A critique of the selection of ?Mathematical objects? as a central metaphor for advanced mathematical thinking

1996 ◽  
Vol 1 (2) ◽  
pp. 139-168 ◽  
Author(s):  
Jere Confrey ◽  
Shelley Costa
Keyword(s):  
Mathematical Thinking ◽  
Advanced Mathematical Thinking ◽  
Mathematical Objects ◽  
Selection Of

scholarly journals Using an inductive approach for definition making: Monotonicity and boundedness of sequences

Pythagoras ◽  
2009 ◽  
Vol 0 (70) ◽  
Author(s):  
Deonarain Brijlall ◽  
Aneshkumar Maharaj
Keyword(s):  
Mathematical Thinking ◽  
School Curriculum ◽  
Further Education ◽  
Teaching Model ◽  
Advanced Mathematical Thinking ◽  
Structured Design ◽  
Kwazulu Natal ◽  
Teaching Of Mathematics ◽  
The University ◽  
And Training

The study investigated fourth–year students’ construction of the definitions of monotonicity and boundedness of sequences, at the Edgewood Campus of the University of KwaZulu –Natal in South Africa. Structured worksheets based on a guided problem solving teaching model were used to help students to construct the twodefinitions. A group of twenty three undergraduateteacher trainees participated in the project. These students specialised in the teaching of mathematics in the Further Education and Training (FET) (Grades 10 to 12) school curriculum. This paper, specifically, reports on the investigation of students’ definition constructions based on a learnig theory within the context of advanced mathematical thinking and makes a contribution to an understanding of how these students constructed the two definitions. It was found that despite the intervention of a structured design, these definitions were partially or inadequately conceptualised by some students.

scholarly journals PENGARUH PEMBELAJARAN CAI-KONTEKSTUAL TERHADAP KEMAMPUAN BERPIKIR MATEMATIK DAN KARAKTER MAHASISWA

2017 ◽  
Vol 9 (1) ◽  
pp. 45
Author(s):  
Nanang Nanang
Keyword(s):  
Student Teacher ◽  
Mathematical Thinking ◽  
Thinking Skills ◽  
Contextual Learning ◽  
Test Method ◽  
Mathematics Students ◽  
Data Value ◽  
Academic Year ◽  
Initial Knowledge ◽  
Selection Of

The purpose of this study to determine the effect of CAI-Contextual learning of the ability to think mathematically and character of the student teacher participants of the course Capita Selecta Mathematical SMA. The population in this study is the fourth semester students of Mathematics Education STKIP Garut academic year 2015/2016. Selection of the sample by means of random sampling, the students obtained grade B as an experimental class and class A as the control class. Experimental class taught by CAI-Contextual learning, whereas the control class was taught by conventional learning. Retrieval of data obtained by the test method to get the data value of the initial knowledge of mathematics students and Mathematical Thinking Skills as well as the method of questionnaire to measure student character, and then analyzed with the average difference. The results showed that there are differences in the ability to think mathematically and character class students experiment with the control class. Since the average mathematical thinking skills and character students experimental class is bigger than the control class, it can be concluded that the CAI-Contextual learning positively affects the ability to think mathematically and character of the student teacher participants of the course Capita Selecta Mathematical SMA.

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.

A Interação de Aspectos Algorítmicos, Intuitivos e Formais e o Desenvolvimento de Processos do Pensamento Matemático Avançado na Aprendizagem Matemática

2018 ◽  
Vol 10 (3) ◽  
pp. 228
Author(s):  
William Vieira ◽  
Vera Helena Giusti de Souza ◽  
Roberto Seidi Imafuku
Keyword(s):  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Advanced Mathematical Thinking ◽  
Thinking Processes

Apresentamos uma situação de aprendizagem matemática na qual pode-se observar o desenvolvimento de processos do Pensamento MatemáticoAvançado como representação, tradução,  visualização e generalização e o papel que a interação de aspectos algorítmicos, intuitivos e formais desempenha no desenvolvimento desses processos.Palavras-chave: Pensamento Matemático Avançado; Aspectos algorítmicos, intuitivos e formais.AbstractWe present a situation of mathematics learning in which one can observe the development of Advanced Mathematical Thinking processes as representation, translation, visualization and generalization and the role the interaction of algorithmic, intuitive and formal aspects plays in the development of these processes.Keywords: Advanced Mathematical Thinking; Algorithmic, intuitive and formal aspects.

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