СOMPUTER VIZUALIZATION IN MATHEMATICS EDUCATION AS A PRACTICAL EDUCATIONAL TASK

2012 ◽  
Vol 49 (1) ◽  
pp. 95-103
Author(s):  
Sergey Sergeev ◽  
Maria Urban
Keyword(s):  
Mathematics Education ◽  
Mathematical Thinking ◽  
Mathematical Object ◽  
Dynamic Visualization ◽  
Mathematical Objects ◽  
Visual Elements ◽  
Computer Technologies ◽  
Educational Task ◽  
Labor Consuming

The appearance of up-to-date computer technologies extended the application of visualization in mathematics itself as well as in mathematics education drastically. In a number of recent studies the problem of design of technological tools, capable of fostering the students’ mathematical thinking has been discussed hotly. Taking into consideration the primary importance of dynamic visualization (DV) in educational multimedia it is necessary to state that the creation of didactically efficient DV becomes an independent and the urgent educational task. Methodically grounded realization of dynamic connection between representations of mathematical objects, design of auxiliary visual elements and effects, as well as highlighting of significant objects and relations are prerequisites of potential DV efficacy. While interacting with DV a student can realize how a certain mathematical construction is “built”, detect essential connections between its elements, and in the long term comprehend the underlying mathematical ideas and concepts. The key advantage of DV in comparison with static vizualization is in the fact that DV gives the opportunity to have a good look at a genesis of a new mathematical object in its dynamics, and to explore the connections between graphical representations without necessity to perform labor-consuming calculations, which gives the possibility to concentrate students’ attention on conceptual aspects of a studied mathematical objects. In teaching DV can be used both as an additional tutorial visualizing some elements of knowledge and as a dominant one influencing significantly all the other components of a methodological system. The latter can include for example software “analogue” of the physically existing artefact – positional abacus. In any case the teacher acquires the opportunity to create new in their essence, often nontrivial didactical tasks with DV employment. Key words: computer technologies, mathematics education, visualization.

scholarly journals Presentation of Mathematics Object in Verbal and Symbolic Forms to Increase Conceptual Understanding in Category Statistics Math

2017 ◽  
Vol 2 (2) ◽  
pp. 253
Author(s):  
Ahmad Yani T ◽  
Lucius Chih Huang Chang
Keyword(s):  
Mathematics Education ◽  
Conceptual Understanding ◽  
Mathematical Object ◽  
Study Program ◽  
Symbolic Form ◽  
Mathematical Objects ◽  
Symbolic Forms ◽  
Statistics Course ◽  
Education Study ◽  
Learning Interest

<p class="Normal1"><strong>Abstract.</strong> This study aims to obtain objective information about the presentation of mathematical objects in the form of verbal and symbolic to improve the conceptual understanding and interest in student learning after being given a lesson with the presentation of mathematical objects in the form of verbal and symbolic in the Mathematical Statistics Course Semester VI Mathematics Education Study Program PMIPA FKIP University of Tanjungpura Pontianak<br />The sample of this research is the fourth semester students who follow the Basic Mathematics course of Mathematics Education program of PMIPA FKIP for the academic year 2016-2017. Data collection is done by giving test result of learning after given treatment. The essay-like test is 10 questions. The result of the research shows that there is an increase of students' learning result through presentation of mathematical object in verbal and symbolic form to improve conceptual understanding in Mathematics Statistics Semester VI Mathematics Education Study Program and there is an increase of learning interest after given learning by presentation of mathematical object in verbal and symbolic form.</p>

scholarly journals Resolución de problemas matemáticos en GeoGebra

2020 ◽  
Vol 9 (1) ◽  
pp. 26-42
Author(s):  
William Enrique Poveda Fernández
Keyword(s):  
Costa Rica ◽  
Problem Solving ◽  
Secondary School ◽  
Secondary School Teachers ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
School Teachers ◽  
Mathematical Objects ◽  
Problem Solving Strategies ◽  
Problem Solving Process

RESUMENEn este artículo se analizan y discuten las ventajas y oportunidades que ofrece GeoGebra durante el proceso de resolución de problemas. En particular, se analizan y documentan las formas de razonamiento matemático exhibidas por ocho profesores de enseñanza secundaria de Costa Rica, relacionadas con la adquisición y el desarrollo de estrategias de resolución de problemas asociadas con el uso de GeoGebra. Para ello, se elaboró una propuesta de trabajo que comprende la construcción y la exploración de una representación del problema, y la formulación y la validación de conjeturas. Los resultados muestran que los profesores hicieron varias representaciones del problema, examinaron las propiedades y los atributos de los objetos matemáticos involucrados, realizaron conjeturas sobre las relaciones entre tales objetos, buscaron diferentes formas de comprobarlas basados en argumentos visuales y empíricos que proporciona GeoGebra. En general, los profesores usaron estrategias de medición de atributos de los objetos matemáticos y de examinación del rastro que deja un punto mientras se arrastra.Palabras claves: GeoGebra; Resolución de problemas; pensamiento matemático. RESUMOEste artigo analisa e discute as vantagens e oportunidades oferecidas pelo GeoGebra durante o processo de resolução de problemas. Em particular, as formas de raciocínio matemático exibidas por oito professores do ensino médio da Costa Rica, relacionadas à aquisição e desenvolvimento de estratégias de resolução de problemas associadas ao uso do GeoGebra, são analisadas e documentadas. Para isso, foi elaborada uma proposta de trabalho que inclui a construção e exploração de uma representação do problema, e a formulação e validação de conjecturas. Os resultados mostram que os professores fizeram várias representações do problema, examinaram as propriedades e atributos dos objetos matemáticos envolvidos, fizeram conjecturas sobre as relações entre esses objetos e procuraram diferentes formas de os verificar com base em argumentos visuais e empíricos fornecidos pelo GeoGebra. Em geral, os professores utilizaram estratégias para medir os atributos dos objetos matemáticos e para examinar o rasto que um ponto deixa enquanto é arrastado.Palavras-chave: GeoGebra; Resolução de problemas; pensamento matemático. ABSTRACTThis article analyzes and discusses the advantages and opportunities offered by GeoGebra during the problem-solving process. In particular, the mathematical reasoning forms exhibited by eight secondary school teachers in Costa Rica, related to the acquisition and development of problem solving strategies associated with the use of GeoGebra, are analyzed and documented. The proposal was developed that includes the elements: construction and exploration of a representation of the problem and formulation and validation of conjectures. The results show that teachers made several representations of the problem, examined the properties and attributes of the mathematical objects involved, made conjectures about the relationships between such objects, and sought different ways to check them based on visual and empirical arguments provided by GeoGebra. In general, the teachers used strategies to measure the attributes of the mathematical objects and to examine the trail that a point leaves while it is being dragged.Keywords: GeoGebra; Problem Solving; Mathematical Thinking.

Multisensory Integration during Short-term Music Reading Training Enhances Both Uni- and Multisensory Cortical Processing

2014 ◽  
Vol 26 (10) ◽  
pp. 2224-2238 ◽  
Author(s):  
Evangelos Paraskevopoulos ◽  
Anja Kuchenbuch ◽  
Sibylle C. Herholz ◽  
Christo Pantev
Keyword(s):  
Multisensory Integration ◽  
Superior Temporal Gyrus ◽  
Music Reading ◽  
Short Term ◽  
Visual Elements ◽  
Human Ability ◽  
Cortical Responses ◽  
Anterior Prefrontal Cortex

The human ability to integrate the input of several sensory systems is essential for building a meaningful interpretation out of the complexity of the environment. Training studies have shown that the involvement of multiple senses during training enhances neuroplasticity, but it is not clear to what extent integration of the senses during training is required for the observed effects. This study intended to elucidate the differential contributions of uni- and multisensory elements of music reading training in the resulting plasticity of abstract audiovisual incongruency identification. We used magnetoencephalography to measure the pre- and posttraining cortical responses of two randomly assigned groups of participants that followed either an audiovisual music reading training that required multisensory integration (AV-Int group) or a unisensory training that had separate auditory and visual elements (AV-Sep group). Results revealed a network of frontal generators for the abstract audiovisual incongruency response, confirming previous findings, and indicated the central role of anterior prefrontal cortex in this process. Differential neuroplastic effects of the two types of training in frontal and temporal regions point to the crucial role of multisensory integration occurring during training. Moreover, a comparison of the posttraining cortical responses of both groups to a group of musicians that were tested using the same paradigm revealed that long-term music training leads to significantly greater responses than the short-term training of the AV-Int group in anterior prefrontal regions as well as to significantly greater responses than both short-term training protocols in the left superior temporal gyrus (STG).

scholarly journals O estado da arte da teoria dos registros de representação semiótica na educação matemática State of the art theory of semiotics representation registers in mathematics education

2017 ◽  
Vol 19 (1) ◽  
Author(s):  
Helaine Maria De Souza Pontes ◽  
Celia FIinck Brandt ◽  
Ana Luiza Ruschel Nunes
Keyword(s):  
Mathematics Education ◽  
Research Design ◽  
Basic Education ◽  
State Of The Art ◽  
Scientific Research ◽  
Mathematical Object ◽  
Art Theory ◽  
Methodological Procedures ◽  
Teaching Of Mathematics ◽  
Object Of Study

O objeto de estudo deste trabalho de investigação consiste em saber como a Teoria dos Registros de Representação Semiótica se evidencia nas pesquisas científicas brasileiras, portanto tem como objetivo revelar o nível de abrangência, objeto matemático, procedimentos metodológicos e aspectos da teoria de Duval mais recorrentes nestas pesquisas. Desta forma, trata-se de uma pesquisa bibliográfica com delineamento do estado da arte. Os resultados apresentados demonstram a predominância da Educação Básica; a variedade dos objetos matemáticos; o destaque tanto das Sequências Didáticas quanto das Atividades Matemáticas como procedimentos metodológicos utilizados e as transformações de tratamento e conversão como aspectos da teoria de Duval mais evidentes nas pesquisas mapeadas. The object of study of this research is how the Theory of Semiotics Representation Registers is evident in Brazilian scientific research therefore aims to reveal the level of coverage, mathematical object, methodological procedures and aspects of Duval most prevalent theory in these research. In this way, it is a bibliographical research design with state of the art. The results show the predominance of Basic Education; the variety of mathematical objects; the highlight of both sequences as Teaching of Mathematics activities as methodological procedures used and the treatment and conversion transformations as aspects of the more obvious Duval theory most evident in the mapped research. 

scholarly journals An alternative route to the Mandelbrot set: connecting idiosyncratic digital representations for undergraduates

2020 ◽  
Author(s):  
Richard Miles
Keyword(s):  
Mathematics Education ◽  
Dynamical Systems ◽  
Mandelbrot Set ◽  
Digital Tools ◽  
Alternative Route ◽  
Mathematical Objects ◽  
Global Perspectives ◽  
Fundamental Properties ◽  
Digital Representations

Abstract Mathematics undergraduates often encounter a variety of digital representations which are more idiosyncratic than the ones they have experienced in school and which often require the use of more sophisticated digital tools. This article analyses a collection of digital representations common to undergraduate dynamical systems courses, considers the significant ways in which the representations are interconnected and examines how they are similar or differ from those students are likely to have experienced at school. A key approach in the analysis is the identification of mathematical objects corresponding to manipulative elements of the representations that are most essential for typical exploratory tasks. As a result of the analysis, augmentations of familiar representations are proposed that address the gap between local and global perspectives, and a case is made for greater use of isoperiodic diagrams. In particular, these diagrams are proposed as a new stimulus for students to generate their own explorations of fundamental properties of the Mandelbrot set. The ideas presented are expected to inform the practice of teachers seeking to develop visually rich exploratory tasks which pre-empt some of the issues of instrumentation that mathematics undergraduates experience when introduced to new digital tools. The overarching aim is to address significant questions concerning visualization and inscriptions in mathematics education.

Exploded Points

1981 ◽  
Vol 36 (1) ◽  
pp. 72-75
Author(s):  
Okan Gurel
Keyword(s):  
Lorenz System ◽  
Stability Index ◽  
Mathematical Object ◽  
Recursive Formula ◽  
Functional Characteristics ◽  
Mathematical Objects ◽  
The Lorenz System ◽  
Definition Of

A new concept of a mathematical object of zero dimension, an exploded point, is introduced. The dimension used is defined on the basis of the functional characteristics of the system, thus it may be referred to as f-dimension. A stability index is also defined for the mathematical objects including exploded points, which can be related to the f-dimension. It is shown that the mathematical object exhibited by the Lorenz system after the second bifurcation is such a point. A recursive formula based on the definition of the exploded point

The Role of Problem Solving

1985 ◽  
Vol 32 (6) ◽  
pp. 48-50
Author(s):  
Randall I. Charles
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Mathematical Thinking ◽  
Development Of Students

The importance of problem solving in mathematics has been attested to by many individuals and groups (e.g., Snowmass 1973; NCSM 1977; CBMS 1982). Furthermore, the belief seems to be common that the development of students' problem-solving abilities is one of the most important goals of mathematics education. In view of the importance of problem solving, it is templing to argue that problem solving and mathematical thinking are in fact different names tor the same activity. However, such an argument would provide too narrow an interpretation of mathematical thinking and too broad a view of problem solving. The purposes of this article are to describe one view of “mathematical thinking” and to describe the characteristics of a problem-solving program necessary to develop this kind of thinking.

Focused Strategies for Middle-Grades Mathematics Vocabulary Development

2007 ◽  
Vol 13 (4) ◽  
pp. 200-207
Author(s):  
Rheta N. Rubenstein
Keyword(s):  
Mathematics Education ◽  
Middle Grades ◽  
Mathematical Thinking ◽  
Vocabulary Development ◽  
School Mathematics ◽  
One Dimension ◽  
Mathematical Language ◽  
Mathematics Vocabulary ◽  
Principles And Standards

Principles and Standards for School Mathematics reminds us that communication is central to a broad range of goals in mathematics education (NCTM 2000). These goals include students' being able to (1) organize and consolidate mathematical thinking; (2) communicate coherently with teachers, peers, and others; (3) analyze and evaluate others' strategies; and (4) use language to express mathematics precisely. One part of communication is acquiring mathematical language and using it fluently. This article addresses learning vocabulary as one dimension of mathematics communication.

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