In this paper, the author gives a further simple generalization of a power series evaluation of an integral using Taylor series to derive the result. The author encourages readers to consider numerical methods to evaluate the integrals and sums. Such methods are suitable for use in courses in advanced calculus and numerical analysis.

Neurophysiological evidence is described showing that some neurons in the macaque inferior temporal visual cortex have responses that are invariant with respect to the position, size and view of faces and objects, and that these neurons show rapid processing and rapid learning. Which face or object is present is encoded using a distributed…

Stuttering characteristics, assessment, and treatment principles present challenges to assessment and treatment that can be addressed with virtual reality (VR) technology. This article describes how VR can be used to assist clinicians in meeting some of these challenges with adults who stutter. A review of current VR research at the Stuttering…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

This paper reports two experiments that investigated the role of verbal behavior in the emergence and generalization of contextually controlled equivalence classes. During both experiments, participants were trained with two different combinations of the same easily nameable, yet formally unrelated, pictorial stimuli. Match-to-sample baselines for…

Recent research in semantics and pragmatics has revived the debate about whether there are two cognitively distinct categories of conversational implicatures: generalised and particularised. Generalised conversational implicatures are so-called because they seem to arise more or less independently of contextual support. Particularised implicatures…

Many students with disabilities continue to struggle with understanding what mathematics means. They memorize basic facts or step-by-step mathematical procedures without understanding the underlying concepts related to the problems. Thus, instruction designed to help students understand the meaning of the mathematics that they are learning in…

The authors' purpose in this study was to evaluate the role of attention, as a central dimension of temperament, in children's real-time acquisition of novel vocabulary. Environmental distractions were administered to 47 22-month-old children as they acquired novel vocabulary in a fast-mapping task. Two distraction conditions impeded novel word…

This study examined the extent to which ethnic-based differences exist in teacher ratings of African American students and White students on the language and literacy domain of a curriculum-embedded performance assessment for students in grade 1. It extended previous research on performance assessments to focus on issues related to equity in…

The paper describes evolution of an approach to teaching mathematically disabled and slow learning students through a Piagetian framework. It is explained that a step-by-step procedure is used to internalize material actions into mental actions via perception and verbalization. Formulae are introduced early, and emphasis is placed on promoting…

Research indicates that people do not spontaneously transfer prior clues to solve problems, even though the necessary information is available in memory. To investigate the effects of the symmetry between clue statements and problem statements on problem solving performance, subjects were asked to provide plausible explanations for five…

The first section of this book presents an overview and history of the problem of skill generalization among students with severe handicaps. Researchers review empirically based strategies proposed to remedy the problem, discuss the characteristics and foundations of decision rules which can be used to determine which strategy will work best in a…

This doctoral dissertation examines the extent to which general case simulation instruction on a janitorial task sequence and a housekeeping task sequence conducted with four secondary and postsecondary age persons with moderate mental retardation resulted in generalized performance. A multiple baseline design across subjects and behaviors was…

The study investigated the potential additive effects of instruction in self-control strategies and behavioral parent training with 24 hyperactive children (7-11 years old) and their parents. It was hypothesized that the combination of treatments would provide maximum benefits by altering those contingencies in the home environment maintaining…

Rasch models for fundamental measurement in the psychological sciences are derived from the principle of specific objectivity, the requirement that the parameter value representing each component in a test situation be independent of the other components. The dichotomous Rasch model for two-faceted analysis, applicable to conventional…