When Is Less More? Investigating Gap-Filling in Proofs without Words Activities

Autor/inn/en	Marco, Nadav; Palatnik, Alik; Schwarz, Baruch B.
Titel	When Is Less More? Investigating Gap-Filling in Proofs without Words Activities
Quelle	In: Educational Studies in Mathematics, 111 (2022) 2, S.271-297 (27 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Marco, Nadav)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-022-10159-z
Schlagwörter	Mathematics Instruction; Cooperative Learning; Mathematics Activities; Secondary School Students; Secondary School Mathematics; Instructional Design; Mathematical Logic; Validity + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Kooperatives Lernen; Sekundarschüler; Lesson concept; Lessonplan; Unterrichtsentwurf; Mathematical logics; Mathematische Logik; Gültigkeit
Abstract	In activities based on proof without words (PWW), we developed, students are given a PWW--a diagram that alludes to the proof of a mathematical theorem. The students work collaboratively to construct a proof alluded by the PWW, and then each student writes and submits a proof attempt. In a 3-year design-based study, we investigate and develop PWW-based activities for advancing upper secondary students' proficiency in constructing proofs. We use the concept of gap-filling as a theoretical framework. In a nutshell, gap-filling is an action of adding information absent in a text that a reader does for sense-making. We inquire whether secondary school students independently construct a proof when a PWW is at their disposal, what characterizes those gaps that students identify and fill, and how PWW design principles influence students' gap-filling. We identified four categories of gaps: key idea, generality, constructional, and figure property justifications. We find that students mainly fill key idea gaps but not generality gaps and that PWWs that presented the construction procedure led more students to fill the constructional gaps. However, PWWs that did not explicitly present some figures' property led more students to fill those justification gaps. We identify five PWW design principles that can enhance secondary students' gap-filling and conclude that a meticulous design paves the way to implement PWW-based activities for fostering mathematical proving. (As Provided).
Anmerkungen	Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01