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McCartney, Mark – International Journal of Mathematical Education in Science and Technology, 2021
An elementary method to calculate the area, centroid and volume of rotation of the Koch curve is presented. Classroom extensions are provided to allow students to investigate the method used.
Descriptors: Mathematics Instruction, Teaching Methods, Geometry, Computation
Sigler, Avi; Stupel, Moshe; Flores, Alfinio – International Journal of Mathematical Education in Science and Technology, 2017
Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas…
Descriptors: Mathematics Instruction, Computer Software, Educational Technology, Geometric Concepts
McCartney, Mark – International Journal of Mathematical Education in Science and Technology, 2017
A number of probabilistic experiments are described to estimate e, p and v2, with results from computer simulations being used to investigate convergence. A number of possible classroom exercises and extensions are presented.
Descriptors: Probability, Mathematics Instruction, Computer Simulation, Teaching Methods
Vorob'ev, Evgenii M. – International Journal of Mathematical Education in Science and Technology, 2015
Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of…
Descriptors: Educational Technology, Computer Uses in Education, Algebra, Calculus
Fedriani, Eugenio M.; Moyano, Rafael – International Journal of Mathematical Education in Science and Technology, 2012
Finding educational truths is an inherently multivariate problem. There are many factors affecting each student and their performances. Because of this, both measuring of skills and assessing students are always complex processes. This is a well-known problem, and a number of solutions have been proposed by specialists. One of its ramifications is…
Descriptors: Mathematics Skills, Mathematics Instruction, Teaching Methods, Computer Software
Dana-Picard, Thierry; Zeitoun, David G. – International Journal of Mathematical Education in Science and Technology, 2012
We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.
Descriptors: Mathematical Formulas, Numbers, Mathematics Instruction, Teaching Methods
Kobayashi, Yukio – International Journal of Mathematical Education in Science and Technology, 2011
The formula [image omitted] is closely related to combinatorics through an elementary geometric exercise. This approach can be expanded to the formulas [image omitted], [image omitted] and [image omitted]. These formulas are also nice examples of showing two approaches, one algebraic and one combinatoric, to a problem of counting. (Contains 6…
Descriptors: Mathematical Formulas, Geometry, Computation, Teaching Methods
Kovacs, Zoltan – International Journal of Mathematical Education in Science and Technology, 2011
Student activities focused on discovering mathematics play an important role in the teaching and learning process. WebMathematics Interactive (WMI2) was developed to offer a fast and user-friendly on-line web interface to enhance the quality of both theoretical and applied mathematics courses. For the teacher, in the classroom, it provides…
Descriptors: Mathematical Concepts, Mathematics Instruction, Teaching Methods, Algebra
Deakin, Michael A. B. – International Journal of Mathematical Education in Science and Technology, 2010
Many familiar household objects (such as sausages) involve the maximization of a volume under geometric constraints. A flexible but inextensible membrane bounds a volume which is to be filled to capacity. In the case of the sausage, a full analytic solution is here provided. Other related but more difficult problems seem to demand approximate…
Descriptors: Geometric Concepts, Calculus, Mathematics Instruction, Problem Solving
Shutler, Paul M. E.; Fong, Ng Swee – International Journal of Mathematical Education in Science and Technology, 2010
Modern Hindu-Arabic numeration is the end result of a long period of evolution, and is clearly superior to any system that has gone before, but is it optimal? We compare it to a hypothetical base 5 system, which we dub Predator arithmetic, and judge which of the two systems is superior from a mathematics education point of view. We find that…
Descriptors: Elementary School Mathematics, Mathematics Instruction, Computation, Arithmetic
Robin, W. A. – International Journal of Mathematical Education in Science and Technology, 2010
Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…
Descriptors: Equations (Mathematics), Computation, Teaching Methods, Problem Solving
Sprows, David J. – International Journal of Mathematical Education in Science and Technology, 2009
A number of schools have recently introduced new courses dealing with various aspects of iteration theory or at least have found ways of including topics such as chaos and fractals in existing courses. In this note, we will consider a family of functions whose members are especially well suited to illustrate many of the concepts involved in these…
Descriptors: Geometric Concepts, Mathematics Education, Mathematics Instruction, Teaching Methods
Shi, Yixun – International Journal of Mathematical Education in Science and Technology, 2009
Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, "Using a sequence of number pairs as an example in teaching mathematics". Math. Comput. Educ., 39 (2005), pp. 198-205; Y. Shi, "Case study projects for college mathematics courses based on a particular…
Descriptors: College Mathematics, Student Interests, Algebra, Mathematics Instruction
Hodnett, P. F.; Courtney, C. – International Journal of Mathematical Education in Science and Technology, 2007
This paper uses a partial differential equation which occurs in a reduced model of large scale circulation in an ocean basin as an educational vehicle through which to demonstrate the usefulness of a set of mathematical techniques in analysing the equation. A parameter occurring in the equation does in reality vary from very small through…
Descriptors: Measurement, Climate, Oceanography, Equations (Mathematics)
Ramasinghe, W. – International Journal of Mathematical Education in Science and Technology, 2002
Simple examples are really encouraging in the understanding of rearrangements of infinite series, since many texts and teachers provide only existence theorems. In the absence of examples, an existence theorem is just a statement and lends little confidence to understanding. Iterated sums of double series seem to have a similar spirit of…
Descriptors: Teaching Methods, Mathematics Instruction, Learning Processes, Mathematical Concepts
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