scholarly journals Visualization of Selected Sangaku Problem as Didactical Phenomenon in GeoGebra

TEM Journal ◽  
2021 ◽  
pp. 540-545
Author(s):  
Dusan Vallo
Keyword(s):  
Geometric Problem ◽  
Mathematical Problems ◽  
Teaching Of Mathematics

In this article, we will focus on visualization solutions within specific geometric problem of the category Sangaku - historical mathematical problems from Japan. We also highlight didactical advantages of experimental activities in the teaching of mathematics and the role of the visualization via using dynamical geometry software GeoGebra.

Mathematical Problems in Transonic Flow

1986 ◽  
Vol 29 (2) ◽  
pp. 129-139 ◽  
Author(s):  
Cathleen Synge Morawetz
Keyword(s):  
Compressible Flow ◽  
Transonic Flow ◽  
Supersonic Flight ◽  
Flow Past ◽  
Mathematical Problems

AbstractWe present an outline of the problem of irrotational compressible flow past an airfoil at speeds that lie somewhere between those of the supersonic flight of the Concorde and the subsonic flight of commercial airlines. The problem is simplified and the important role of modifying the equations with physics terms is examined.

scholarly journals Computational Complexity Theory and the Philosophy of Mathematics†

2019 ◽  
Vol 27 (3) ◽  
pp. 381-439
Author(s):  
Walter Dean
Keyword(s):  
Computational Complexity ◽  
Computer Science ◽  
Complexity Theory ◽  
Philosophy Of Mathematics ◽  
Computability Theory ◽  
Computational Complexity Theory ◽  
Mathematical Problems ◽  
Np Problem

Abstract Computational complexity theory is a subfield of computer science originating in computability theory and the study of algorithms for solving practical mathematical problems. Amongst its aims is classifying problems by their degree of difficulty — i.e., how hard they are to solve computationally. This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof.

One Point of View: Setting Our Sights High

1983 ◽  
Vol 31 (1) ◽  
pp. 4
Author(s):  
Douglas A. Grouws
Keyword(s):  
Young People ◽  
Everyday Life ◽  
Mathematics Instruction ◽  
Point Of View ◽  
Technological Changes ◽  
High Expectations ◽  
The Future ◽  
Teaching Of Mathematics ◽  
Made In

The way mathematics instruction accommodates the large technological changes sweeping society will profoundly affect the ability of young people to adjust to everyday life situations and perform efficiently in the skilled professions of the future. In particular, continued thoughtful attention must be given to the role of microcomputers in all aspects of the teaching of mathematics. Many significant issues in this area will need to be discussed and important decisions made in the months ahead. We need to set high expectations in these discussions and the decisions that follow from them. Settling for what can be done easily or selling short the talents of our students or our colleagues will be a mistake.

scholarly journals Communicating Mathematics and Science in the Classroom: Exploring the Interactive Route

2015 ◽  
Vol 1 (1) ◽  
pp. 30-43
Author(s):  
Landa Nhlanhla ◽  
◽  
Sindiso Zhou ◽  
Keyword(s):  
Teaching And Learning ◽  
Mathematical Problem ◽  
Structured Interview ◽  
Effective Teacher ◽  
Scientific Concepts ◽  
Teacher Needs ◽  
Mathematical Problems ◽  
Teaching Of Mathematics ◽  
And Mathematics ◽  
Mathematics And Science

Communicating mathematical problems and scientific concepts is considered as a complex and difficult endeavour. Teaching, whether of complex mathematical problems and scientific concepts or of 'straightforward and clear' ideas in the humanities, is a process of communication. This paper argues that communication skills are an integral part of the teaching of Science and Mathematics. Communicating Science and Mathematics in the classroom involves thorough explanations and, because the concepts dealt with are in themselves complex, this may involve going over the concepts repeatedly. This ability to put across the mathematical or scientific message is the ability by the teacher to communicate. Research has insisted that the ability to communicate and to pose questions are central attributes of an effective teacher. This paper argues that more than being able to communicate and ask questions, for effective teaching of Mathematics and Science the teacher needs to employ interactive teaching techniques to involve learners; this way the teacher actively involves learners in communication and therefore in both the teaching and learning process. The teacher and learner roles in the contemporary classroom need not be distinctively outlined as this creates an obstacle to understanding. This allows both the teacher and student to understand concepts from each other's perspective. Through interaction between teacher and student, the teacher is able to explain the mathematical problem to the student from the student's perspective. Through a semi-structured interview and observation the study involves a sample of 32 students from four secondary schools in the two provinces of Midlands and Bulawayo.

scholarly journals Examining Mathematical Problem-Solving Beliefs among Rwandan Secondary School Teachers

2021 ◽  
Vol 20 (7) ◽  
pp. 227-240
Author(s):  
Aline Dorimana ◽  
Alphonse Uworwabayeho ◽  
Gabriel Nizeyimana
Keyword(s):  
Problem Solving ◽  
Secondary School Teachers ◽  
Mathematics Classroom ◽  
Mathematical Problem ◽  
Real Life ◽  
Mathematical Problem Solving ◽  
Teachers Beliefs ◽  
Mathematical Problems ◽  
Teacher Professional

This study explored teachers' beliefs about mathematical problem-solving. It involved 36 identified teachers of Kayonza District in Rwanda via an explanatory mixed-method approach. The findings indicate that most teachers show a positive attitude towards advancing problem-solving in the mathematics classroom. However, they expose different views on its implementation. Role of problem-solving, Mathematical problems, and Problem-solving in Mathematics were identified as main themes. Problem-solving was highlighted as an approach that helps teachers use time adequately and helps students develop critical thinking and reasoning that enable them to face challenges in real life. The study recommends teacher professional development initiatives with their capacity to bring problem-solving to standard.

scholarly journals THE ROLE OF EVALUATION AND SELF-EVALUATION IN ACHIEVING STELLAR LEARNING RESULTS IN MATHEMATICS TEACHING

2013 ◽  
Vol 3 (3) ◽  
pp. 42-52
Author(s):  
Sead Rešić ◽  
◽  
Edina Alimanović ◽  
Keyword(s):  
Mathematics Teaching ◽  
Survey Method ◽  
Self Assessment ◽  
Essential Characteristic ◽  
Self Evaluation ◽  
Teaching Of Mathematics ◽  
Descriptive Method

This paper elaborates the concept of evaluation and self-assessment in the teaching of mathematics and other concepts important to explain the image on the realization winning learning. Also, the essential characteristic that influences this study is education. In a sample of 120 respondents, it was attempted to determine the significance of differences between evaluation and self-assessment in mathematics, in contrary the role of evaluation and self-evaluation in achieving winning learning in mathematics. Analytical - descriptive method and survey method were used in this study, which helped to confirm the hypotheses. The results were shown in tables and graphs and explained with the discussion. The whole operation was rounded with the conclusion.

scholarly journals Futuros professores de Matemática nos Anos Iniciais e suas estratégias diante de problemas do campo conceitual aditivo Future teachers of Mathematics in the Early Years and its strategies in the problems of the additive conceptual field

2017 ◽  
Vol 19 (1) ◽  
Author(s):  
Veridiana Rezende ◽  
Fábio Alexandre Borges
Keyword(s):  
Public University ◽  
Early Years ◽  
Future Teachers ◽  
Mathematical Problems ◽  
Teaching Of Mathematics ◽  
Addition And Subtraction ◽  
Two Stages ◽  
Positional Value ◽  
Inverse Operation ◽  
Research In Mathematics Education

O ensino de Matemática nos Anos Iniciais vem ganhando espaço cada vez maior de discussões, com destaque para as pesquisas em Educação Matemática. Dentre tais pesquisas, temos as contribuições de Gérard Vergnaud acerca do campo conceitual aditivo. Neste texto, apresentamos uma investigação com a qual objetivamos analisar as estratégias de acadêmicos formandos em Pedagogia, quando deparados com uma proposta de resolução de problemas do campo conceitual aditivo. A pesquisa foi desenvolvida em duas etapas: na primeira, acadêmicos do 2º ano do curso de Licenciatura em Matemática de uma universidade pública do Estado do Paraná formularam problemas que contemplavam as diferentes estruturas relacionadas às operações de adição e subtração abordadas por Vergnaud; na segunda, os problemas foram propostos e resolvidos por acadêmicos do 4º ano do curso de Pedagogia da mesma instituição. Nossa análise das resoluções indica que, em geral, não houve dificuldades maiores em relação às diferentes classes de situações propostas por Vergnaud. Por outro lado, pudemos verificar outras incoerências relacionadas ao valor posicional, contagem, uso da operação inversa, uso incorreto da vírgula em operações com números decimais, ausência de notações matemáticas (sinais de adição, subtração etc.), dentre outros. Consideramos, com isso, o fato de que estes futuros professores de Matemática nos Anos Iniciais não participam de discussões em sua formação inicial acerca de problemas matemáticos que contemplam as diferentes situações e conceitos presentes no campo das estruturas aditivas.  The teaching of Mathematics in the Early Years has been gaining an increasing space of discussions, with emphasis on research in Mathematics Education. Among such researches we have the contributions of Gérard Vergnaud on the additive conceptual field. In this text, we present an investigation with which we aim to analyze the strategies of academic graduates in Pedagogy, when faced with a proposal to solve problems of the additive conceptual field. The research was developed in two stages: first, academics of the 2nd year of the Degree in Mathematics of a public university of the State of Paraná formulated problems that contemplated the different structures related to the addition and subtraction operations addressed by Vergnaud; in the second, the problems were proposed and solved by academics of the 4th year of the Pedagogy course of the same institution. Our analysis of the resolutions indicates that, in general, there were no major difficulties in relation to the different classes of situations proposed by Vergnaud. On the other hand, we were able to verify other inconsistencies related to positional value, counting, use of the inverse operation, incorrect use of the comma in operations with decimal numbers, absence of mathematical notations (addition, subtraction, etc.), among others. We thus consider the fact that these future teachers of Mathematics in the Early Years do not participate in discussions in their initial formation about mathematical problems that contemplate the different situations and concepts present in the field of additive structures.

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