Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA

Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA

This paper presents a networking of two theories, the APOS Theory and the ontosemiotic approach (OSA), to compare and contrast how they conceptualize the notion of a mathematical object. As context of reflection, we designed an APOS genetic decomposition for the derivative and analyzed it from the p...

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Veröffentlicht in:Educational studies in mathematics 2016-01, Vol.91 (1), p.107-122
Hauptverfasser: Font Moll, Vicenç, Trigueros, María, Badillo, Edelmira, Rubio, Norma
Format: Artikel
Sprache:eng
Schlagworte:
Cognition
Cognitive models
Construction engineering
Constructivism (Learning)
Education
Mathematical Concepts
Mathematical functions
Mathematical objects
Mathematics
Mathematics Education
Mental objects
Methods
Philosophical object
Schematic Studies
Semiotics
Study and teaching
Theories
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Beschreibung
Zusammenfassung:This paper presents a networking of two theories, the APOS Theory and the ontosemiotic approach (OSA), to compare and contrast how they conceptualize the notion of a mathematical object. As context of reflection, we designed an APOS genetic decomposition for the derivative and analyzed it from the point of view of OSA. Results of this study show some commonalities and some links between these theories and signal the complementary nature of their constructs.
ISSN:0013-1954
1573-0816
DOI:10.1007/s10649-015-9639-6