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Showing 1 to 15 of 178 results Save | Export
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Baum, Dave – Physics Teacher, 2020
In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of…
Descriptors: Physics, Problem Solving, Calculus, Trigonometry
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Lingefjärd, Thomas; Hatami, Russell – Policy Futures in Education, 2020
This is an article about abstraction, generalization, and the beauty of mathematics. We claim that abstraction and generalization in of itself may very well be a beauty of the human mind. The fact that we humans continue to explore and expand mathematics is truly beautiful and remarkable. Many years ago, our ancestors understood that seven stones,…
Descriptors: Abstract Reasoning, Aesthetics, Mathematics, Mathematical Concepts
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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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Vladimir Miškovic – Australian Mathematics Education Journal, 2023
The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…
Descriptors: Algebra, Geometric Concepts, Plane Geometry, Mathematical Formulas
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Dorce, Carlos – International Journal of Mathematical Education in Science and Technology, 2022
For quite some time, research on the use of the History of Mathematics in the classroom has confirmed a lot of academic benefits for students. However, the History of Mathematics can also be used as an inclusion tool in classrooms where there are foreign students because it allows working with the specific contexts of other cultures. This article…
Descriptors: Social Integration, Units of Study, Mathematics Instruction, Educational Benefits
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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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Pujol, Jose – International Journal of Mathematical Education in Science and Technology, 2018
Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…
Descriptors: Mathematics Instruction, Algebra, Geometric Concepts, Problem Solving
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Gibbons, Alanna – Journal of Mathematics Education at Teachers College, 2019
Maryam Mirzakhani is the first and the only female winner of the Fields Medal since its establishment in 1936. She is arguably one of the greatest mathematicians of our generation. This biographical paper outlines her life and work. Her mathematical theorems and noteworthy accomplishments are just as impressive as her determination, imagination,…
Descriptors: Mathematics, Professional Personnel, Biographies, Females
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Quinnell, Lorna – Australian Primary Mathematics Classroom, 2018
Successful mathematical problem-solving relies on choices about how best to represent and solve problems. In this article, a range of methods and strategies are presented for solving a single mathematical problem, including novel methods posed by in-service teachers at one Australian university. The variety of problem-solving strategies rely on…
Descriptors: Problem Solving, Selection, Mathematics, Methods
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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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Trenkler, Götz; Trenkler, Dietrich – International Journal of Mathematical Education in Science and Technology, 2017
Given three planes in space, a complete characterization of their intersection is provided. Special attention is paid to the case when the intersection set does not exist of one point only. Besides the vector cross product, the tool of generalized inverse of a matrix is used extensively.
Descriptors: Algebra, Geometric Concepts, Equations (Mathematics), Matrices
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Bardell, Nicholas S. – Australian Senior Mathematics Journal, 2016
The cubic polynomial with real coefficients has a rich and interesting history primarily associated with the endeavours of great mathematicians like del Ferro, Tartaglia, Cardano or Vieta who sought a solution for the roots (Katz, 1998; see Chapter 12.3: The Solution of the Cubic Equation). Suffice it to say that since the times of renaissance…
Descriptors: Algebra, Mathematical Formulas, Mathematics, Mathematics Education
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Fitzherbert, John – Australian Senior Mathematics Journal, 2017
Jagadguru Shankaracharya Swami Bharati Krishna Tirtha (commonly abbreviated to Bharati Krishna) was a scholar who studied ancient Indian Veda texts and between 1911 and 1918 (vedicmaths.org, n.d.) and wrote a collection of 16 major rules and a number of minor rules which have collectively become known as the "sutras of Vedic…
Descriptors: Mathematics, Professional Personnel, Mathematics Instruction, Equations (Mathematics)
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Shaw, Christopher – PRIMUS, 2018
We present a short-term class project used in an introductory linear algebra course, designed to engage students in matrix algebra. In this activity, students responded to a survey of their pop culture tastes. Using the survey responses, they worked to design a series of matching algorithms, using matrices, with the goal of matching the students…
Descriptors: Algebra, Mathematics Instruction, Matrices, Popular Culture
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