The present study investigates the effect of high variability phonetic training (HVPT) on the discrimination of second language (L2) vowel contrasts by adult speakers who live in a country where the L2 is dominant. The same subjects who participated in a previous discrimination task were trained in the discrimination of four L2 vowel contrasts…

Functional communication training (FCT) is a strategy to address problem behavior for students with various disabilities that is supported by a broad evidence base. Despite this support, multiple factors continue to dissuade educators from utilizing FCT in their classrooms. This article outlines the process of developing and implementing FCT plans…

Geometry education is an important aspect of STEM education and career development, but it is often overlooked in K-12 education in the United States. Although there is some research on teaching geometry to students with learning difficulties at the elementary level, there is a lack of research on teaching advanced geometry skills at high school…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Although abstraction is widely understood to be one of the primary components of computational thinking, the roots of abstraction may be traced back to different fields. Hence, the meaning of abstraction in the context of computational thinking is often confounded, as researchers interpret abstraction through diverse lenses. To disentangle these…

A great deal of research on second language (L2) input has provided useful linguistic evidence for the development of generalizations about and hypotheses on the usage-based nature of L2 knowledge. However, despite the fact that classrooms are one of the most ubiquitous sites of L2 learning, we still know very little about the linguistic quality…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…

Generalisation is a skill that enables learners to acquire knowledge in general, and mathematical knowledge in particular. It is a core aspect of algebraic thinking and, in particular, of functional thinking, as a type of algebraic thinking. Introducing primary school children to functional thinking fosters their ability to generalise, explain and…

Investigating symmetric dot patterns provides opportunities for foundational mathematical learning that is not restricted to multiplication alone. Students have opportunities to learn about the properties of symmetry, about the generalization of patterns, about writing and interpreting equations--all areas of study in grades 3-5. And symmetric dot…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

This paper presents the design and initial learning research with the MMM modeling platform, seeking to advance middle school students' learning through constructing computational models of complex physical and chemical systems. A complexity-based structure of an MMM interface is introduced. It suggests that a complex system can be described and…

Conceptual model-based problem solving (COMPS) was tested for its efficacy in teaching a student diagnosed with autism spectrum disorder to solve word problems involving multiplication and division. A single-case, multiple-baseline across behaviors design was conducted. The ability to solve each of three types of multiplication problems examined…

A multiple probe across participants design was used to examine the effects of intervention on reality-based fictional narratives. Four boys with autism spectrum disorder (ASD) and language disorder, aged 9-10, participated in a 1:1 intervention targeting the narrative macrostructure elements of character, setting, problem, feelings, and fix.…

Given the importance of social integration and participation in inclusive settings for young children with autism spectrum disorder (ASD), the purpose of this systematic review was to examine instructional outcomes and participant, teacher, group, and instructional characteristics that may be pertinent to successful group instruction for young…