This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game"…

This study investigates sixth-grade Turkish students' pattern-generalization approaches among arithmetical generalization, algebraic generalization, and naïve induction. A qualitative case study design was employed. The data was collected from four sixth-grade students through the Pattern Questionnaire (PQ) and individual interviews based on the…

Improving the ability to solve mathematical word problems is one of the most critical issues facing students with developmental disabilities, because it is directly related to their independent living skills. The purpose of this study was to propose a teaching model that implements augmented reality (AR) and video modeling (VM), and to validate…

Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

Early childhood care and education providers provide instruction to diverse learners, including children with developmental delays, but often lack training in the use of evidence-based instructional strategies to support children's meaningful learning engagement. This preliminary study examined effects of the Early Achievements for Child Care…

We evaluated a method for teaching children with autism spectrum disorder to respond to tactile stimulation of multiple body parts. Various objects (e.g., hairbrush) produced the sensations (e.g., prickly). In a multiple baseline design across participants, participants learned 9 sensation body part tacts and the evaluation concluded with tests of…

Children with autism spectrum disorder (ASD) have difficulty generalizing from directly trained responses to untrained responses (i.e., emergent responding). In this study, we used a chain prompt combined with matrix training to teach 2 participants with ASD to tact 192 three-digit numerals. We used a multiple-baseline design across matrices to…

For most children with autism spectrum disorder (ASD), manding for information is an important skill that must be systematically taught. Although previous studies have evaluated interventions for teaching other mands for information, to date no studies have demonstrated effective procedures for teaching the mand "why?" The purpose of the…

Generalizing is a critical aspect of mathematics learning, with researchers and policy documents highlighting generalizing as a core mathematical practice. It can also be challenging to foster in class settings, and teachers need access to better resources to teach generalizing, including an understanding of effective forms of instruction. This…

In this study, hypothetical samples of students' work on a task involving pattern generalizations were used to examine the characteristics of the ways in which 154 elementary prospective teachers (PSTs) paid attention to students' work in mathematics. The analysis included what the PSTs attended to, their interpretations, and their suggestions for…

Individuals with autism spectrum disorder (ASD) experience difficulties with daily life skills (DLS). Difficulties with DLS create obstacles to independence. To move into adulthood more smoothly, it is critical to teach some DLS during certain periods, such as adolescence. In the present study, the skills of preparing an instant soup, setting the…

This study aims to develop a conceptual framework regarding practitioner knowledge and describe how one mathematics teacher generates her practitioner knowledge based on the framework. The characteristic of this framework is a combination of static and dynamic aspects of knowledge based on the teacher's perception and interpretation. The research…

Whether a child with autism spectrum disorder will exhibit observational learning may depend on their attention to and the stimulus modalities of the observed contingency. We used multiple-probe and repeated-acquisition designs to test observational learning across a diverse set of contingencies, which included hidden edible, hidden toy, hidden…

Researchers established virtual manipulatives as an evidence-based practice for students with intellectual and developmental disabilities (IDD). However, much of the existing research for this population targets middle school students with IDD. This study examined a virtual number line paired with teacher modeling and the system of least prompts…

Twelve college students learned to tact the names of notes and rhythms and play them when presented with compound stimuli (visuals of notes and rhythms on a musical staff). In Experiment 1, we assessed generalization by presenting novel notes, rhythms, and compound stimuli not previously paired together. In the second experiment, we added a…