Advanced Mathematical Thinking

2013 ◽  
Author(s):  
Annie Selden
Keyword(s):  
Mathematical Thinking ◽  
Advanced Mathematical Thinking

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.

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.

scholarly journals Uma proposta de articulação entre teoria e prática no estudo da integral definida

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
JANINE FREITAS MOTA ◽  
CELINA APARECIDA ALMEIDA PEREIRA ABAR
Keyword(s):  
Teaching And Learning ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Definite Integral ◽  
Advanced Mathematical Thinking ◽  
Practical Application ◽  
Integral Calculus ◽  
Mathematical Programs ◽  
Strategy Planning

ResumoEste trabalho é um recorte de uma tese de doutorado, em desenvolvimento, cujo objetivo é de desenvolver uma alternativa pedagógica e tecnologógica, que contemple aspectos do Pensamento Matemático Avançado, bem como, aplicações, aprimoramento do conhecimento e do significado da Integral Definida, em contextos intramatemáticos e extramatemáticos, em cursos de Matemática. Neste recorte, apresentamos o percurso de nossa investigação, abordando, inicialmente, os aspectos relacionados às dificuldades na aprendizagem do Cálculo Integral, em particular, da Integral Definida. Ainda, destacamos que a exploração de aplicações desse conteúdo, em distintas áreas, é considerada como uma possibilidade para o seu ensino e para sua aprendizagem. Aspectos teóricos, metodológicos e tecnológicos são apresentados, como orientadores do planejamento da estratégia pedagógica. É destacado um exemplo de aplicação teórico-prática, na perspectiva de melhorias na qualidade do ensino e da aprendizagem desse tópico. Palavras-chave: Integral Definida; Conexões Intramatemáticas; Conexões Extramatemáticas; Educação Matemática no Ensino Superior.AbstractThis work is an doctoral thesis excerpt, under development, whose objective is to construct a pedagogical and technological alternative that contemplates Advanced Mathematical Thinking aspects and applications, improvement of knowledge and the meaning of the Definite Integral, in intramathematical and extramathematical contexts, inside the  mathematical programs. In this excerpt, it is presented the research way, initially approaching the aspects related to the learning disabilities in Integral Calculus, particularly Definite Integral. Still, it is emphasized that the exploitation of applications of this content, in different areas, is considered as a possibility for its teaching and learning. Theoretical, methodological and technological aspects are presented as guide of pedagogical strategy planning. An example of theoretical-practical application is highlighted, with a view to improving the quality of teaching and learning on this topic.Keywords: Definite Integral; Intramathematics Connections; Extramathematcal Connections; Mathematics Learning in Higher Education.   

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