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Gordon, Sheldon P. – Mathematics and Computer Education, 2011

This article presents an applied calculus exercise that can be easily shared with students. One of Kepler's greatest discoveries was the fact that the planets move in elliptic orbits with the sun at one focus. Astronomers characterize the orbits of particular planets by their minimum and maximum distances to the sun, known respectively as the…

Descriptors: Space Sciences, Mathematical Concepts, Calculus, College Mathematics

Jerome, Lawrence – Mathematics and Computer Education, 2011

As anyone who has taught or taken a statistics course knows, statistical calculations can be tedious and error-prone, with the details of a calculation sometimes distracting students from understanding the larger concepts. Traditional statistics courses typically use scientific calculators, which can relieve some of the tedium and errors but…

Descriptors: Textbooks, Visual Learning, Graphs, Hypothesis Testing

Carley, Holly – Mathematics and Computer Education, 2011

This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

Descriptors: Number Concepts, Mathematics, Mathematical Concepts, Mathematics Instruction

Ponce-Campuzano, Juan Carlos; Rivera-Figueroa, Antonio – Mathematics and Computer Education, 2011

It is common to see, in the books on calculus, primitives of functions (some authors use the word "antiderivative" instead of primitive). However, the majority of authors pay scant attention to the domains over which the primitives are valid, which could lead to errors in the evaluation of definite integrals. In the teaching of calculus, in…

Descriptors: Calculus, Mathematics Instruction, Mathematical Concepts, Teaching Methods

Nord, Gail M. – Mathematics and Computer Education, 2011

Calculators and computers make new modes of instruction possible; yet, at the same time they pose hardships for school districts and mathematics educators trying to incorporate technology with limited monetary resources. In the "Standards," a recommended classroom is one in which calculators, computers, courseware, and manipulative materials are…

Descriptors: Computer Software, Educational Technology, Mathematical Concepts, Calculus

Skurnick, Ronald – Mathematics and Computer Education, 2011

This classroom note is presented as a suggested exercise--not to have the class prove or disprove Goldbach's Conjecture, but to stimulate student discussions in the classroom regarding proof, as well as necessary, sufficient, satisfied, and unsatisfied conditions. Goldbach's Conjecture is one of the oldest unsolved problems in the field of number…

Descriptors: Mathematical Formulas, Numbers, Number Concepts, High School Students

Savoye, Philippe – Mathematics and Computer Education, 2011

The development, in an introductory differential equations course, of boundary value problems in parallel with initial value problems and the Fredholm Alternative. Examples are provided of pairs of homogeneous and nonhomogeneous boundary value problems for which existence and uniqueness issues are considered jointly. How this heightens students'…

Descriptors: Equations (Mathematics), Calculus, Mathematics Instruction, College Mathematics

Klikovac, Ida; Riedinger, Michael – Mathematics and Computer Education, 2011

The method of "Double False Position" is an arithmetic approach to solving linear equations that pre-dates current algebraic methods by more than 3,000 years. The method applies to problems that, in algebraic notation, would be expressed as y = L(x), where L(x) is a linear function of x. Double False Position works by evaluating the described…

Descriptors: Equations (Mathematics), Algebra, Problem Solving, Mathematics Instruction

Umar, Abdullahi; Alassar, Rajai – Mathematics and Computer Education, 2011

Diophantine equations constitute a rich mathematical field. This article may be useful as a basis for a student math club project. There are several situations in which one needs to find a solution of indeterminate polynomial equations that allow the variables to be integers only. These indeterminate equations are fewer than the involved unknown…

Descriptors: Equations (Mathematics), Mathematics Instruction, Clubs, Problem Solving

Gordon, Sheldon P. – Mathematics and Computer Education, 2011

In both baseball and mathematics education, the conventional wisdom is to avoid errors at all costs. That advice might be on target in baseball, but in mathematics, it is not always the best strategy. Sometimes an analysis of errors provides much deeper insights into mathematical ideas and, rather than something to eschew, certain types of errors…

Descriptors: Mathematics Instruction, Calculus, Error Patterns, Mathematical Concepts

Marrero, Osvaldo; Pasles, Paul C. – Mathematics and Computer Education, 2011

Like many mathematics teachers, the authors often find that students who struggle with a difficult concept may be assisted by the use of a well-chosen graph or other visual representation. While one should not rely solely on such tools, they can suggest possible theorems which then might be proved with the proper rigor. Even when a picture…

Descriptors: Probability, Calculus, Mathematics Instruction, College Mathematics

Ahmad, Faiz – Mathematics and Computer Education, 2011

It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…

Descriptors: Textbooks, Matrices, Mathematics Instruction, College Mathematics

Lubowsky, Jack – Mathematics and Computer Education, 2011

In Pre-Calculus courses, students are taught the composition and combination of functions to model physical applications. However, when combining two or more functions into a single more complicated one, students may lose sight of the physical picture which they are attempting to model. A block diagram, or flow chart, in which each block…

Descriptors: Graphing Calculators, Flow Charts, Calculus, Educational Technology

Vega, Tina; Travis, Betty – Mathematics and Computer Education, 2011

Progress in secondary education today is measured primarily through high stakes testing administered on a state-by-state basis. While states may require a common assessment instrument, how the objectives are to be taught, however, is generally up to the schools. This results in debates among educators as to the best curricula for all students.…

Descriptors: African American Students, Ethnicity, Socioeconomic Status, Mathematics Achievement

Calzada, Maria E.; Gardner, Holly – Mathematics and Computer Education, 2011

The results of a simulation conducted by a research team involving undergraduate and high school students indicate that when data is symmetric the student's "t" confidence interval for a mean is superior to the studied non-parametric bootstrap confidence intervals. When data is skewed and for sample sizes n greater than or equal to 10,…

Descriptors: Intervals, Effect Size, Simulation, Undergraduate Students