Using the History of Mathematics as a Motivational Factor in Teaching Math

2021 ◽  
Author(s):  
Daniel Doz ◽  
Keyword(s):  
Student Learning ◽  
Student Motivation ◽  
History Of Mathematics ◽  
Motivational Factor ◽  
Mathematical Concepts ◽  
Positive Effects ◽  
Teaching Math ◽  
Mathematical Anxiety ◽  
History Of ◽  
Regular Classes

Several studies have explored the importance and benefits of teaching the history of mathematics as part of regular math classes. Some of these studies addressed the question of using the history of mathematics as a motivational factor. For instance, some found that teaching or using the history of mathematics boosted students‟ interest in the topics, lowered mathematical anxiety, and increased motivation, as well as supporting student learning and increasing the understanding of mathematical concepts. In the present paper, we analyze the positive effects that integrating elements of the history of mathematics into regular math classes could have on student motivation. We argue that students could greatly benefit from the inclusion of topics from the history of mathematics in regular classes.

scholarly journals INTERFACES ENTRE HISTORIA DE MATEMÁTICAS Y ENSEÑANZA A TRAVÉS DE ANTIGUOS INSTRUMENTOS MATEMÁTICOS: UNA EXPERIENCIA EN LA INVESTIGACIÓN ACADÉMICA

PARADIGMA ◽  
2020 ◽  
pp. 160-179
Author(s):  
Ana Carolina Costa Pereira
Keyword(s):  
History Of Mathematics ◽  
Academic Research ◽  
Teaching Experience ◽  
Sao Paulo ◽  
Scientific Instrument ◽  
Mathematical Education ◽  
São Paulo ◽  
Mathematical Concepts ◽  
History Of ◽  
Petrus Ramus

Los estudios que cubren la relación entre Historia y Educación Matemática han suscitado varios debates, entre ellos, sus diferentes perspectivas pedagógicas y didácticas vinculadas a las posibles formas de abordarlas en el aula. Los vínculos entre historia, enseñanza y aprendizaje pueden ofrecer recursos que reflejarán directamente la forma de concebir ciertos conceptos matemáticos. Entre algunas posibilidades, consideramos que el estudio de los aspectos teóricos y prácticos del conocimiento y los procedimientos involucrados en la construcción y uso de instrumentos matemáticos antiguos puede llevar al estudiante a comprender no solo el proceso de producción de conocimiento, sino también la formulación de conceptos matemáticos. Así, basado en una perspectiva historiográfica actualizada, este artículo es el resultado de la pasantía postdoctoral relacionada con el proyecto "Construcción de interfaces entre la historia de las matemáticas y la enseñanza a través de instrumentos matemáticos antiguos para la elaboración de una propuesta didáctico-pedagógica dirigida a la enseñanza de conceptos matemáticos en educación básica ”, que tenía como objetivo principal investigar el instrumento científico en la articulación entre la historia de las matemáticas y la enseñanza con el fin de debatir y reflexionar, así como investigar, sobre las potencialidades didácticas de un antiguo instrumento matemático. Con este fin, proponemos presentar un informe centrado en la investigación, la experiencia docente y las propuestas teóricas desarrolladas en la pasantía postdoctoral en la Pontificia Universidad Católica de São Paulo (PUCSP) en el Programa de Estudios de Postgrado en Educación Matemática supervisado por el Prof. Dr. Fumikazu.Palabras clave: Interfaz entre la historia y la enseñanza de las matemáticas. Instrumentos matemáticos. Petrus Ramus personal. INTERFACES BETWEEN HISTORY OF MATHEMATICS AND TEACHING THROUGH OLD MATHEMATICAL INSTRUMENTS: AN EXPERIENCE IN ACADEMIC RESEARCH AbstractStudies covering the relation between History and Mathematical Education have raised several debates, among them, their different pedagogical and didactic perspectives linked to the possible ways of approach in the classroom. The articulations between history, teaching, and learning can offer means that will reflect directly on how certain mathematical concepts are conceived. Among some possibilities, we consider that the study of theoretical and practical aspects of knowledge and procedures involved in the construction and use of old mathematical instruments may lead the student to understand not only the process of production of knowledge, but also the formulation of mathematical concepts. Thus, based on an updated historiographical perspective, this article is the result of the postdoctoral training course concerning the project “Building Interfaces between the History of Mathematics and Teaching through Old Mathematical Instruments for the Development of a Didactic-Pedagogical Proposal Teaching Mathematical Concepts in Basic Education ”whose main objective was to investigate the scientific instrument in the articulation between the history of Mathematics and teaching in order to discuss and reflect, as well as to investigate, the didactic potentialities of an ancient mathematical instrument. To this end, we propose to present a report focusing on research, teaching experience and theoretical propositions developed in the postdoctoral internship at the Pontifical Catholic University of São Paulo (PUCSP) in the Program of Postgraduate Studies in Mathematical Education supervised by Prof. Dr. Fumikazu.Keywords: Interface between history and math education. Mathematical instruments. Baculum of Petrus Ramus.  INTERFACES ENTRE HISTÓRIA DA MATEMÁTICA E ENSINO POR MEIO DE ANTIGOS INSTRUMENTOS MATEMÁTICOS: UMA EXPERIÊNCIA EM PESQUISA ACADÊMICA ResumoEstudos abrangendo as relações entre História e Educação Matemática vêm levantando diversos debates, dentre eles, suas diferentes perspectivas pedagógicas e didáticas ligadas aos possíveis caminhos de abordagem em sala de aula. As articulações entre história, ensino e aprendizagem podem oferecer recursos que irão refletir diretamente no modo de conceber certos conceitos matemáticos. Dentre algumas possibilidades, consideramos que o estudo de aspectos teóricos e práticos dos conhecimentos e dos procedimentos implicados na construção e no uso de antigos instrumentos matemáticos pode levar o discente compreender não só o processo da produção do saber, mas também da formulação de conceitos matemáticos. Dessa forma, baseado em uma perspectiva historiográfica atualizada, este artigo é resultado do estágio de pós-doutorado referente ao projeto “Construção de interfaces entre história da matemática e ensino por meio de antigos instrumentos matemáticos para a elaboração de uma proposta didático-pedagógica voltada para o ensino de conceitos matemáticos na educação básica” que tinha como objetivo principal investigar o instrumento científico na articulação entre história da Matemática e ensino com vistas a discutir e refletir, bem como investigar, sobre as potencialidades didáticas de um instrumento matemático antigo. Para tanto, propomos aqui apresentar um relato enfocando a pesquisa, experiência docente e proposições teóricas desenvolvidas no estágio pós-doutoral na Pontifícia Universidade Católica de São Paulo (PUCSP) no Programa de Estudos Pós Graduados em Educação Matemática supervisionado pelo Prof. Dr. Fumikazu.Palavras-chave: Interface entre história e ensino de matemática. Instrumentos matemáticos. Báculo de Petrus Ramus.

Mathematics and Politics: Thomas Pynchon, against the Day

2018 ◽  
pp. 24-58
Author(s):  
Nina Engelhardt
Keyword(s):  
Thomas Pynchon ◽  
History Of Mathematics ◽  
First Century ◽  
Complex Numbers ◽  
Mathematical Concepts ◽  
Crisis Of Representation ◽  
History Of ◽  
Crisis Of Modernity ◽  
Concrete Concepts

Chapter 1 on Pynchon’s Against the Day focuses on interrelations between mathematics and politics as domains that are both shaken by crises of fundamental beliefs. It examines how Pynchon’s novel draws on the history of mathematics and on concrete concepts to explore the crisis of representation, the transformation of anarchism from political to artistic expression, and the possibilities inherent in imaginary domains. Main mathematical concepts and metaphors include imaginary and complex numbers and the ‘foundational crisis of mathematics’, which Against the Day establishes as producing a mathematics that is ‘an-archistic’ in terms of its loss of foundations and that forms part of the exploration of anarchism across the twentieth century. This chapter demonstrates the centrality of mathematics to Against the Day’s renegotiations of possibilities and responsibilities of the political and the literary, and it shows how the novel’s reimagining of modernism illustrates the relevance of mathematics in developing twenty-first-century responses to the crisis of modernity.

Prospective teachers’ beliefs and self-efficacy beliefs about inquiry-based teaching approach in mathematics

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Areti Chr Panaoura
Keyword(s):  
Prospective Teachers ◽  
Time Allocation ◽  
Self Efficacy ◽  
History Of Mathematics ◽  
Real Life ◽  
Efficacy Beliefs ◽  
Teaching Approach ◽  
Mathematical Concepts ◽  
Teachers Beliefs ◽  
History Of

<p align="justify">The present study focuses on the investigation of prospective teachers’ beliefs and self-efficacy beliefs about the use of the inquiry-based teaching approach in mathematics education during their studies, before and after fieldwork. The aim of the two courses they attended during their studies in a pedagogical department emphasized the understanding of the human involvement on the development of the mathematical concepts through the history of mathematics and the role of investigation and exploration at the teaching of mathematics, as a part of the inquiry-based approach. At the final year of their studies, during the fieldwork they were expected to implement the acquired knowledge about innovative processes in real life classroom situations. The study which conducted with the participation of 73  prospective teachers is divided into three main phases: a) examining their beliefs and self-efficacy beliefs after attending a course about Basic Mathematical Concepts based on the History of Mathematics, b) examining their beliefs and their self-efficacy beliefs after attending a course about the Methodology of Teaching Mathematics in primary education and c) examining the difficulties they face during their first teaching experiences in real life school situations during the last year of their studies. Results indicated that participants seemed to believe in the value of inquiry-based approach and they had high self-efficacy beliefs about using explorations and investigations which were presented at the textbooks; however they had low self-efficacy beliefs about constructing mathematical investigations and explorations by themselves and overcoming teaching difficulties which were related with children’s misunderstandings and time allocation management, during the fieldwork experience. </p>

Notes On the History of Mathematics

1950 ◽  
Vol 43 (6) ◽  
pp. 292-294
Author(s):  
Vera Sanford
Keyword(s):  
History Of Mathematics ◽  
Economic Importance ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Weights And Measures ◽  
Body Of Knowledge ◽  
Class Discussions ◽  
The Social ◽  
History Of ◽  
The Subject

One of the difficulties we meet in teaching mathematics is the conviction which many people have that mathematics is a finished body of knowledge. Our pupils tend to take for granted that mathematics has always been as it now is and that it will always remain in that state. The use of materials from the history of mathematics helps to meet this situation, and class discussions become more interesting when it is realized that mathematical concepts, notations, and processes are the product of an evolution that is not yet complete, and that will probably continue to advance as our civilization becomes even more complex. Students are annoyed when they are introduced to fractional exponents when radical signs seem an adequate way to indicate roots. Why not choose one method and stay with it? It is a matter of surprise to discover that today 3.50 means the product of 3 and 50 in England and that the number an American writes as 3,500 would be written as 3.500 by a Frenchman. Apparently even ordinary notations are not entirely international. The topic of weights and measures becomes much more alive when a class discusses the social and economic importance of standardized units and then brings the subject down to earth by investigating the ways in which people have coped with this problem.

scholarly journals DIFFERENTIAL CALCULUS: THE USE OF NEWTON’S METHODUS FLUXIONUM ET SERIERUM INFINITARUM IN AN EDUCATION CONTEXT

2015 ◽  
Vol 65 (1) ◽  
pp. 39-65
Author(s):  
Paolo Bussotti
Keyword(s):  
Mathematics Education ◽  
General Theory ◽  
Differential Calculus ◽  
History Of Mathematics ◽  
First Year ◽  
Education History ◽  
Mathematical Concepts ◽  
History Of ◽  
One Year ◽  
The University

What is the possible use of history of mathematics for mathematics education? History of mathematics can play an important role in a didactical context, but a general theory of its use cannot be constructed. Rather a series of cases, in which the resort to history is useful to clarify mathematical concepts and procedures, can be shown. A significant example concerns differential calculus: Newton’s Methodus fluxionum et serierum infinitarum is a possible access-key to differential calculus. For, many concepts introduced by Newton ought be useful for the pupils/students (last or last but one year at the high school and first year at the university) to reach a more intuitive, geometrical and problem-oriented approach to calculus. The motivation to consider history of mathematics as an important didactical support is that the pupils/students often learn mathematics in a too formal manner, without understanding the real reasons for the introduction of several mathematical concepts. The problem is that the potential of such support is not exploited. The educational proposal is hence to show a concrete case to highlight what the teaching of mathematics based on history means. The conclusion is that a general theory, as differential calculus, should be considered by the pupils/students as a necessity, deriving from a specification, improvement and extension of the techniques used to solve significant problems posed and developed in the course of history. In this manner, mathematics appears as a human activity comparable with other activities and not as a merely formal exercise. Key words: mathematics education, history of mathematics, Newton, fluxions, tangents, maxima and minima, problem solving approach to mathematics education.

Mathematics and Cognition

2017 ◽  
Author(s):  
Roi Wagner
Keyword(s):  
Mental Representation ◽  
Concept Formation ◽  
Cognitive Theory ◽  
History Of Mathematics ◽  
Mathematical Practice ◽  
Mathematical Concept ◽  
Mathematical Cognition ◽  
Mathematical Concepts ◽  
Cognitive Theories ◽  
History Of

This chapter introduces the notion of embodied mathematical cognition by reviewing some neuro-cognitive theories of mathematical concept formation. It first considers the neuro-cognitive debate on the mental representation of numbers, focusing on Stanislas Dehaene's notion of “number sense” and Vincent Walsh's ATOM (acronym for a theory of magnitude), before presenting the cognitive theory of mathematical metaphor and relating it to Water J. Freeman III's theory of meaning. It also examines Gilles Deleuze's Logic of Sensation in the context of mathematical practice, the link between the history of mathematics and neuro-cognition through an analysis of theories that explicitly engage the formation of higher mathematical concepts, and some challenges to the theory of mathematical metaphors.

A Diagrammatic Subsystem of Hilbert's Geometry

1996 ◽  
Author(s):  
Isabel Luengo
Keyword(s):  
History Of Mathematics ◽  
Visual Representations ◽  
Diagrammatic Reasoning ◽  
Main Role ◽  
Topological Properties ◽  
Mathematical Concepts ◽  
Inference System ◽  
Deductive Systems ◽  
History Of ◽  
Diagrammatic Representations

In the last few years there has been an increasing interest in the visual representation of mathematical concepts. The fact that computers can help us perform graphical tasks very easily has been translated into an increasing interest in diagrammatic representations in general. Several experiments have shown that diagrammatic reasoning plays a main role in the way in which experts in several areas solve problems (Gobert and Freferiksen [1992] and Kindfield [1992]). Two kinds of explanations have been given for the advantages of visual representations over linguistic ones. The first kind of explanation is psychological. It has been argued that visual representations are easier to use because they resemble the mental models hurnans build to solve problems Stenning and Oberlander [1991], Johnson-Laird and Byrne [1991], arid Tverski [1991]. The second kind of explanation is related to computational efficiency. Larkin and Simon [1987] have argued that diagrammatic representations are computationally more efficient than sentential representations because the location of each element in the diagram corresponds to the spatial or topological properties of the objects they represent. However, the efficiency of the use of diagrams is not enough justification for their use in analytical areas of knowledge. Mathematical discoveries often have been made using visual reasoning, but those very same discoveries were not justified by the visual reasoning. Diagrams are associated with intuitions and illustrations, not with rigorous proofs. Visual representations are allowed in the context of discovery, not in the context of justification. Many authors have considered diagrams in opposition to deductive systems. Lindsay [1988], for instance, has claimed that the main feature of visual representations is that they correspond to a non-deductive kind of inference system. Koedinger and Anderson [1991] have related diagrammatic reasoning in geometry to informal, inductive strategies to solve problems. Thus, though we have an empirical justification for the use of diagrams in mathematics (people use them and they work!) we do not usually have an analytical justification. In fact, the history of mathematics, and especially the history of geometry, is full of mistakes related to the use of diagrams.

scholarly journals A história da matemática contribuindo para a formação de professores indígenas: um olhar sobre a perspectiva sociocultural The history of mathematics contributing to the formation of indigenous teachers: a glimpse at the sociocultural perspective

2017 ◽  
Vol 19 (2) ◽  
Author(s):  
Jonisario Littig ◽  
Leonardo Correia Alves ◽  
Lidiane Lahass
Keyword(s):  
Qualitative Methodology ◽  
Teaching Practice ◽  
History Of Mathematics ◽  
Cultural Representations ◽  
Sociocultural Perspective ◽  
Mathematical Concepts ◽  
Training Course ◽  
History Of ◽  
The City ◽  
Indigenous Teachers

ResumoEsse artigo analisa relatos de formadores de professores indígenas realizado em dezembro de 2014 no município de Aracruz – ES. O curso foi oferecido por meio do projeto “Saberes indígenas”. O artigo objetiva explicitar as contribuições da história da matemática e as representações desse grupo cultural para a formação de seus professores. A metodologia, qualitativa, foi desenvolvida a partir de intervenções por meio do curso de formação. Os instrumentos de coleta de dados foram diários de bordo e entrevista com os formadores. Os resultados apontam as dificuldades de relacionar as representações culturais à matemática apresentada no curso. Concluímos que contemplar a história da matemática desse grupo no curso de formação pode contribuir na construção de conceitos matemáticos e na prática docente.AbstractThis article analyzes reports of trainers of indigenous teachers achieved in December 2014 in the city of Aracruz - ES. The course was offered through the project "Indigenous Knowledge". The article aims to make explicit the contributions of the history of mathematics and the representations of this cultural group to the formation of its teachers. The qualitative methodology was developed from interventions through the training course. The instruments of data collection were logbook and interview with the trainers. The results point out the difficulties of relating the cultural representations to the mathematics presented in the course. We conclude that contemplating the history of mathematics in this group in the training course can contribute to the construction of mathematical concepts and teaching practice.

scholarly journals IMPLEMENTASI PEMBELAJARAN SEJARAH DENGAN TEKNIK KONTEKTUAL COMMUNITY UNTUK MENINGKATKAN MOTIVASI DAN PRESTASI BELAJAR SISWA KELAS XII/IPS.4 SMAN 1 KERTOSONO NGANJUK

2019 ◽  
Vol 5 (1) ◽  
pp. 93-110
Author(s):  
Sawin
Keyword(s):  
Student Learning ◽  
Learning Community ◽  
Learning Outcomes ◽  
Student Motivation ◽  
Contextual Learning ◽  
Community Learning ◽  
Learning Achievement ◽  
Learning Techniques ◽  
History Of ◽  
Motivation And Learning

Abstract: Learning History in SMAN 1 Kertosono Nganjuk in its implementation still leaves various problems. The majority of learning methods so far are more emphasized on memorization which results in that students lack understanding of the uses and benefits of what has been learne d and cause a decrease in student motivation. One alternative that can be used is the application of contextual learning with Community Learning techniques. With the use of this technique, it is hoped that History subjects can be easily understood and can increase student motivation and learning achievement. Departing from the above problems, in general the problems formulated in this study are 1) How is the motivation and learning achievement of the history of class XII / IPS.4 students before applying con textual learning to the Learning Community technique? 2) How is the contextual learning implementation with the Learning Community technique in increasing motivation and learning achievement History, 3) How is the motivation and learning achievement Histor y of class XII / IPS students.4 SMAN 1 Kertosono Nganjuk after applying contextual learning with the Learning Community technique? This research was conducted at SMAN 1 Kertosono Nganjuk. This research is a class action research with collaborative type. Th is research phase follows the Kemmis and Taggart models which include planning, implementing actions, observing, and reflecting activities. Data collection techniques used are: (1) observation; (2) measurement of learning outcomes tests; and (3) documentat ion. The results of the research that have been carried out that 1) Research teachers carry out pre - cycle learning by applying lecture and test methods. 2) Implementation of Contextual Learning with Community Learning Techniques on the History of Class XII / IPS.4 Student History is carried out with 3 cycles consisting of 6 meetings. During the learning process observations are carried out to determine student motivation and at the end of the cycle a final test is carried out to determine student learning o utcomes. 3) Student's motivation and learning achievement towards History through contextual learning with Learning Community techniques has increased student learning motivation from pre - research by 14.29% to 17.14% in cycle I and in cycle II to 22.14%. I n cycle III it increased to 32.14%. The increase in learning outcomes at the time of pre - study average class of 65.74 increased in the first cycle to 66.48. In cycle II it increased to 73.16 and in cycle III it increased to 82.04. Likewise the completeness of the Annaba : Jurnal Pendidikan Islam Volume 5 No. 2 , 1 September 2019   Sawin 202 Annaba : Jurnal Pendidikan Islam class at the time of the pre cycle by 37.04% increased to 51.85% in the first cycle and increased in the second cycle to 70.37% and in the third cycle increased to 88.89%

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