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Learners' mathematical reasoning when generalizing from number patterns in the general education and training phase.Ndlovu, Williams Chapasuka 20 September 2011 (has links)
This study aims to explore GET learners’ mathematical (algebraic) reasoning when
generalizing from number patterns. Data was collected in a former model C school in greater
Johannesburg area by means of a questionnaire based task involving number patterns. The
mathematical reasoning of the grade 9 participants when generalizing from number patterns
was examined within a commognitive framework. According to this perspective, thinking is a
special activity of communication in which a participant of a discourse engages. The
participants’ responses to questions in the questionnaire based task were classified according
to particular aspects of the discourse they used, specifically routines (strategies) and visual
mediators. The participants’ generalization routines were further classified into one of the
three main categories; numeric, figural and pragmatic generalizations. The analysis focused
on how the learners’ derived rules for the nth term and their justifications for their responses.
The results of this study strongly support the notion that students’ algebraic reasoning when
generalizing in number patterns is intertwined with their choices of routines and mediators.
Most learners used recursive routines while a few used explicit routines (classified and
categorized as numeric routines) and number-mediators. Also, most participants found it
easier to informally verbalize their generalizations. However participants’ spoken
justifications of their written and spoken responses often did not match their use of routines
and visual mediators. As such, an awareness and appreciation (by teachers) of students’
diverse use of routines and mediators when generalizing from number patterns could have
direct pedagogical implications in the mathematics classrooms.
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Plenary Address: Language and Mathematics, A Model for Mathematics in the 21st CenturyPugalee, David K. 28 March 2012 (has links)
No description available.
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