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Park, Jungeun; DiNapoli, Joseph; Mixell, Robert A.; Flores, Alfinio – International Journal of Mathematical Education in Science and Technology, 2017
This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual…
Descriptors: Mathematics, Mathematics Instruction, Mathematical Models, Equations (Mathematics)
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López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael – International Journal of Mathematical Education in Science and Technology, 2016
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
Descriptors: Equations (Mathematics), Semi Structured Interviews, Undergraduate Students, Calculus
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Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2013
A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.
Descriptors: Mathematics, Mathematical Formulas, Introductory Courses, Mathematics Instruction
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Ho, Weng Kin; Ho, Foo Him; Lee, Tuo Yeong – International Journal of Mathematical Education in Science and Technology, 2012
This article gives an elementary proof of the famous identity [image omitted]. Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity [image omitted].
Descriptors: Calculus, Mathematics Instruction, Mathematical Logic, Mathematical Concepts
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Debnath, Lokenath – International Journal of Mathematical Education in Science and Technology, 2010
This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Konigsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real…
Descriptors: Topology, Geometric Concepts, Mathematics, Theories
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Man, Yiu-Kwong – International Journal of Mathematical Education in Science and Technology, 2007
A simple algorithm for computing the partial fraction expansions of proper rational functions with multiple poles is presented. The main idea is to use the Heaviside's cover-up technique to determine the numerators of the partial fractions and polynomial divisions to reduce the multiplicities of the poles involved successively, without the use of…
Descriptors: Calculus, Mathematics, Computation, Methods
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Asiru, M. A. – International Journal of Mathematical Education in Science and Technology, 2007
Under predetermined conditions on the roots and coefficients, necessary and sufficient conditions relating the coefficients of a given cubic equation x[cubed] + ax[squared] + bx + c = 0 can be established so that the roots possess desired properties. In this note, the condition for one root of a cubic equation to be "the negative reciprocal of…
Descriptors: Equations (Mathematics), Algebra, College Mathematics, Computation
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International Journal of Mathematical Education in Science and Technology, 2007
In this issue's "Classroom Notes" section, the following papers are discussed: (1) "Constructing a line segment whose length is equal to the measure of a given angle" (W. Jacob and T. J. Osler); (2) "Generating functions for the powers of Fibonacci sequences" (D. Terrana and H. Chen); (3) "Evaluation of mean and variance integrals without…
Descriptors: Mathematics, College Mathematics, Units of Study, Lesson Plans
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Chen, Hongwei – International Journal of Mathematical Education in Science and Technology, 2002
In this note, using the method of undetermined coefficients, we obtain the power series for exp ( f ( x )) and ln ( f ( x )) by means of a simple recursion. As applications, we show how those power series can be used to reproduce and improve some well-known results in analysis. These results may be used as enrichment material in an advanced…
Descriptors: Calculus, Mathematical Formulas, Mathematics, Multiplication