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Gourley, Patrick – Journal of Economic Education, 2018

The Coase Theorem is a fundamental tenet of environmental economics and is taught to thousands of principles of microeconomics students each year. Its counterintuitive conclusion, that a Pareto optimal solution can result between private parties regardless of the initial allocation of property rights over a scarce resource, is difficult for…

Descriptors: Economics Education, Microeconomics, Theories, Environmental Education

Bardell, Nicholas S. – Australian Senior Mathematics Journal, 2014

This paper describes how a simple application of de Moivre's theorem may be used to not only find the roots of a quadratic equation with real or generally complex coefficients but also to pinpoint their location in the Argand plane. This approach is much simpler than the comprehensive analysis presented by Bardell (2012, 2014), but it does not…

Descriptors: Mathematics Instruction, Mathematical Logic, Equations (Mathematics), Problem Solving

Çeziktürk, Özlem – International Technology and Education Journal, 2020

Functional dependency is a term coming out of mathematical software terminology. It shows the dependency of one representation (either diagrammatic or algebraic) to one another in the form of a formula, a conceptual relation or an algorithm. In mathematics, it is important since it shows students' understanding of those conceptual relationships if…

Descriptors: Geometry, Mathematics Instruction, Computer Software, Material Development

Hong, Seok-Cheol; Hong, Seok-In – Physics Teacher, 2013

Calculation of moments of inertia is often challenging for introductory-level physics students due to the use of integration, especially in non-Cartesian coordinates. Methods that do not employ calculus have been described for finding the rotational inertia of thin rods and other simple bodies. In this paper we use the parallel axis theorem and…

Descriptors: Physics, Scientific Concepts, Computation, Mathematical Logic

Levesque, Luc – Physics Education, 2014

Inaccurate measurements occur regularly in data acquisition as a result of improper sampling times. An understanding of proper sampling times when collecting data with an analogue-to-digital converter or video camera is crucial in order to avoid anomalies. A proper choice of sampling times should be based on the Nyquist sampling theorem. If the…

Descriptors: Video Technology, Motion, Physics, Scientific Concepts

Janji, Milan – International Journal of Mathematical Education in Science & Technology, 2005

A short proof of Laplace's expansion theorem is given. The proof is elementary and can be presented at any level of undergraduate studies where determinants are taught. It is derived directly from the definition so that the theorem may be used as a starting point for further investigation of determinants.

Descriptors: Mathematics Education, Theories, College Mathematics, Undergraduate Study

Oman, Greg – College Mathematics Journal, 2009

We give an irredundant axiomatization of the complete ordered field of real numbers. In particular, we show that all the field axioms for multiplication with the exception of the distributive property may be deduced as "theorems" in our system. We also provide a complete proof that the axioms we have chosen are independent.

Descriptors: Mathematics Instruction, Numbers, College Mathematics, Validity

Sauerheber, Richard D. – International Journal of Mathematical Education in Science and Technology, 2012

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Mathematical Concepts

Gomez, E.; Plaza, A. – International Journal of Mathematical Education in Science and Technology, 2002

One of the most astonishing properties when studying numerical series is that the sum is not commutative, that is the sum may change when the order of its elements is altered. In this note an example is given of such a series. A well-known mathematical proof is given and a MATLAB[C] program used for different rearrangements of the series…

Descriptors: Mathematical Logic, Validity, Intervals, Mathematics

Wang, Jinhui; Ricardo, Bernard – Physics Teacher, 2019

Moments of inertia (MOIs) are usually derived via substantial integration and may intimidate undergraduates without prior backgrounds in calculus. This paper presents an intuitive geometric operation, termed "squashing," that transforms an object into an equivalent one with a reduced dimension, whose MOI is simpler to determine. The…

Descriptors: Undergraduate Students, Mechanics (Physics), Geometric Concepts, Science Process Skills

Ruggieri, Eric – PRIMUS, 2016

The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…

Descriptors: College Mathematics, Mathematics Instruction, Undergraduate Study, Mathematical Logic

David, Erika J.; Hah Roh, Kyeong; Sellers, Morgan E. – PRIMUS, 2020

This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Students, Calculus

Bokosmaty, Sahar; Sweller, John; Kalyuga, Slava – American Educational Research Journal, 2015

Research has demonstrated that instruction that relies heavily on studying worked examples is more effective for less experienced learners compared to instruction emphasizing problem solving. However, the guidance associated with studying some worked examples may reduce the performance of more experienced learners. This study investigated…

Descriptors: Geometry, Problem Solving, Expertise, Teaching Methods

Dawkins, Paul Christian; Zazkis, Dov – Journal for Research in Mathematics Education, 2021

This article documents differences between novice and experienced undergraduate students' processes of reading mathematical proofs as revealed by moment-by-moment, think-aloud protocols. We found three key reading behaviors that describe how novices' reading differed from that of their experienced peers: alternative task models, accrual of…

Descriptors: Mathematics Instruction, Validity, Mathematical Logic, Undergraduate Students

Merrotsy, Peter – Australian Mathematics Education Journal, 2020

This is the first of two articles on the life and mathematical legacy of the Indian mathematician Ramanujan, who died one hundred years ago. Here, the story of Ramanujan's life is related. His cultural and social background are briefly described and his educational experiences are outlined. Attention is then drawn to the deep nature of his…

Descriptors: Mathematics, Professional Personnel, Biographies, Cultural Background