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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
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Zengin, Yilmaz – International Journal of Mathematical Education in Science and Technology, 2018
The purpose of this study was to investigate pre-service teachers' views about the history of mathematics course in which GeoGebra was used. The qualitative research design was used in this study. The participants of the study consisted of 23 pre-service mathematics teachers studying at a state university in Turkey. An open-ended questionnaire was…
Descriptors: Mathematics Instruction, Computer Software, Mathematical Concepts, Mathematical Logic
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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
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Stewart, Sepideh; Schmidt, Ralf – International Journal of Mathematical Education in Science and Technology, 2017
In this study, we examined a mathematician and one of his students' teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Tall's framework of three worlds of mathematical thinking as well as Piaget's notion of accommodation to theoretically study the…
Descriptors: Mathematical Logic, Validity, Teaching Methods, Mathematics Instruction
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Weber, Keith; Mejia-Ramos, Juan Pablo – International Journal of Mathematical Education in Science and Technology, 2014
We argue that mathematics majors learn little from the proofs they read in their advanced mathematics courses because these students and their teachers have different perceptions about students' responsibilities when reading a mathematical proof. We used observations from a qualitative study where 28 undergraduates were observed evaluating…
Descriptors: Majors (Students), Mathematics Instruction, College Mathematics, Undergraduate Students
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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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Debnath, L. – International Journal of Mathematical Education in Science and Technology, 2013
This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…
Descriptors: Equations (Mathematics), Geometry, Calculus, Algebra
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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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Smith, Christopher J.; Tefera, Akalu; Zeleke, Aklilu – International Journal of Mathematical Education in Science and Technology, 2012
The use of computer algebra systems such as Maple and Mathematica is becoming increasingly important and widespread in mathematics learning, teaching and research. In this article, we present computerized proof techniques of Gosper, Wilf-Zeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete…
Descriptors: Algebra, Mathematics Education, Undergraduate Students, Higher Education
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Fay, Temple H. – International Journal of Mathematical Education in Science and Technology, 2002
This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…
Descriptors: Calculus, Mathematical Concepts, Mathematics Education, Equations (Mathematics)
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Guyker, James – International Journal of Mathematical Education in Science and Technology, 2002
A lively example to use in a first course in linear algebra to clarify vector space notions is the space of square matrices of fixed order with its subspaces of affine, coaffine, doubly affine, and magic squares. In this note, the projection theorem is illustrated by explicitly constructing the orthogonal projections (in closed forms) of any…
Descriptors: Geometric Concepts, Matrices, Algebra, Computation
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Martinez, F.; Vinuesa, C. – International Journal of Mathematical Education in Science and Technology, 2002
This note presents some simple examples illustrating the differences between the concepts of continuity, existence of partial derivatives and differentiability. (Contains 2 tables and 10 figures.)
Descriptors: Mathematics, Calculus, Mathematical Logic, Validity
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Kasturiarachi, A. Bathi – International Journal of Mathematical Education in Science and Technology, 2002
Using Newton's method as an intermediate step, we introduce an iterative method that approximates numerically the solution of f(x) = 0. The method is essentially a leap-frog Newton's method. The order of convergence of the proposed method at a simple root is cubic and the computational efficiency in general is less, but close to that of Newton's…
Descriptors: Algebra, Graphing Calculators, Mathematics, Mathematics Education