Irrational Gap: Sensemaking Trajectories of Irrational Exponents

Autor/inn/en	Marmur, Ofer; Zazkis, Rina
Titel	Irrational Gap: Sensemaking Trajectories of Irrational Exponents
Quelle	In: Educational Studies in Mathematics, 107 (2021) 1, S.25-48 (24 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Marmur, Ofer) ORCID (Zazkis, Rina)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-021-10027-2
Schlagwörter	College Students; Comprehension; Graphs; Task Analysis; Learning Processes; Abstract Reasoning; Mathematics Skills; Number Concepts + Suchen Sie Ihr Suchwort? Collegestudent; Verstehen; Verständnis; Grafische Darstellung; Aufgabenanalyse; Learning process; Lernprozess; Abstraktes Denken; Denken; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Number concept; Zahlbegriff
Abstract	We investigate how students make sense of irrational exponents. The data comprise 32 interviews with university students, which revolved around a task designed to examine students' sensemaking processes involved in predicting and subsequently interpreting the shape of the graph of f(x)=x[superscript square root of 2]. The task design and data analysis relied on the concept of sensemaking trajectories, blending the notions of sensemaking and (hypothetical/actual) learning trajectories. The findings present four typical sensemaking trajectories the participants went through while coping with the notion of an irrational exponent, alongside associated reasoning themes that seemed to have guided these trajectories. In addition to irrational exponents, the analysis revealed the participants' reasoning and sensemaking of related mathematical ideas, such as rational exponents, approximations of irrational numbers by rational numbers, even/odd functions and numbers, and the meaning of exponentiation in general. The findings provide a step towards a better understanding of students' conceptual development of irrational exponents, which could in turn be used for the refinement of tasks aimed at promoting students' comprehension of the topic. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01