Original Research

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

Deonarain Brijlall, Aneshkumar Maharaj
Pythagoras | Issue 70 | a40 | DOI: https://doi.org/10.4102/pythagoras.v0i70.40 | © 2009 Deonarain Brijlall, Aneshkumar Maharaj | This work is licensed under CC Attribution 4.0
Submitted: 01 September 2009 | Published: 01 September 2009

About the author(s)

Deonarain Brijlall, School of Science, Maths and Technology Education, University of KwaZulu‐Natal, South Africa
Aneshkumar Maharaj, School of Mathematical Sciences, University of KwaZulu‐Natal, South Africa

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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.


APOS theory;


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doi: 10.1080/0976691X.2015.11884860