Layers of generality and types of generalization in pattern activities

Pattern generalization is considered one of the prominent routes for in-troducing students to algebra. However, not all generalizations are al-gebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this arti-cle I suggest a characterization of algebraic generalizations. This char-acterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples

Adult participation in children’s word searches: on the use of prompting, hinting, and supplying a model

Although word searching in children is very common, very little is known about how adults support children in the turns following the child’s search behaviours, an important topic because of the social, educational and clinical implications. This study characterises, in detail, teachers’ use of prompting, hinting and supplying a model. From a classroom dataset of 53 instances, several distinctive patterns emerged. A prompted completion sequence is initiated by a ‘word retrieval elicitor’ (‘fishing’) and is interpreted as a request to complete the phrase. Non-verbal prompting is accomplished through a combination of gaze and gesture and, also, as a series of prompts. Hinting supplies a verbal clue, typically via a wh-question, or by specifying the nature of the repairable. In contrast, the strategies that supply a linguistic model include both embedded and exposed corrections and offers of candidates. A sequential relationship was found between prompting, hinting and supplying a model which has implications for how clinicians and teachers can foster self-repair

On the Development of Early Algebraic Thinking

This article deals with the question of the development of algebraic thinking in young students. In contrast to mental approaches to cognition, we argue that thinking is made up of material and ideational components such as (inner and outer) speech, forms of sensuous imagination, gestures, tactility, and actual actions with signs and cultural artifacts. Drawing on data from a longitudinal classroom-based research program where 8-year old students were followed as they moved from Grade 2 to Grade 3 to Grade 4, our developmental research question is investigated in terms of the manner in which new relationships between embodiment, perception, and symbol-use emerge and evolve as students engage in patterning activities

Cooperative artificial propagation programs for salmon and steelhead, 1995-1996

Fifteen cooperative fish rearing and planting programs for salmon and steelhead were active from July 1, 1995 through June 30, 1996. For all programs, 134,213 steelhead trout,(Oncorhynchus mykiss), 7,742,577 chinook salmon,(~ tshawytscha),and 25,075 coho salmon(~ kisutch) were planted. (PDF contains 26 pages.

Word searches: on the use of verbal and non-verbal resources during classroom talk

Word finding difficulties in children are typically characterised by search behaviours such as silence, circumlocution, repetition and empty words. Yet, how children’s word searches are constructed (including gesture, gaze and prosody) and the actions accomplished during interaction have not yet been researched. In this study, eightyear- old Ciara is interacting with her teacher in the classroom. 37 segments containing word searches were analysed according to the procedures used by conversation analysts. Ciara’s interactional resources include co-ordinated deployment of syntax, pitch height and downward gaze during solitary searching that assist the enterprise of self-repair. Gaze shift towards the teacher signals a transition relevance place, thus constituting a direct invitation for her to participate in the search. Ciara’s interactional resources include semantic category labelling, phonological self-cuing and pronominal substitution that supply valuable linguistic information to the teacher and trigger production of the searched-for item. Recommendations for language teaching and therapy are presented

Staunin Ma Lane: Chinese Verse in Scots and English, translated by Brian Holton

No abstract available