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A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equation


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Title A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equation
Creator Roberts, Anthea le Roux, Kate
Subject Mathematics Education; Education; Mathematics school mathematics; discourse; algebra; linear equations; commognition
Description Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations.This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their solutions to linear equations in interviews. The article stems from a study that describes whether learners use mathematically endorsable narratives to explain and justify their solutions. Sfard’s theory of commognition is used to develop a framework for analysis of their discourse.The findings show that all learners use ritualised rather than explorative discourse, characterised by applying strict rules to operations with disobjectified entities. The only mathematical objects they produce endorsed narratives about are positive integers. Thus they do not meet the relevant curriculum requirements. Nevertheless, the analytic tools – adapted from Sfard specifically for the study of linear equations – give a particularly nuanced account of differences in the learners’ ritualised discourse. For example, some learners used endorsed narratives about negative integers, algebraic terms and the structure of an equation when prompted by the interviewer.There is not sufficient evidence to suggest that any learners are in transition to explorative discourse. However, the article shows that learner discourse is a rich resource for teachers to understand the extent to which learners are thinking exploratively, and offers suggestions for how their thinking can be shifted. This is an opportunity for teacher professional development and further research.
Publisher AOSIS Publishing
Contributor Data for the study on which this article is based was made possible by the Schools Development Unit at the University of Cape Town. The original research was conducted under the auspices of an affiliated project. We also wish to acknowledge the Centre fo
Date 2019-03-28
Type info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion — Interview; discourse analysis
Format text/html application/epub+zip application/xml application/pdf
Identifier 10.4102/pythagoras.v40i1.438
Source Pythagoras; Vol 40, No 1 (2019); 15 pages 2223-7895 1012-2346
Language eng
The following web links (URLs) may trigger a file download or direct you to an alternative webpage to gain access to a publication file format of the published article:
Coverage South Africa Middle school; Senior Phase; 13 - 15 year-old Working class schools
Rights Copyright (c) 2019 Anthea Roberts