analyzed by document analysis method, and this research attempted to determine to what extent the history of mathematics was used in these coursebooks. While making this analysis and analyzing the data, the categories proposed by Erdoğan et al. (2015) were used, including “historical notes,” “notes on usage areas of mathematics,” “applications with historical notes,” and “historical elements in students‟ extracurricular activities.” As a result of the study, it was found out that the 27 elements of the history of mathematics used in the coursebooks were mostly included at the fifth grade, in thelead-in stage, in the area of learning numbers and operations, in the form of small historical snippets about the historical development of situations other than mathematics. In light of these findings, it can be suggested that the history of mathematics is not used sufficiently in secondary school mathematics coursebooks.

A História Institucional no campo da História da Educação Matemática no BrasilInstitutional History within the context of the History of Mathematical Education in Brazil

ResumoO presente trabalho reflete as experiências vivenciadas pelos autores em pesquisas científicas no tema da História Institucional e as discussões mobilizadas no Grupo de Estudos em História da Matemática e Educação Matemática da Universidade Estadual de Maringá (GHMEM-UEM) e tem por objetivo caracterizar metodologicamente o campo de pesquisa em História Institucional no âmbito da História da Educação Matemática no Brasil. Para tanto, valemo-nos dos pressupostos metodológicos da pesquisa de natureza qualitativa. O estudo caracteriza-se, também, pela abordagem holística, abrangente, detalhada e amparada em um contexto determinado pela problemática, baseado em fragmentos históricos. Além disso, utilizamos a técnica de revisão de literatura, buscando trabalhos afins, para situarmos este trabalho em um processo de produção de conhecimento da comunidade científica de modo a coletar informações nas quais se amplia o contexto para se enxergar a problemática. A partir do levantamento bibliográfico realizado, caracterizamos cinco campos de investigação no tema da História Institucional, a saber: História Institucional via personas; História Institucional via matriz curricular; História Institucional via contextos; História Institucional via influências e intercâmbios; e História Institucional via atas e/ou documentos. As nossas análises evidenciaram que o campo História Institucional via personas foi escolhido por todas as pesquisas consultadas, o que evidencia as potencialidades da História Oral.Palavras-chave: História da Matemática, História da Educação Matemática, História Institucional, Campos de investigação, Metodologia.AbstractThis study reflects the experience of the authors in researching Institutional History and the discussions raised in the History of Mathematics and Mathematical Education Study Group of Maringá State University (GHMEM-UEM) and aims to methodologically characterize Institutional History within the context of the History of Mathematical Education in Brazil. To this end, we use the methodological assumptions of qualitative research, as it rests on understanding, interpretation and data analysis. It is also characterized by a detailed, comprehensive, and holistic approach that is supported in a context determined by the problem, based on historical fragments. In addition, we use the literature review technique to place this work in a knowledge production process of the scientific community, in which the context is broadened in order to collect information to see the problem, and to look for similar works in the literature. Grounded in the bibliographic survey carried out, we characterize five research fields in Institutional History: Institutional History via personas; Institutional History via curriculum matrices; Institutional History via contexts; Institutional History via influences and exchanges; and Institutional History via minutes and/or documents. Our analyses show that Institutional History via personas was chosen by all the research consulted, which highlights the potential of Oral History.Keywords: History of Mathematics, History of Mathematical Education, Institutional History, Research fields, Methodology.ResumenEl presente trabajo refleja las experiencias vividas por los autores en la investigación científica sobre el tema de la Historia Institucional y las discusiones movilizadas en el Grupo de Estudios sobre Historia de la Matemática y la Educación Matemática de la Universidad Estadual de Maringá (GHMEM-UEM), y tiene como objetivo caracterizar metodológicamente el campo investigacional en Historia Institucional dentro de la Historia de la Educación Matemática en Brasil. Para ello, utilizamos los supuestos metodológicos de la investigación cualitativa, ya que se basa en la comprensión, la interpretación y en el análisis de datos. También se caracteriza por un enfoque holístico, integral, detallado y sustentado en un contexto determinado por la problemática, a partir de fragmentos históricos. Además, utilizamos la técnica de revisión de la literatura para ubicar este trabajo en un proceso de producción de conocimiento de la comunidad científica con el objetivo de recolectar información en la que se amplía el contexto para ver el problema, buscando trabajos similares en la literatura. A partir del estudio bibliográfico realizado, caracterizamos cinco campos de investigación sobre el tema de la Historia Institucional. Son ellos: Historia Institucional vía personas; Historia institucional vía matriz curricular; Historia institucional a partir de contextos; Historia institucional a partir de influencias e intercambios e Historia Institucional a partir de Actas y / o documentos. Nuestros análisis mostraron que el campo Historia Institucional vía personas fue elegido por todas las investigaciones consultadas, lo que destaca el potencial de la Historia Oral.Palabras clave: Historia de la Matemáticas, Historia de la Educación Matemática, Historia Institucional, Campos de investigación, Metodología.

Muslims in Pioneering Modern Knowledge: Chronicles of The Freely or Unconsciously Surrendered Legacies To The West

The paper dwelt on exemplification of the role of early Muslim world in pioneering modern knowledge with a magnification of the legacies that these torchbearers in Islam bequeathed to the world. The peculiarity of Nigeria as a nation with more than half of its entire population as Muslims was retrospectively reviewed from the pre-colonial to colonial-era; focusing on scholasticism. The study was examined purely from the historical perspective, to appraise how the impressive efforts of the early Muslim pioneers of modern knowledge in Medicine, Chemistry, Physics, Astronomy, Geometry, Mathematics, History, Geography and Biological Sciences were undertaken. The study did not finish without the expression of concern on how the golden legacies of the early Muslim pioneers have been played down by the Muslims of today, where knowledge or groundbreaking discoveries are now credited to the West, making it look like stolen legacies or freely surrendered legacies to those who are currently worried about the development. Based on these genuine concerns, several wells thought out recommendations were penned down, not limited to a suggestion on growing above externally triggered wars and hostilities among Muslim nations, and giving peace and unity chance, to settle down to reflect on how sustainable progress can be achieved in the world of knowledge economy.