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Showing 1 to 15 of 167 results Save | Export
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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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Rojo, Megan; Wakim, Noura – Intervention in School and Clinic, 2023
Students with learning disabilities in mathematics often struggle with the underlying concepts of multidigit addition and subtraction. To help students build a conceptual understanding of these computations, teachers can utilize evidence-based practices such as the concrete-semi-concrete-abstract framework and the use of multiple visual…
Descriptors: Addition, Subtraction, Mathematics, Learning Disabilities
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Vozzo, Enzo – Australian Senior Mathematics Journal, 2017
Ever since their serendipitous discovery by Italian mathematicians trying to solve cubic equations in the 16th century, imaginary and complex numbers have been difficult topics to understand. Here the word complex is used to describe something consisting of a number of interconnecting parts. The different parts of a complex number are the…
Descriptors: Mathematics Instruction, Mathematics, Professional Personnel, Numbers
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Throndsen, Jennifer; MacDonald, Beth; Hunt, Jessica – Australian Primary Mathematics Classroom, 2017
Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.
Descriptors: Mathematics, Mathematics Instruction, Kindergarten, Numbers
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Sureda, Patricia; Otero, Rita – International Electronic Journal of Mathematics Education, 2019
The construction of the exponential function of a real exponent from the definition of the powers of a real number, and its properties, requires the notion of successions, a decimal approximation of a rational number, convergence, and limit of a function. In Argentina, this construction would exceed what could be taught at the secondary level, but…
Descriptors: Mathematics, Numbers, Foreign Countries, Preservice Teacher Education
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Hurst, Chris; Hurrell, Derek – Australian Primary Mathematics Classroom, 2018
This article describes some of the essential mathematics that underpins the use of algorithms through a series of learning pathways. To begin, a graphic depicting the mathematical ideas and concepts that underpin the learning of algorithms for multiplication and division is provided. The understanding and use of algorithms is informed by two…
Descriptors: Mathematics, Mathematics Instruction, Multiplication, Division
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Ghergu, Marius – International Journal of Mathematical Education in Science and Technology, 2018
We explore the connection between the notion of critical point for a function of one variable and various inequalities for iterated exponentials defined on the positive semiline of real numbers.
Descriptors: Mathematics, Mathematics Instruction, Mathematical Concepts, Numbers
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Herzinger, K.; Kunselman, C.; Pierce, I. – International Journal of Mathematical Education in Science and Technology, 2018
Theon's ladder is an ancient method for easily approximating "n"th roots of a real number "k." Previous work in this area has focused on modifying Theon's ladder to approximate roots of quadratic polynomials. We extend this work using techniques from linear algebra. We will show that a ladder associated to the quadratic…
Descriptors: Algebra, Mathematics Instruction, Mathematical Formulas, Mathematics
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Coggins, Porter E., III; Glatzer, Tim – PRIMUS, 2020
We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…
Descriptors: Mathematics Instruction, Matrices, Technology, Addition
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Yang, Yajun; Gordon, Sheldon P. – PRIMUS, 2016
This article looks at the effects that adding a single extra subdivision has on the level of accuracy of some common numerical integration routines. Instead of automatically doubling the number of subdivisions for a numerical integration rule, we investigate what happens with a systematic method of judiciously selecting one extra subdivision for…
Descriptors: Numbers, Accuracy, Computation, Mathematics
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Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2017
Let R be a ring with identity. Then {0} and R are the only additive subgroups of R if and only if R is isomorphic (as a ring with identity) to (exactly) one of {0}, Z/pZ for a prime number p. Also, each additive subgroup of R is a one-sided ideal of R if and only if R is isomorphic to (exactly) one of {0}, Z, Z/nZ for an integer n = 2. This note…
Descriptors: Numbers, Mathematics Instruction, Mathematics, Algebra
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Wheeler, Ann; Champion, Joe – Mathematics Teaching in the Middle School, 2016
Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…
Descriptors: Probability, Middle School Students, Mathematics, Mathematics Instruction
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McMullen, Jake; Chan, Jenny Yun-Chen; Mazzocco, Michèle M. M.; Hannula-Sormunen, Minna M. – Research in Mathematics Education, 2019
A growing body of evidence reveals the need for research on, and consideration for, children's and students' own--self-guided--spontaneous use of mathematical reasoning and knowledge in action. Spontaneous focusing on numerosity (SFON) and quantitative relations (SFOR) have been implicated as key components of mathematical development. In this…
Descriptors: Mathematics, Logical Thinking, Numbers, Mathematics Skills
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Gough, John – Australian Mathematics Teacher, 2017
When computers started having screens (or monitors), as well as printers, a new alphanumeric display was created using dots. A crucial variable in designing alphabet letters and digits, using dots, is the height of the display, measured in dots. This article addresses the same design questions tackled by designers of typefaces or fonts, and shows…
Descriptors: Design, Mathematics, Computer System Design, Computers
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Cereceda, José Luis – International Journal of Mathematical Education in Science and Technology, 2017
In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, P[subscript k](n) and Q[subscript k](n), such that P[subscript k](n) = Q[subscript k](n) = f[subscript k](n) for n = 1, 2,… , k, where f[subscript k](1), f[subscript k](2),… , f[subscript k](k) are k arbitrarily chosen…
Descriptors: Algebra, Mathematical Formulas, Numbers, Mathematics
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