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Gordon, Sheldon P.; Gordon, Florence S. – PRIMUS, 2020
This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to hypothesis testing to increase student understanding of the concepts and methods in elementary statistics courses. The article considers hypothesis tests for the population mean with large or…
Descriptors: Hypothesis Testing, Computer Software, Educational Technology, Technology Uses in Education
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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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Yang, Yajun; Gordon, Sheldon P. – PRIMUS, 2016
This article takes a close look at Lagrange and Newton interpolation by graphically examining the component functions of each of these formulas. Although interpolation methods are often considered simply to be computational procedures, we demonstrate how the components of the polynomial terms in these formulas provide insight into where these…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Mathematical Formulas
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Gordon, Sheldon P. – PRIMUS, 2015
This article introduces the notion of the quartile-quartile line as an alternative to the regression line and the median-median line to produce a linear model based on a set of data. It is based on using the first and third quartiles of a set of (x, y) data. Dynamic spreadsheets are used as exploratory tools to compare the different approaches and…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Mathematical Concepts
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Gordon, Sheldon P. – PRIMUS, 2013
The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…
Descriptors: Data Analysis, Investigations, Numeracy, Number Concepts
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Gordon, Sheldon P. – PRIMUS, 2012
Data analysis methods, both numerical and visual, are used to discover a variety of surprising patterns in the errors associated with successive approximations to the derivatives of sinusoidal and exponential functions based on the Newton difference-quotient. L'Hopital's rule and Taylor polynomial approximations are then used to explain why these…
Descriptors: Mathematics Instruction, Mathematical Concepts, Error Patterns, Data Analysis
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Gordon, Sheldon P.; Gordon, Florence S. – PRIMUS, 2009
The authors describe a collection of dynamic interactive simulations for teaching and learning most of the important ideas and techniques of introductory statistics and probability. The modules cover such topics as randomness, simulations of probability experiments such as coin flipping, dice rolling and general binomial experiments, a simulation…
Descriptors: Intervals, Hypothesis Testing, Statistics, Probability
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Gordon, Sheldon P. – PRIMUS, 2009
The exponential growth model and the logistic model typically introduced in the mathematics curriculum presume that a population grows exclusively. In reality, species can also die out and more sophisticated models that take the possibility of extinction into account are needed. In this article, two extensions of the logistic model are considered,…
Descriptors: Mathematics Curriculum, Test Items, Population Growth, Models
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Gordon, Sheldon P. – PRIMUS, 2008
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Descriptors: Calculus, Mathematics Instruction, Calculators, Spreadsheets
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Gordon, Sheldon P. – PRIMUS, 2008
The article describes the performance of several individual students in a college algebra/precalculus course that focuses on the development of conceptual understanding and the use of mathematical modeling and discusses the likely differences in outcome if the students took a traditional algebra-skills focused course.
Descriptors: Calculus, Algebra, College Students, College Mathematics
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Gordon, Sheldon P. – PRIMUS, 2008
Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…
Descriptors: Calculus, Algebra, College Mathematics, Mathematics Instruction
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Gordon, Sheldon P. – PRIMUS, 2007
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
Descriptors: Calculus, Mathematics Instruction, Mathematical Concepts, Numbers
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Gordon, Sheldon P. – PRIMUS, 2006
The problem of fitting a surge function to a set of data such as that for a drug response curve is considered. A variety of different techniques are applied, including using some fundamental ideas from calculus, the use of a CAS package, and the use of Excel's regression features for fitting a multivariate linear function to a set of transformed…
Descriptors: Maximum Likelihood Statistics, Calculus, Transformations (Mathematics), Mathematical Applications
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Gordon, Sheldon P. – PRIMUS, 2005
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Descriptors: Mathematics, Theories, Mathematics Education, Calculus
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Gordon, Sheldon P. – PRIMUS, 2005
The standard derivative tests for extrema and inflection points from Calculus I can be revisited subsequently from the perspective of Taylor polynomial approximations to provide additional insights into those tests, as well as to extend them to additional criteria. (Contains 3 figures.)
Descriptors: Calculus, Tests, Mathematics Instruction, Theories
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