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Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2019

Recently, claims of a 'new and straightforward' method of solution to second-order linear difference equations have appeared in the mathematics education literature from Rivera-Figueroa and Rivera-Rebolledo. The claim of novelty is based on an assumption that 'since the equation is worked in its canonical form', the method within this context must…

Descriptors: Mathematical Concepts, Equations (Mathematics), Problem Solving, Teaching Methods

Walsh, Richard; Guerin, Aoife – International Journal of Mathematical Education in Science and Technology, 2019

This paper uses a framework established by one of the author's in a previous study and refines it to develop a rubric for mathematics tutor training in third-level education. The paper further opens the discussion on the necessity of, and practical methods for, providing high quality, efficient tutor training at third-level. Models of mathematics…

Descriptors: Mathematics Teachers, Tutors, Tutor Training, Mathematics Education

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2019

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…

Descriptors: Mathematics Instruction, Problem Solving, Equations (Mathematics), Teaching Methods

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2019

Recently, Robin claimed to introduce clever innovations ('wrinkles') into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving…

Descriptors: Problem Solving, Equations (Mathematics), Mathematics Education, Mathematics Instruction

Radmehr, Farzad; Drake, Michael – International Journal of Mathematical Education in Science and Technology, 2019

This paper compares Revised Bloom's Taxonomy (RBT) and some of the major theories and frameworks that influence the teaching, learning, and assessment of mathematics. This comparison has been made to help students and researchers make decisions about which of the available theories and frameworks might best suit their study. The comparison…

Descriptors: Taxonomy, Educational Theories, Learning Theories, Mathematics Education

Mingari Scarpello, Giovanni; Ritelli, Daniele – International Journal of Mathematical Education in Science and Technology, 2019

When Johann Bernoulli published his lectures on integrals in 1742, integral calculus had become very advanced since the time of their composition in 1692. Nevertheless, these lectures are of excellent clarity and simplicity even when the book deals with major problems of Mathematical Physics. Just to pique some interest, we offer a commented…

Descriptors: Educational History, Textbooks, Mathematics Education, Calculus

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…

Descriptors: Teaching Methods, Mathematics Instruction, Calculus, Motion

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

Abernethy, Gavin M. – International Journal of Mathematical Education in Science and Technology, 2018

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course.

Descriptors: Mathematical Models, Mathematics, Equations (Mathematics), Mathematical Concepts

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas – International Journal of Mathematical Education in Science and Technology, 2017

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

Descriptors: Problem Solving, Mathematics, Physics, Foreign Countries

Ramírez, José L.; Rubiano, Gustavo N. – International Journal of Mathematical Education in Science and Technology, 2017

In the present article, we introduce a generalization of the spherical inversion. In particular, we define an inversion with respect to an ellipsoid, and prove several properties of this new transformation. The inversion in an ellipsoid is the generalization of the elliptic inversion to the three-dimensional space. We also study the inverse images…

Descriptors: Generalization, Transformations (Mathematics), Geometric Concepts, Geometry

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

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

Dana-Picard, Thierry; Zeitoun, David – International Journal of Mathematical Education in Science and Technology, 2017

We study a 1-parameter family of trigonometric definite integrals, showing how the joint usage of Information and Communication Technologies and paper-and-pencil work lead to different outputs, revealing different mathematical meanings and different concrete meanings. This family of integrals is useful for describing a phenomenon in soil…

Descriptors: Trigonometry, Information Technology, Computation, Soil Science

Cortez, L. A. B.; de Oliveira, E. Capelas – International Journal of Mathematical Education in Science and Technology, 2017

Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…

Descriptors: Thermodynamics, Calculus, Mathematical Concepts, Mathematical Models