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Daugulis, Peteris; Sondore, Anita – PRIMUS, 2018
Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach by using block matrices to make computations more visual. We find this method a…
Descriptors: Mathematics Instruction, Matrices, Visualization, Multiplication
Murray, Natasha T. K. – Mathematics Teacher, 2018
How can we make sense of what we learned today?" This is a question the author commonly poses to her algebra students in an effort to have them think about the connections between the new concept they are learning and concepts they have previously learned. For students who have a strong, expansive understanding of previously learned topics,…
Descriptors: Mathematical Concepts, Number Concepts, Algebra, Mathematics Instruction
Quane, Kate; Brown, Leni – Australian Primary Mathematics Classroom, 2022
Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…
Descriptors: Mathematics Instruction, Toys, Manipulative Materials, Foreign Countries
Selby, Christina – PRIMUS, 2016
Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Algebra
Bismarck, Stephen F.; Zelkowski, Jeremy; Gleason, Jim – Mathematics Teacher, 2014
Like many commodities, the price of gasoline continues to rise, and these price changes are readily observed in gas stations' signage. Moreover, algebraic methods are well suited to model price change and answer the student's question. Over the course of one ninety-minute block or two forty-five-minute classes, students build functions…
Descriptors: Mathematics Instruction, Prediction, Fuels, Algebra
Suh, Jennifer M.; Seshaiyer, Padmanabhan – Rowman & Littlefield Publishers, 2016
"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…
Descriptors: Elementary School Mathematics, Secondary School Mathematics, Mathematics Instruction, Problem Solving
Kalman, Dan; Teague, Daniel J. – Mathematics Teacher, 2013
Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…
Descriptors: Mathematics Instruction, Measurement, Motion, Physics
Gavin, M. Katherine; Sheffield, Linda Jensen – Mathematics Teaching in the Middle School, 2015
For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…
Descriptors: Mathematics Instruction, Secondary School Mathematics, Middle School Students, Algebra
Fay, Temple H.; Joubert, Stephan V. – International Journal of Mathematical Education in Science and Technology, 2010
In this article we examine 2 x 2 first-order systems of ordinary differential equations and show how to identify separatrices for phase plane portraits when the system has a saddle point critical value. We describe how to use a computer algebra system to generate trajectories from contour plots, when possible, and determine the equation of the…
Descriptors: Calculus, Algebra, Equations (Mathematics), Models
Mungan, Carl E. – Physics Teacher, 2009
Rayleigh's criterion states that a pair of point sources are barely resolved by an optical instrument when the central maximum of the diffraction pattern due to one source coincides with the first minimum of the pattern of the other source. As derived in standard introductory physics textbooks, the first minimum for a rectangular slit of width "a"…
Descriptors: Optics, Physics, Science Instruction, Textbooks
Mark, June; Cuoco, Al; Goldenberg, E. Paul; Sword, Sarah – Mathematics Teaching in the Middle School, 2010
"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…
Descriptors: Calculus, Arithmetic, Algebra, Mathematics Instruction
Peralta, Javier – Teaching Mathematics and Its Applications: An International Journal of the IMA, 2008
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Descriptors: Numbers, Mathematics Instruction, Mathematical Concepts, Computation
Muschla, Judith A.; Muschla, Gary Robert; Muschla, Erin – Jossey-Bass, An Imprint of Wiley, 2012
The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. "Hands-on Activities for Teaching the Common Core Math…
Descriptors: State Standards, Mathematics Instruction, Academic Standards, Experiential Learning
Enderson, Mary C.; Klerlein, Jacob T.; Johnson, Jason D. – New England Mathematics Journal, 2010
Today's classrooms pose many challenges for new mathematics teachers joining the teaching force. As they enter the teaching field, they bring a wide range of mathematical experiences that are often focused on calculations and memorization of concepts rather than problem solving and representation of ideas. Such experiences generally minimize what…
Descriptors: Mathematics Education, Mathematics Teachers, Teacher Student Relationship, Computation
Schmidt, Karsten – International Journal of Mathematical Education in Science and Technology, 2008
In this paper "Derive" functions are provided for the computation of the Moore-Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore-Penrose inverse. Making it possible to compute the Moore-Penrose inverse easily with one of the most commonly used Computer Algebra Systems--and to have the blueprint…
Descriptors: Programming Languages, Computer Uses in Education, Programming, Algebra