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…

Most speech-language pathologists (SLPs) in Malaysia practice with an undergraduate degree, which provides them with limited knowledge about and training in augmentative and alternative communication (AAC). This limited knowledge and training may affect their confidence and competence when introducing and using AAC with individuals for whom it is…

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…

The aim of this study is to analyse the importance of the number of raters and compare the results obtained by techniques based on Classical Test Theory (CTT) and Generalizability (G) Theory. The Kappa and Krippendorff alpha techniques based on CTT were used to determine the inter-rater reliability. In this descriptive research data consists of…

Two distinctive types of complex predicates found in English are separable verb-particle combinations ("particles") and adjectival resultatives ("ARs"). Snyder ties both to the positive setting of the Compounding Parameter ("TCP"). This predicts that during the acquisition of a [+TCP] language, any child who has…

The prerequisite for teaching many skills and behaviors to children with intellectual disabilities is that the child has acquired the basic concepts. Teaching concepts plays a very active role in the independence of the child with intellectual disabilities and in the acquisition of higher level skills that they will learn in the future. The…

Data-driven learning uncontroversially plays a role in human language acquisition--how large a role is a matter of much debate. The success of artificial neural networks in NLP in recent years calls for a re-evaluation of our understanding of the possibilities for learning grammar from data alone. This dissertation argues the case for using…

Teachers whose mathematical meanings support understanding across different contexts are likely to convey them in productive ways for coherent student learning. This exploratory study sought to elicit 67 secondary mathematics pre-service teachers' (PSTs) meanings for quadratics with growing pattern creation and multiple translation tasks. A…

Background: This paper contributes to current discussions about supporting prospective teachers (PSTs) in developing skills of noticing students' mathematical thinking. We draw attention to PSTs' initial noticing skills (prior to instruction focused on supporting noticing) as PSTs engage in analyzing written artifacts of student work and…

Morphological variability in bilingual language production is widely attested. Producing inflected words has been found to be less reliable and consistent in bilinguals than in first-language (functionally monolingual) L1 speakers, even for bilingual speakers at advanced proficiency levels. The sources for these differences are not well…

Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers' perceptions of inductive…

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…