Generalization is critical to mathematical thought and to learning mathematics. However, students at all levels struggle to generalize. In this paper, I present a theoretical analysis connecting Piaget's assimilation and accommodation constructs to Harel and Tall's (1991) framework for generalization in advanced mathematics. I offer a theoretical…

Purpose: This study examined how lexical representations and intervention intensity affect phonological acquisition and generalization in children with speech sound disorders. Method: Using a single-subject multiple baseline design, 24 children with speech sound disorders (3;6 to 6;10 [years;months]) were split into 3 word lexicality types…

There is limited research using small-scale simulation in applied behavior analysis. We used small-scale simulation to train firearm safety skills to 3- to 5-year-old children and assessed whether the skills generalized to the natural environment through in situ assessment. Three participants completed the training, and all participants learned…

School practitioners increasingly use functional behavior assessments to design behavior intervention plans when students engage in challenging behavior that is not improved by classroom management or standard interventions. Behavior intervention plans should aim to produce behavior change that maintains across time and generalizes to relevant…

Learning naturalistic categories, which tend to have fuzzy boundaries and vary on many dimensions, can often be harder than learning well defined categories. One method for facilitating the category learning of naturalistic stimuli may be to provide explicit feature descriptions that highlight the characteristic features of each category. Although…

Dutch and German employ voicing contrasts, but Dutch lacks the 'voiced' dorsal plosive /g/. We exploited this accidental phonological gap, measuring the presence of prevoicing and voice onset time durations during speech production to determine (1) whether preliterate bilingual Dutch-German and monolingual Dutch-speaking children aged 3;6-6;0…

This paper presents information from a comprehensive review of 28 experimental studies that investigated the effectiveness and efficiency of the simultaneous prompting procedure with individuals with autism. Twenty of the 25 variables examined across the 28 studies are reported on in this paper. The results reported across the studies indicated…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

In traditional, generative phonology, sound patterns are represented in terms of abstract features, typically based on the articulatory properties of the sounds. The present study makes use of an artificial language learning experiment to explore when and how learners extend a novel phonological pattern to novel segments. Adult, English-speaking…

Students with exceptionalities who do not make adequate progress with core instruction in mathematics require more intensive research-based interventions such as explicit instruction or video modeling to address instructional needs. This study examined the effects of combining point-of-view video modeling, explicit instruction, and augmented…

This study examined the use of an iPhone and the List Recorder Application to teach three adolescents with autism spectrum disorder to acquire, maintain, and generalize interpersonal daily living skills (DLS) in a community setting. A multiple probe design across participants was used to teach participants to use interpersonal DLS to order and…

Of all the tasks that special education teachers are charged with completing, managing classroom behaviors has been reported as one of the most challenging and one of the top reasons the teachers are leaving the field. The task of providing effective support in classroom management is also daunting for leadership personnel in school systems. This…

In this note, we propose a generalization of the famous Bernoulli differential equation by introducing a class of nonlinear first-order ordinary differential equations (ODEs). We provide a family of solutions for this introduced class of ODEs and also we present some examples in order to illustrate the applications of our result.

The study investigates upper secondary school students' use of counterfactual reasoning when engaging in a task concerning historical explanation. The study analyses student answers to a prompt asking them to evaluate the causal importance of a historical actor for a historical event, aiming to characterize the counterfactuals used, as well as…

Learning to categorize perceptually similar stimuli can result in people becoming more sensitive to differences along perceptual dimensions that are relevant to category membership and/or less sensitive to equivalent differences along irrelevant perceptual dimensions. These effects of acquired distinctiveness and acquired equivalence may be caused…