If students are presented the standard proof of irrationality of [square root]2, can they generalize it to a proof of the irrationality of "[square root]p", "p" a prime if, instead of considering divisibility by "p", they cling to the notions of even and odd used in the standard proof?

We examined the effects of constructed-response matching-to-sample (CRMTS) training on the generalization of reading and spelling skills in three Japanese children with autism using a series of overlapping-syllable word sets. We taught them to construct printed words to match printed words, spoken words, and pictures through the CRMTS procedure.…

What is the role of linguistic labels in inductive generalization? According to one approach labels denote categories and differ from object features, whereas according to another approach labels start out as features and may become category markers in the course of development. This issue was addressed in four experiments with 4- and 5-year-olds…

Almost 20 years ago, Cuoco, Goldenberg, and Mark wrote a seminal paper for the "Journal of Mathematical Behavior" entitled "Habits of Mind: An Organizing Principle for Mathematics Curricula" (Cuoco et al., 1996). The article remains as relevant today as when it was originally published. The premise of their paper is that…

Languages differ in how they package the components of an event into words to form sentences. For example, while some languages typically encode the manner of motion in the verb (e.g., running), others more often use verbs that encode the path (e.g., ascending). Prior research has demonstrated that children and adults have lexicalization biases;…

Attaining reliable estimates of observational measures can be challenging in school and classroom settings, as behavior can be influenced by multiple contextual factors. Generalizability (G) studies can enable researchers to estimate the reliability of observational data, and decision (D) studies can inform how many observation sessions are…

Several types of converging evidence have suggested recently that skilled adults solve very simple addition problems (e.g., 2 + 1, 4 + 2) using a fast, unconscious counting algorithm. These results stand in opposition to the long-held assumption in the cognitive arithmetic literature that such simple addition problems normally are solved by fact…

Each day, people encounter stimuli they find unpleasant. Some children with autism may require systematic instruction to acquire the communication skills necessary to request the termination of such aversive stimuli. We taught 2 school-aged boys with autism a mand (e.g., signing "stop") that could be used to escape a variety of aversive…

This study examined the utility of brief academic assessments to identify effective generalization procedures for individual students. Specifically, the study built on the proposal that brief assessments of antecedent and consequence manipulations can identify the most effective generalization strategy for individual students. The design was an…

Observational learning is a critical skill needed for the acquisition of social skills and is likely an important skill for learning within traditional educational settings. Although several varying definitions of observational learning have been posited, for the purpose of the present study, observational learning (OL) was defined as differential…

Accurate recovery of predicate-argument dependencies is vital for interpretation tasks like information extraction and question answering, and unbounded dependencies may account for a significant portion of the dependencies in any given text. This thesis describes a Generalized Categorial Grammar (GCG) which, like other categorial grammars,…

This case study takes the perception of ethnography as not being generalisable and questions whether such an understanding is correct and also whether a different perspective on generalisability might be helpful in developing formative approaches to educational technology research. The aim is to encourage discussion about ethnography as a tool for…

Teaching in Vietnam recently, I had opportunities to work with some amazing students and teachers. Being in such a position lent itself well to cultural exchanges inside and outside the classroom. However, it was clear to me, to my colleagues, and I believe to the majority of students that there was a need to dig deeper--to move beyond the…

Early foreign language (FL) programmes have grown rapidly worldwide in the past two decades, resting on the assumption that "earlier is better" for learning a FL. However, the majority of empirical studies that investigated the "earlier is better" hypothesis were conducted in naturalistic immersion contexts. Given the…

This exploratory study examined the influence of different virtual manipulative (VM) types on the nature of student pairs' techno-mathematical discourse (TMD). Three fifth-grade student pairs participated in 9 sessions of mathematics instruction using VMs. The study compared three VM types: linked, pictorial, and tutorial. Students' levels of…