Learners' mathematical reasoning when generalizing from number patterns in the general education and training phase.

Ndlovu, Williams Chapasuka
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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.
Algebra, Generalization, Commognition, Thinking, Communication and reasoning