A Visual Approach for Solving Problems with Fractions

This article discusses the importance of visual models in problem solving, in the scope of rational numbers. We seek to highlight the potential of this approach, as a structuring theme in the mathematical development of students in elementary education and the connections it allows to establish. In order for students to be mathematically competent and creative, they must be able not only to solve traditional computational problems but also to use models/visual representations when solving all types of mathematical problems, including those in which the visual component is not evident. We developed a qualitative study based on a didactical experience involving 14 future teachers who were attending a Didactics of Mathematics unit course that included a module about problem solving with emphasizes in visual approaches. The main purpose of the study was to identify the strategies used by the future teachers when solving problems with multiple solutions, before and after that module. Data was collected through observation and the written productions of the participants. It was possible to conclude that they tended to privilege analytical approaches before the intervention and, after the teaching experience, they started to value visual approaches, which generated an increase of the productions involving this type of solutions.

Multiple-Solution Tasks in Pre-Service Teachers Course on Combinatorics

In the paper, we present a study devoted to the utilization of multiple-solution tasks (MSTs) in combinatorics as a part of a pre-service teachers course on didactics of mathematics from the view of the mathematics teachers’ specialized knowledge (MTSK) theoretical framework. The study was carried out over the standard course of a summer semester in 2021. The course was attended by 13 pre-service teachers (PSTs). It was carried out online, due to COVID-19 restrictions. Ten combinatorial multiple-solution tasks were assigned to the PSTs. Analyzing pre-service teachers solutions to these tasks, we sought the description and better understanding of the combinatorial knowledge of the topic from the perspective of MSTK. The results revealed some critical aspects of mathematical knowledge in combinatorics that pre-service teachers education should focus on.

Jonas Mašiotas the mathematics teacher

Mathematics teacher Jonas Mašiotas (1897–1953) was the son of Pranas Mašiotas (1863–1940) – the famous Lithuania author of mathematical coursebooks and didactic articles as well as the a creator of books for children. JonasMašiotas studied mathematics in Germany and Switzerland. Prior to the studies, he was engaged as a teacher in Marijampol˙e, after completion of the studies – in Kaunas and during the World War II – in Vilkija. He published 2 articles in didactics of mathematics and 5 coursebooks (including one that consisted of 7 parts), edited and published the coursebook in trigonometry prepared by his father P. Mašiotas. He was one of the enthusiasts for introducing the concept of a function into the school curriculum in mathematics.

Study of the Presence of Sustainability Competencies in Teacher Training in Mathematics Education

This article presents the results of the analysis of the presence of the sustainability competencies proposed by the Sectoral Commission of the Conference of Rectors of Spanish Universities in three degrees in the area of Didactics of Mathematics of the Faculty of Education Sciences at the Universidad de Cádiz (Spain): the degree in Early Childhood Education, the degree in Primary Education, and the Master’s degree in Teacher Training for Compulsory Secondary and Upper Secondary School Education (specialisation in mathematics). The research method used is content analysis, reflected in the syllabi of the subjects of the degrees analysed. To carry out the analysis, two instruments were used: an adaptation of the model of the Green Curriculum in Higher Education and the map of generic competencies in sustainability of the EDINSOST project. The global results show a very low relative presence of sustainability competences in the area of Didactics of Mathematics (25%), the competency related to ethical aspects having the lowest relative presence (10%). For the most part, the competencies related to sustainability are established for the lowest level of mastery, “know”. When comparing the degree programmes, the Master’s degree in Teacher Training for Compulsory Secondary and Upper Secondary School Education (specialisation in mathematics) is the degree that contributes the most to the development of the sustainability competency (32%), followed by the degree in Early Childhood Education (25%), and the degree in Primary Education (18%). Including sustainability in the curriculum of mathematics education in higher education can improve the training of professionals who engage in reflective and critical thinking. However, these results show there is still a long way to go.

Dissertações brasileiras relacionadas ao ensino de função afim sob a perspectiva das teorias da Didática da MatemáticaBrazilian dissertations regarding the teaching of linear functions from the perspective of the Didactics of Mathematics theories

ResumoA presente pesquisa teve o objetivo de realizar um levantamento bibliográfico para a identificação das dissertações de mestrado que se utilizaram de alguma teoria da didática da matemática como subsídios teóricos e/ou metodológicos para o ensino e a aprendizagem de função afim. Com o propósito de alcançar o objetivo, foi realizado um levantamento de trabalhos já produzidos no Catálogo de Teses e Dissertações da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES. Por meio das análises foi possível identificar a quantidade de trabalhos que abordavam as teorias da didática da matemática e como foi abordado o ensino e aprendizagem da função afim. As análises indicam também que a teoria dos registros de representação semiótica foi a mais utilizada nas dissertações.Palavras-chave: Educação matemática, Didática da matemática, Função afim.AbstractThis research aimed to carry out a bibliographic survey to identify master’s degree theses that used some theory of the didactics of mathematics as a theoretical and/or methodological support for teaching and learning the linear function. To achieve the objective, a survey of papers already produced in the Catálogo de Teses e Dissertações da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior/Catalogue of Dissertations and Theses of the Coordination for the Improvement of Higher Level Personnel (CAPES) was carried out. Through the analyses, it was possible to identify the number of works that approached the didactics of mathematics theories and how the teaching and learning of the linear function were approached. The analyses also indicated that the theory of registers of semiotic representation was the most used in the theses.Keywords: Mathematics education, Mathematics didactics, Linear function.ResumenLa presente investigación tuvo el objetivo de realizar un levantamiento bibliográfico para la identificación de las disertaciones de maestría que se utilizaron de alguna teoría de la didáctica de las matemáticas como base teórica y/o metodológica para la enseñanza de función afín. Con el propósito de alcanzar el objetivo, se realizó un levantamiento de trabajos ya producidos en el Catálogo de Teses e Dissertações da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES. Por medio de los análisis fue posible identificar la cantidad de trabajos que abordaban las teorías de la didáctica de las matemáticas y como se abordó la enseñanza y el aprendizaje de la función afín. Los análisis indican, también, que la teoría de los registros de representación semiótica fue la más utilizada en las disertaciones.Palabras clave: Educación matemática, Didáctica de las matemáticas, Función afín.

Recent Nordic Research in Mathematics Education Illustrated by Examples from NORMA17

A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers, teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed.

Revisiting the French Didactic Tradition through Technological Lenses

There is, in France, a long-term tradition of research in the didactics of mathematics. In this paper, we revisit this tradition using, as a specific lens, the research carried out on the educational use of digital tools and resources for teaching and learning mathematics. We first briefly introduce this tradition and the three main theories at the base of it: the theory of didactical situations, the theory of conceptual fields, and the anthropological theory of the didactic. Then, considering three different technological lenses, i.e., dynamic geometry environments, computer algebra systems, and digital resources, we show how these theories and the long-term connection established in this tradition with the fields of cognitive ergonomics and computer sciences have influenced technological research and its outcomes. We also show that, conversely, didactic technological research has led to original and influential theoretical constructions, such as the instrumental approach and the documentational approach to didactics, and that it has contributed in a substantial way to the opening of this didactic tradition to other didactic cultures and other communities, beyond the didactic one.