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…

This paper explored the following: (1) teachers' ways of attending to students' written responses in pattern generalization tasks and (2) differences in the ways of attending to students' responses associated with different factors. A questionnaire was developed to classify teachers' ways of attending to students' written responses. The…

The concept of pattern recognition lies at the heart of numerous deliberations concerned with new mathematics curricula, because it is strongly linked to improved generalised thinking. However none of these discussions has made the deceptive nature of patterns an object of exploration and understanding. Yet there is evidence showing that pattern…

The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

Electronic language corpora, and their attendant computer software, are proving increasingly influential in language teaching as sources of language descriptions and pedagogical materials. However, few teachers are clear about their nature or their relevance to language teaching. This paper defines corpora and their types, discusses their…

Chess experts remember meaningful knowledge in the form of networks or patterns. Applied to mathematics instruction, effective classroom approaches can use investigation to identify patterns or rules. Described are a class activity and a small-group activity to investigate addition of signed numbers and linear relationships. (MDH)