A Commognitive Perspective on Grade 8 and Grade 9 Learner Thinking about Linear Equations

Autor/inn/en	Roberts, Anthea; le Roux, Kate
Titel	A Commognitive Perspective on Grade 8 and Grade 9 Learner Thinking about Linear Equations
Quelle	In: Pythagoras, 40 (2019) 1, Artikel 438 (15 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Zusatzinformation	ORCID (Roberts, Anthea) ORCID (le Roux, Kate)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1012-2346
Schlagwörter	Foreign Countries; Mathematics Instruction; Equations (Mathematics); Grade 8; Grade 9; Thinking Skills; Algebra; Problem Solving; Numbers; Number Concepts; Mathematical Logic; South Africa + Suchen Sie Ihr Suchwort? Ausland; Mathematics lessons; Mathematikunterricht; Equations; Mathematics; Gleichungslehre; School year 08; 8. Schuljahr; Schuljahr 08; School year 09; 9. Schuljahr; Schuljahr 09; Denkfähigkeit; Problemlösen; Zahlenraum; Number concept; Zahlbegriff; Mathematical logics; Mathematische Logik; Südafrika; Süd-Afrika; Republik Südafrika; Südafrikanische Republik
Abstract	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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01