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Maxwell, Mary; Gleason, Jim – International Journal of Mathematical Education in Science and Technology, 2019

Many large universities, community colleges and some smaller four-year colleges are turning to hybrid or online instruction for remedial and entry level mathematics courses, often assessed using online exams in a proctored computer lab environment. Faculty face the task of choosing questions from a publisher's text bank with very little, if any,…

Descriptors: Item Response Theory, Test Reliability, Item Banks, Algebra

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2019

The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.

Descriptors: Mathematics Instruction, Teaching Methods, Manipulative Materials, Mathematical Concepts

Hoban, Richard A. – International Journal of Mathematical Education in Science and Technology, 2019

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students…

Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Calculus

Gero, Aharon; Levin, Ilya – International Journal of Mathematical Education in Science and Technology, 2019

The invention of the computer has led to the establishment of a new research paradigm, computation, which has recently become more and more popular in scientific exploration. However, computation is not well represented in high school and university curricula in science and engineering, although it applies to a wide range of disciplines beyond…

Descriptors: Computation, Thinking Skills, Problem Solving, Mathematics Skills

Caglayan, Günhan – International Journal of Mathematical Education in Science and Technology, 2018

This linear algebra note offers teaching and learning ideas in the treatment of the inner product space R[superscript m x n] in a technology-supported learning environment. Classroom activities proposed in this note demonstrate creative ways of integrating MATLAB technology into various properties of Frobenius inner product as visualization tools…

Descriptors: Algebra, Class Activities, Mathematics Instruction, Computer Uses in Education

Pujol, Jose – International Journal of Mathematical Education in Science and Technology, 2018

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…

Descriptors: Mathematics Instruction, Algebra, Geometric Concepts, Problem Solving

Vandenbussche, J.; Ritter, L.; Scherrer, C. – International Journal of Mathematical Education in Science and Technology, 2018

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea…

Descriptors: Calculus, Mathematics Instruction, Remedial Mathematics, At Risk Students

McAlevey, Lynn G.; Stent, Alan F. – International Journal of Mathematical Education in Science and Technology, 2018

The treatment of kurtosis in textbooks is both sparse and contradictory with applications rarely discussed. To address this, an easily understood definition of kurtosis is introduced and important applications are demonstrated. Two different approaches to teaching kurtosis are presented based on a financial application.

Descriptors: Statistical Distributions, Undergraduate Students, Probability, Statistical Data

Buchbinder, Orly – International Journal of Mathematical Education in Science and Technology, 2018

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

Descriptors: Mathematical Logic, Validity, Geometry, Geometric Concepts

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

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2017

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching "well posedness" of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a…

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

Brandt, Keith – International Journal of Mathematical Education in Science and Technology, 2017

I propose that students pay more attention to the approximations that lead to integral formulas when they study applications of the definite integral. The goal is to focus students on the underlying concepts and the definition of the definite integral--and to steer them away from memorizing formulas. To address this goal, I have written some…

Descriptors: Concept Teaching, Mathematical Formulas, Mathematical Applications, Mathematics Activities

Abernethy, Gavin M.; McCartney, Mark – International Journal of Mathematical Education in Science and Technology, 2017

Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.

Descriptors: Classroom Techniques, Class Activities, Investigations, Mathematics Activities

Kontorovich, Igor' – International Journal of Mathematical Education in Science and Technology, 2017

These classroom notes are focused on undergraduate students' understanding of the polysemous symbol of superscript (-1), which can be interpreted as a reciprocal or an inverse function. Examination of 240 scripts in a mid-term test identified that some first-year students struggle with choosing the contextually correct interpretation and there are…

Descriptors: Misconceptions, Mathematical Aptitude, Mathematics Achievement, Undergraduate Students

Jones, Stephen L. – International Journal of Mathematical Education in Science and Technology, 2017

Dr RL Moore was undoubtedly one of the finest mathematics teachers ever. He developed a unique teaching method designed to teach his students to think like mathematicians. His method was not designed to convey any particular mathematical knowledge. Instead, it was designed to teach his students to think. Today, his method has been modified to…

Descriptors: Mathematics Education, Mathematics Instruction, Mathematics Teachers, Teaching Methods