Changing between Representations of Elementary Functions: Students' Competencies and Differences with a Specific Perspective on School Track and Gender

Autor/inn/en	Sproesser, Ute; Vogel, Markus; Dörfler, Tobias; Eichler, Andreas
Titel	Changing between Representations of Elementary Functions: Students' Competencies and Differences with a Specific Perspective on School Track and Gender
Quelle	In: International Journal of STEM Education, 9 (2022), Artikel 33 (18 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Sproesser, Ute)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2196-7822
DOI	10.1186/s40594-022-00350-2
Schlagwörter	Thinking Skills; Mathematics Skills; Mathematical Concepts; Competence; Problem Solving; Difficulty Level; Track System (Education); Gender Differences; Mathematics Instruction; Item Response Theory + Suchen Sie Ihr Suchwort? Denkfähigkeit; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Kompetenz; Problemlösen; Schwierigkeitsgrad; Leistungsgruppe; Leistungsdifferenzierung; Geschlechterkonflikt; Mathematics lessons; Mathematikunterricht; Item-Response-Theorie
Abstract	Background: Functional thinking is characterized as a specific way of thinking in relationships, dependencies, and changes. Hence, beyond mathematics, it is also crucial for other (STEM) disciplines as well as for everyday situations. In particular, dealing with different representations of functions and changing between them are core function-related competencies, which are correspondingly needed for the formation of appropriate concepts and flexible problem-solving in various situations. Therefore, this study investigated students' (N = 856) competencies related to representational changes of elementary functions and, in particular, assessed which changes are especially easy or difficult for students. Moreover, possible school track and gender differences were investigated by performing DIF analyses within the framework of Rasch modeling. The data were gathered using a paper-pencil test administered after the students had completed the teaching unit on linear functions in their mathematics lessons. Results: Altogether, students were found to have limited competencies related to representational changes of elementary functions. There was no clear pattern regarding the types of representational change that were difficult or easy for them. Moreover, girls performed better on purely mathematical tasks, whereas boys did better at a complex modeling and problem-solving task. Classes from the academic track produced better results in tasks with a situational context compared to their peers from non-academic tracks, who performed relatively strongly on purely mathematical tasks. Conclusions: These findings imply that various representations and representational changes should be included in lessons on functions to support students in building a rich concept of function and flexible problem-solving skills, thus fulfilling curricular requirements and responding to didactical considerations. In particular, the teaching of functions should be more balanced by mixing tasks with and without a situational context and the corresponding representational changes. These findings should motivate teachers, in particular those teaching non-academic tracks, to give a more prominent role to situational contexts in their lessons on functions in order to foster their students' learning and build a bridge between mathematics and real-world situations. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01