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Giovanni Vincenzi – International Journal of Mathematical Education in Science and Technology, 2025
Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…
Descriptors: Mathematical Logic, Validity, Numbers, Mathematics
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Firozzaman, Firoz; Firoz, Fahim – International Journal of Mathematical Education in Science and Technology, 2017
Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the…
Descriptors: Mathematics Instruction, Numbers, Mathematical Concepts, Equations (Mathematics)
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Son, Ji-Won; Hu, Qintong; Lim, Woong – International Journal of Mathematical Education in Science and Technology, 2019
Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers' estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the…
Descriptors: Computation, Mental Computation, Mathematics Instruction, Preservice Teachers
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Abd-Elhameed, W. M.; Zeyada, N. A. – International Journal of Mathematical Education in Science and Technology, 2017
This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which…
Descriptors: Generalization, Numbers, Number Concepts, Number Systems
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Brown, Jill Patricia; Stillman, Gloria Ann – International Journal of Mathematical Education in Science and Technology, 2017
A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…
Descriptors: Mathematical Models, Foreign Countries, Mathematical Concepts, Mathematics
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Mamolo, Ami; Bogart, Tristram – International Journal of Mathematical Education in Science and Technology, 2011
This article presents a novel re-conceptualisation to a well-known problem--The Ping-Pong Ball Conundrum. We introduce a variant of this super-task by considering it through the lens of "measuring infinity"--a conceptualisation of infinity that extrapolates measuring properties of numbers, rather than cardinal properties. This approach is…
Descriptors: Number Concepts, Experiments, Intervals, Numbers
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Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2012
It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…
Descriptors: Introductory Courses, Number Concepts, Numbers, Algebra
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Gagatsis, Athanasios; Panaoura, Areti – International Journal of Mathematical Education in Science and Technology, 2014
The study aimed to investigate students' conceptions on the notion of absolute value and their abilities in applying the specific notion in routine and non-routine situations. A questionnaire was constructed and administered to 17-year-old students. Data were analysed using the hierarchical clustering of variables and the implicative method, while…
Descriptors: Mathematics Instruction, Mathematical Concepts, Questionnaires, Mathematical Logic
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Mortici, Cristinel – International Journal of Mathematical Education in Science and Technology, 2012
The floor function maps a real number to the largest previous integer. More precisely, floor(x)=[x] is the largest integer not greater than x. The square bracket notation [x] for the floor function was introduced by Gauss in his third proof of quadratic reciprocity in 1808. The floor function is also called the greatest integer or entier (French…
Descriptors: Numbers, Number Concepts, Geometric Concepts, Mathematics Education
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Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him – International Journal of Mathematical Education in Science and Technology, 2014
Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…
Descriptors: Problem Solving, Number Concepts, Numbers, Teaching Methods
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Gauthier, N. – International Journal of Mathematical Education in Science and Technology, 2011
Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus…
Descriptors: Introductory Courses, Numbers, Number Concepts, Calculus
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Sprows, David J. – International Journal of Mathematical Education in Science and Technology, 2010
This note can be used to illustrate to the student such concepts as periodicity in the complex plane. The basic construction makes use of the Tent function which requires only that the student have some working knowledge of binary arithmetic.
Descriptors: Arithmetic, Intervals, Mathematics, Mathematical Formulas
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Kalapodi, A. – International Journal of Mathematical Education in Science and Technology, 2010
The representation of natural numbers in decimal form is an unequivocal procedure while for the representation of real numbers some ambiguities concerning the existence of infinitely many digits equal to 9 still emerge. One of the most frequently confronted misunderstandings is whether 0.999...equals 1 or not, and if not what number does this…
Descriptors: Numbers, Number Concepts, Concept Formation, Mathematics Education
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Abu-Saris, Raghib M. – International Journal of Mathematical Education in Science and Technology, 2009
In this note, we show that if the integral of a continuous function, h, vanishes over an interval [a, b], then so does the integral of w(x)h(x) over [a, c] for some c in (a, b), where w is a monotonic increasing (decreasing) function on [a, b] with w(a) is non-negative (non-positive).
Descriptors: Numbers, Number Concepts, Numeracy, Mathematical Applications
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Capelas de Oliveira, E.; Rosa, M. A. F.; Vaz, J., Jr. – International Journal of Mathematical Education in Science and Technology, 2009
We present a calculation involving a wide class of real integrals by means of integration in the complex plane. Some particular cases where Euler numbers and Bell polynomials appear are discussed and a generalisation of some previous results is also provided. (Contains 1 table and 1 figure.)
Descriptors: Numbers, Number Concepts, Computation, Mathematical Formulas
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