Combined Use of the Extended Theory of Connections and the Onto-Semiotic Approach to Analyze Mathematical Connections by Relating the Graphs of f and f'

Autor/inn/en	Rodríguez-Nieto, Camilo Andrés; Rodríguez-Vásquez, Flor Monserrat; Moll, Vicenç Font
Titel	Combined Use of the Extended Theory of Connections and the Onto-Semiotic Approach to Analyze Mathematical Connections by Relating the Graphs of f and f'
Quelle	In: Educational Studies in Mathematics, 114 (2023) 1, S.63-88 (26 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Rodríguez-Nieto, Camilo Andrés) ORCID (Rodríguez-Vásquez, Flor Monserrat) ORCID (Moll, Vicenç Font)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-023-10246-9
Schlagwörter	Mathematics Education; Problem Solving; Graphs; College Freshmen; Foreign Countries; Symbols (Mathematics); Mathematics Activities; Concept Formation; Mexico + Suchen Sie Ihr Suchwort? Mathematische Bildung; Problemlösen; Grafische Darstellung; Studienanfänger; Ausland; Concept learning; Begriffsbildung; Mexiko
Abstract	The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f'. The research goal is to analyze the mathematical connections that university students establish when solving tasks that involve the graphs of f and f' when the two functions do not have associated symbolic expressions. Seven students from the first year of undergraduate studies in mathematics from a university in southern Mexico participated. For data collection, two tasks involving the graphical context of the derivative were applied. An analysis of the mathematical activity was carried out by the participants with the analysis model proposed by the onto-semiotic approach, and thematic analysis with types of mathematical connections from the extended theory of connections was carried out to infer the connections made in that mathematical activity, which allowed us to consider the reversibility connection between the graphs of f and f' as the encapsulation of a portion of the mathematical activity. Four students establish the reversibility relationship between the graph of f and the graph of f'. It has been concluded that some students can establish the reversibility connection between the graphs of f and f', but the complexity of the mathematical activity that encapsulates the connection explains (by showing everything that the student must do) why some students are not able to establish it. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01