A simple nonstiff linear initial-value problem is used to demonstrate the amplification of round-off error in the course of using a second-order Runge-Kutta method. This amplification is understood in terms of an appropriate expression for the global error. An implicit method is then used to show how the roundoff error may actually be suppressed.…

Every language has its own rhythm. Unlike many other languages in the world, English depends on the correct pronunciation of stressed and unstressed or weakened syllables recurring in the same phrase or sentence. Mastering the rhythm of English makes speaking more effective. Experiments have shown that we tend to hear speech as more rhythmical…

Nonword repetition tasks (NWRTs) are employed widely in various studies on language development and are often relied upon as diagnostic tools. However, the mechanisms that underlie children's performance in NWRTs are very little understood. In this paper we present NWRT data from typically developing 5- to 6-year-olds (5:4-6:8) and examine the…

One technique for identifying and addressing common student errors is the method of classroom voting, in which the instructor presents a multiple-choice question to the class, and after a few minutes for consideration and small group discussion, each student votes on the correct answer, often using a hand-held electronic clicker. If a large number…

Student errors are springboards for analyzing, reasoning, and justifying. The mathematics education community recognizes the value of student errors, noting that "mistakes are seen not as dead ends but rather as potential avenues for learning." To induce specific errors and help students learn, choose tasks that might produce mistakes.…

This article compares the claims of rule- and constraint-based accounts of three seemingly distinct error patterns, namely, Deaffrication, Consonant Harmony and Assibilation, in the sound system of a child with a phonological delay. It is argued that these error patterns are not separate problems, but rather are symptoms of a larger conspiracy to…

Two Monte Carlo simulation studies investigated the effectiveness of the mean adjusted X[superscript 2]/df statistic proposed by Drasgow and colleagues and, because of problems with the method, a new approach for assessing the goodness of fit of an item response theory model was developed. It has been previously recommended that mean adjusted…

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…

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…

In mathematics, as in baseball, the conventional wisdom is to avoid errors at all costs. That advice might be on target in baseball, but in mathematics, avoiding errors is not always a good idea. Sometimes an analysis of errors provides much deeper insights into mathematical ideas. Certain types of errors, rather than something to be eschewed, can…

In a recent study we (Greaney & Arrow, 2009) undertook an analysis of the types of spelling errors that students had made during a National Education Monitoring Project writing task (Crooks, Flockton & White, 2007). We discussed several issues related to spelling, including the value of analysing students' error-response patterns as a way…

Asked to complete a decimal-ordering task, several preservice teachers were unable to arrange the values from smallest to largest. Even more surprising to the authors were the number who could solve this task correctly but could not justify their solution by representing each decimal in an area model using a decimal grid. Their preservice teachers…

Ask any teacher what he or she needs more of, and it is a good bet that time will top the list. Anything that promises to recoup a little bit of their workday time is sure to be a best seller. One overlooked time-saver is in how they use feedback. Teachers know that feedback is important for teaching and learning. Unfortunately, most secondary…

Early in their study of one-dimensional kinematics, my students build an algebraic model that describes the effects of a rolling ball's (perpendicular) collision with a wall. The goal is for the model to predict the ball's velocity when it returns to a fixed point approximately 50-100 cm from the wall as a function of its velocity as it passes…

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.…