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Shahar Rozenstin; Shai Gul – International Journal of Mathematical Education in Science and Technology, 2023
Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…
Descriptors: Design, Topology, Classification, Mathematics Education
Nigmatulin, Ravil; Vaguina, Mariya – International Journal of Mathematical Education in Science and Technology, 2022
The topic of recurrence relations has recently been introduced in many discrete mathematics textbooks. Recurrence relations are efficient modelling and problem-solving techniques used in mathematics. Combinatorial problems are often used to introduce recurrence relations. However, many textbooks consider problems that can be reduced only to the…
Descriptors: Teaching Methods, Mathematics Instruction, Problem Solving, Textbooks
Ngu, Bing Hiong; Phan, Huy P. – International Journal of Mathematical Education in Science and Technology, 2022
Capitalizing on cognitive load theory and learning by analogy, we propose two instructional methods to learn a complex linear equation (e.g. two-step equation) by building on prior knowledge of a simpler linear equation (e.g. one-step equation). We will examine the proposal theoretically in this paper. In line with the design principles of…
Descriptors: Short Term Memory, Schemata (Cognition), Prior Learning, Cognitive Ability
Hoban, Richard A. – International Journal of Mathematical Education in Science and Technology, 2021
Many students do not have a deep understanding of slope. This paper defines what a deep understanding of slope is in terms of mathematics-education theory. The various factors which help explain why such a deep understanding is difficult to acquire are then discussed. These factors include the following: the different representations for slope;…
Descriptors: Mathematical Concepts, Concept Formation, Mathematics Instruction, College Freshmen
Burazin, Andrijana; Kajander, Ann; Lovric, Miroslav – International Journal of Mathematical Education in Science and Technology, 2021
Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…
Descriptors: Mathematical Formulas, Mathematics Instruction, Teaching Methods, Geometry
Kojic, Vedran; Krpan, Mira; Lukac, Zrinka – International Journal of Mathematical Education in Science and Technology, 2021
One of the fundamental topics taught in the microeconomics class is minimizing economic costs. It includes understanding the concept of derivatives and applying them. However, most of the first-year undergraduate students find calculus difficult to understand, which also results in poor knowledge of optimization. We use the method based on the…
Descriptors: Microeconomics, Mathematical Concepts, Costs, Mathematics Instruction
de la Rosa, Félix Martínez – International Journal of Mathematical Education in Science and Technology, 2021
The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…
Descriptors: Mathematics Instruction, Mathematical Concepts, Secondary School Mathematics, Algebra
Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2021
The purpose of this work is to explore alternative geometric pedagogical perspectives concerning justifications to 'fast' multiplication algorithms in a way that fosters opportunities for skill and understanding within younger, or less algebraically inclined, learners. Drawing on a visual strategy to justify these algorithms creates pedagogical…
Descriptors: Teaching Methods, Mathematics Instruction, Multiplication, Geometric Concepts
Barahmand, Ali – International Journal of Mathematical Education in Science and Technology, 2020
The purpose of the present article is to investigate the definition of matrix multiplication as a central issue in linear algebra courses. Applying both historical and pedagogical approaches, it focuses on the philosophy of generating the usual matrix multiplication, as a special binary operation, with its partly unexpected form compared with the…
Descriptors: Definitions, Matrices, Multiplication, Algebra
Hillock, Poh Wah; Khan, R. Nazim – International Journal of Mathematical Education in Science and Technology, 2019
This article is a follow-up to an earlier paper on the mathematics support learning tutorial programme (SLT), an intervention programme at The University of Queensland that targets students considered to be at risk of failing Calculus and Linear Algebra I, the first tertiary level mathematics subject at The University of Queensland. The first…
Descriptors: Tutorial Programs, College Freshmen, Remedial Mathematics, Foreign Countries
Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2018
This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around…
Descriptors: Mathematics Instruction, Calculus, Problem Solving, Case Studies
Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A. – International Journal of Mathematical Education in Science and Technology, 2017
In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our…
Descriptors: Algebra, Mathematics Instruction, Undergraduate Students, Computer Uses in Education
Griffiths, Martin; MacHale, Des – International Journal of Mathematical Education in Science and Technology, 2017
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
Descriptors: Arithmetic, Geometry, Geometric Concepts, Algebra
Sangwin, Christopher J. – International Journal of Mathematical Education in Science and Technology, 2015
The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…
Descriptors: Algebra, Mathematics Instruction, Mathematical Concepts, Computer Software
Hillock, Poh Wah; Jennings, Michael; Roberts, Anthony; Scharaschkin, Victor – International Journal of Mathematical Education in Science and Technology, 2013
This article describes a mathematics support programme at the University of Queensland, targeted at first-year engineering students identified as having a high risk of failing a first-year mathematics course in calculus and linear algebra. It describes how students were identified for the programme and the main features of the programme. The…
Descriptors: Engineering Education, College Freshmen, Calculus, Algebra
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