scholarly journals Mathematical generalization from the articulation of advanced mathematical thinking and knot theory

2020 ◽  
Vol 22 (3) ◽  
pp. 65-81
Author(s):  
Enrique Mateus-Nieves ◽  
Cristian Andrés Rojas-Jimenez
Keyword(s):  
Knot Theory ◽  
Mathematical Thinking ◽  
Advanced Mathematical Thinking ◽  
Mathematical Generalization

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.

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