Functions and formulas in spreadsheets provide an instructional opportunity to help students build their skills in identifying errors in their own work and identifying a path to go about correcting the errors. This paper provides examples of functions and equations used to create two approaches to calculating the solution to one problem, such as a…

We discuss the limits of the equation of the period of a simple pendulum, T[subscript s] = 2[pi][square root]l/g, frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one,…

Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.

Summary Employing a Wald confidence interval to test hypotheses about population proportions could lead to an increase in Type I or Type II errors unless the hypothesized value, p0, is used in computing its standard error rather than the sample proportion. Whereas the Wald confidence interval to estimate a population proportion uses the sample…

Teachers often promote care in doing calculations, but for most students a single mistake rarely has major consequences. This article presents several real-life events in which relatively minor mathematical errors led to situations that ranged from public embarrassment to the loss of millions of dollars' worth of equipment. The stories here…

Sprego is programming with spreadsheet functions. The present paper provides introductory Sprego examples which have so far only been available in Hungarian. Spreadsheet environments offer both a programming tool which best serves beginner and end-user programmers' interest, and an approach which lightens the burden of coding and language details.…

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

This paper presents the Agresti & Coull "Adjusted Wald" method for computing confidence intervals and margins of error for common proportion estimates. The presented method is easily implementable by business students and practitioners and provides more accurate estimates of proportions particularly in extreme samples and small…

At our university, students in introductory physics classes perform a laboratory exercise to measure the range of a projectile fired at an assigned angle. A set of photogates is used to determine the initial velocity of the projectile (the launch velocity). We noticed a systematic deviation between the experimentally measured range and the range…

By following learned rules rather than reasoning, students often fall into common error patterns, something every experienced teacher has observed in the classroom. In their effort to circumvent the developing common error patterns of their students, the authors decided to supplement their math text with two weeklong investigations. The first was…

The purpose of this article was to extend the use of standard errors for equated score differences (SEEDs) to traditional equating functions. The SEEDs are described in terms of their original proposal for kernel equating functions and extended so that SEEDs for traditional linear and traditional equipercentile equating functions can be computed.…

In a provocative and influential paper, Jesse Rothstein (2010) finds that standard value-added models (VAMs) suggest implausible future teacher effects on past student achievement, a finding that obviously cannot be viewed as causal. This is the basis of a falsification test (the Rothstein falsification test) that appears to indicate bias in VAM…

Mathematics teachers are often asked, "What is the most difficult topic for you to teach?" Their answer is teaching students to count. The concepts can be challenging and slippery to apply in problems. Many times, no rigid procedures or formulas can be used to solve the problems directly, and students simply do not know where or how to approach…

A method is derived for the numerical evaluation of the error term arising in some Gauss-type formulae modified so as to approximate Cauchy Principal Value integrals. The method uses Chebyshev polynomials of the first kind. (Contains 1 table.)

This note suggests delta method implementations for deriving confidence intervals for a latent mean effect size measure for the case of 2 independent populations. A hypothetical kindergarten reading example using these implementations is provided, as is supporting LISREL syntax. (Contains 1 table.)