History Of Mathematics In Teaching Research Articles

Istorijska geneza pojma broja i brojevnih sistema - mogućnosti primene u početnoj nastavi matematike (I)

The notion of natural number, as the basis of the entire further development of mathematics, appears as a result of gradual abstraction. The very notion of number has not been precisely defined and has changed throughout history, as has the way of recording. This paper aims to present the origin of natural numbers and their development to the present form. The essentially most important number systems that have evolved in parallel with the development of human consciousness, and which are guided by the need for man to record important events and facts, are discussed and presented. The importance of positional number systems, such as the Indo-Arabic number system we use today, was emphasized. Numerous studies show that the use of the history of mathematics in the teaching of mathematics can increase students 'motivation and students' interest in the subject. Based on a brief overview of existing research on the use of the history of mathematics in mathematics teaching, the paper presents examples of tasks for classroom teaching, which include elements of the history of natural numbers and number systems.

Integration of the History of Mathematics in Mathematics Education: A Systematic Literature Review

The history of mathematics (HoM) is important for mathematics to be enriched, in the evaluation of the development of the mathematics based on scholars and subjects. However, many students often have a bad impression of Mathematics. Therefore, a lot of alternatives have been used by Mathematics educators to change this sceptical view of Mathematics. One of the methods is by using the history in Mathematics in the teaching and learning process. Therefore, this study aims to identify Mathematics teachers’ views towards the integration of the HoM and the implementation of HoM in teaching and learning in a systematic literature review context. Using the guidelines by Preferred Reporting Items for Systematic Review and Meta-Analyzes (PRISMA) and the combination of keywords such as “integration of History of Mathematics”, “using History of Mathematics”, “implementing History of Mathematics” and “integrating History of Mathematics”. 30 out of 1412 articles used in this study were chosen from two electronic databases which are ERIC, and Google Scholar without restricting the year of publication. The article selection was done based on a few criteria such that the variables in previous research were focused on the views and opinions of teachers about the usage of HoM and the usage of HoM in Mathematics education. Extraction of data was based on the name of the researcher, year, country, title, sample size, instrument used, field of study, methodology and analysis and findings. The findings reveal that Mathematics’ teachers have positive views about the integration of HoM in teaching and learning. Teachers did not use HoM in class due to problems such as lack of knowledge and skill to integrate HoM, insufficient materials, resources and time and exclusion of HoM in the Mathematics syllabus and examination. To conclude, Mathematics teachers should consider integrating HoM in their teaching and choosing history as an alternative way to teach Mathematics. As for future works, Mendeley, Scopus and Web of Science are highly recommended to be databases of the study using should extensive related keywords.

Aporte para a promoção de atividades-históricas-com-tecnologia

Fruto da construção humana, a matemática é gerada pelas necessidades construídas para atender a certas demandas da sociedade. O trabalho em sala de aula representa um desafio para o professor na medida em que exige que ele o conduza de forma significativa e estimulante para o aluno. A abordagem de aliar a História da Matemática (HM), com Tecnologias Digitais de Informação e Comunicação (TDIC), proporciona uma alternativa de trabalhar a matemática contemplando seu ensino. Assim, esse trabalho apresenta os resultados de pesquisa que almeja promover aporte para o fomento de atividades-históricas-com-tecnologia enquanto recurso para o ensino da matemática. Tais atividades existem na direção da conexão entre HM e TDIC e consistem em atividades elaboradas com base no uso da HM no ensino, sobretudo, com abordagem de temas/problemas históricos que possam ser investigados via TDIC à luz do processo de Investigação Matemática (IM). Para promover o aporte proposto foi desenvolvida uma pesquisa de abordagem qualitativa com objetivo exploratório de procedimento bibliográfico em que se fez um levantamento sistemático em trabalhos acadêmicos do tipo dissertação. Como resultado foram obtidos os elementos essenciais para produção de tais atividades, a saber: os elementos pré-textuais, as informações básicas, o desenvolvimento da atividade e a avaliação, além da elucidação da definição de tais atividades. Deste modo, como conclusão do estudo chegamos que o apontamento dos elementos que compõem as atividades-históricas-com-tecnologia juntamente com o esclarecimento do que as consiste pode servir de fomento da elaboração de mais atividades nesta direção em prol do ensino de matemática.

A framework for integrating the history of mathematics into teaching in Shanghai

One major obstacle for integrating the history of mathematics in teaching (hereafter referred to as IHT) is how to help teachers, particularly those who lack experience in IHT, use historical materials in their teaching. Based on many IHT practices in Shanghai, this paper proposes an IHT framework including two parts: one is a triangular pyramid IHT model, and the other is a design-based IHT procedure. The pyramid model is composed of three different communities: teachers, researchers, and historians of mathematics. The design-based procedure, also called operating model, includes cyclic stages, which are investigation, design, implementation, assessment, and publication. The primary purpose of this framework is to build a bridge between theory and practice by combining the two models to address particular teaching concerns and improve teaching. In addition, this paper details the process of the dynamic pyramid model and the design-based IHT procedure, and illustrates an example of the application of this framework. Finally, this paper discusses the differences and similarities between this model and others and also discusses the challenge of applying this model in practice.

The role and importance of history of mathematics in teaching

The history of mathematics, as part of all history and universal human culture, tells about the origin of mathematical phenomena and problems; to which extent they are connected to practice, either because they grew from it, or they developed in the human mind and found their application in practice; the tendencies for generalization and confirmation of scientific hypotheses etc. It represents the basis of modern scientific methodology, and is one of the most important sources of the thinking process. The facts studied in the course of mathematics education appeared many centuries ago, and they can therefore be completely understood only in the historical context and ambiance. The very methodical way during the formation of mathematical concepts often develops in the same way in which those concepts first appeared: by direct counting, measuring, noticing etc. real objects. The aim of our work was to show why the history of mathematics is needed in education, and to point out some ways in which the history of mathematics can find more space in mathematics teaching. In the work, we will discuss the general history of mathematics, its educational role in teaching mathematics, we will draw attention to some facts why a wider presence of the history of mathematics is needed in teaching, will give some suggestions how to achieve a wider presence of the history of mathematics elements in teaching, and we will examine the extent to which the elements of the history of mathematics are present in education in the world.

History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers

The use of the history of mathematics in teaching has long been considered a tool for enriching students’ mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of research conducted over four semesters in which I sought to characterize what prospective mathematics teachers (PMTs) understand about the topics that they will be called upon to teach in the future and how that teaching might include an historical component. In particular, I focus on how the study and application of the history of solving quadratic equations illuminates what PMTs know (or do not know) about this essential secondary school algebraic topic. Additionally, I discuss how the results signal important considerations for mathematics teacher preparation programs with regard to connecting PMTs' mathematical and pedagogical knowledge, and their ability to engage in historical perspectives to improve their own and their future students' understanding of solving quadratic equations.

Using History to Teach Mathematics: The Case of Logarithms

Many authors have discussed the question why we should use the history of mathematics to mathematics education. For example, Fauvel (For Learn Math, 11(2): 3–6, 1991) mentions at least fifteen arguments for applying the history of mathematics in teaching and learning mathematics. Knowing how to introduce history into mathematics lessons is a more difficult step. We found, however, that only a limited number of articles contain instructions on how to use the material, as opposed to numerous general articles suggesting the use of the history of mathematics as a didactical tool. The present article focuses on converting the history of logarithms into material appropriate for teaching students of 11th grade, without any knowledge of calculus. History uncovers that logarithms were invented prior of the exponential function and shows that the logarithms are not an arbitrary product, as is the case when we leap straight in the definition given in all modern textbooks, but they are a response to a problem. We describe step by step the historical evolution of the concept, in a way appropriate for use in class, until the definition of the logarithm as area under the hyperbola. Next, we present the formal development of the theory and define the exponential function. The teaching sequence has been successfully undertaken in two high school classrooms.

A study of two-term unit fraction expansions via geometric approach

In this article, we report a study of two-term unit fraction expansions using a geometric approach. It provides us insight on how to find all two-term unit fraction expansions and identify the property of the expansions with smallest maximal denominators, for a given unit fraction. These findings will be useful to lecturers or teachers involved in teaching history of mathematics or elementary number theory.

Newsletter on teaching history of mathematics

Newsletter on teaching history of mathematics