This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of…

The present research examines the effect of the costliness of an information source on children's selective learning. In three experiments (total N?=?112), 4-to 7-year-olds were given the opportunity to acquire and endorse information from one of two sources. One source, a computer, was described as always accurate; the other source, a…

Parent involvement in a child's education has been demonstrated to increase child maintenance and generalization of skills taught in early intensive behavioral intervention (EIBI) settings to their home environments, improve parent-child relationships, and decrease parent stress. Parent coaching is a way to support parents' development of…

In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an…

Knowing the way children and adolescents assess the risk of disease transmission is important because this kind of knowledge may allow health caregivers to better communicate with them. We had 587 students in Spain and France aged 7-16 judge the risk of disease transmission in 28 scenarios of students visiting a sick friend. The scenarios were…

This study examined the use of an iPhone and List Recorder application to teach three adolescents with autism spectrum disorder to enhance their interpersonal daily living skills in a community setting. Participants were taught to use interpersonal skills to perform an ordering and purchasing task. A multiple probe design across participants was…

Important and favorable health effects of physical activity have been well documented. Unfortunately, school-aged individuals who are visually impaired tend to be less physically active than their peers without visual impairments. Although students with visual impairments learn skills to participate in physical activities during their PE classes,…

Fiction presents a unique challenge to the developing child, in that children must learn when to generalize information from stories to the real world. This study examines how children acquire causal knowledge from storybooks, and whether children are sensitive to how closely the fictional world resembles reality. Preschoolers (N = 108) listened…

Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…

Second language acquisition researchers often face particular challenges when attempting to generalize study findings to the wider learner population. For example, language learners constitute a heterogeneous group, and it is not always clear how a study's findings may generalize to other individuals who may differ in terms of language background…

Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…

This paper explores students' ways of thinking about the average rate of change of a multivariable function and how they generalize those ways of thinking from rate of change of single-variable functions. I found that while students thought about the average rate of change of a multivariable function as the change in the independent quantity with…

Dynamic assessment (DA) research, still in its infancy, takes its roots from Vygotsky's concept of zone of proximal development (ZPD) to account for learner's developmental process. Breaking away from a static, incomplete and, thus, unethical assessment of learner's abilities, DA came to the fore to better crystallize learner's levels of abilities…

Participants first became familiar with an image showing moderate symptoms of the skin cancer melanoma. In a generalization test, they indicated whether images showing more and less pronounced symptoms were "like the original." Some groups (cancer context) were told that the images depicted melanoma and that the disease is deadly unless…

During small group instruction, two groups of children--each group comprised of one child with a disability and two without disabilities--were taught to read words using a progressive time delay procedure (PTD). Apart from the children with disabilities, two typically developing peers in each group were taught to comment on tokens given for…