"Specific Mathematics Assessment that Reveal Thinking" (abbreviated as "smart tests") provide an on-line formative assessment of middle years students. They aim to put information from research on students' understanding directly into the hands of teachers, by providing quick automated diagnosis of learning for all students in…

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…

Necessary and sufficient criteria for reaction spontaneity in a given direction and for spontaneity of finite transformations in single-reaction, closed systems are developed. The criteria are general in that they hold for reactions conducted under either conditions of constant T and p or constant T and V. These results are illustrated using a…

Pam Shanks describes the stages in the child's development of language and reminds us that the Montessori principle of observation should guide the support of the child with articulation errors. For most children with developmental articulation delays, the directress can implement Montessori materials and use conversational strategies to emphasize…

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 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…

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…