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- W2263539850 abstract "This study takes an activity-theoretic approach to abstraction in context recently proposed byHershkowitz, Schwarz and Dreyfus (2001, HSD hereafter). Key to HSD's theory of abstractionis the construction of new mathematical knowledge and consolidation of it. In this connection,this study aims to investigate three particular issues: (1) the construction of mathematicalknowledge through scaffolding, (2) the nature of the consolidation process and (3) the validityofHSD's abstraction theory.In order to investigate these issues, a qualitative research design methodology with explanatoryand exploratory inquiry purposes was taken. This study employed multiple case study strategywith the purpose of literal and theoretical replications. A number of cases were designed withstudents working as pairs and individuals such that some of the students worked with thescaffolded help and others without. All participants worked on four days over four sequentialtasks connected with the graphs of absolute value functions. Tasks were applied in paper-andpencilformat. The data for this study was composed of the participant's written works andaudio records of the sessions.In relation to the first issue, analysing the students' verbal data suggests certain causativerelationships between the scaffolder's interventions and the students' developing constructions.It is also observed that the scaffolder's interventions mediate the students' constructions.Analysis of the data further suggests that construction through scaffolding is a subtle andintricate phenomenon which involves a complex set of social, cultural, historical, contextual andsemiotic issues. It is argued, with examples, that scaffolded discourse involves many dynamicssuch as value judgements, individuals' personal histories, common cultural practices,individuals' emergent goals, voices of absent others and certain patterns of interaction. Regarding the second issue, the data suggest that newly formed constructions are fragile entitiesand in need of consolidation. In the course of consolidation, it is observed that earlierconstructions are reconstructed, used in a flexible manner and expressed confidently withgeneral mathematical statements. These observations lead to the argument that an abstraction isa consolidated construction that can be used to create new constructions.With regard to the final issue, on the basis of the students' verbal data, this study provides acritical evaluation of HSD's theory of abstraction by focusing on three key dimensions whichcharacterise it: its epistemological and sociocultural principles, epistemic actions and genesis ofan abstraction. Throughout this evaluation some clarifications and amendments are proposed tothis theory." @default.
- W2263539850 created "2016-06-24" @default.
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- W2263539850 date "2005-07-01" @default.
- W2263539850 modified "2023-09-27" @default.
- W2263539850 title "An investigation of the formation of mathematical abstractions through scaffolding" @default.
- W2263539850 hasPublicationYear "2005" @default.
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