Examples and Generalizations in Mathematical Reasoning -- A Study with Potentially Mathematically Gifted Children

Autor/inn/en	Jablonski, Simone; Ludwig, Matthias
Titel	Examples and Generalizations in Mathematical Reasoning -- A Study with Potentially Mathematically Gifted Children
Quelle	In: Journal on Mathematics Education, 13 (2022) 4, S.605-630 (26 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Zusatzinformation	ORCID (Jablonski, Simone) ORCID (Ludwig, Matthias)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2087-8885
Schlagwörter	Mathematical Logic; Thinking Skills; Mathematics Education; Academically Gifted; Elementary School Students; Grade 3; Grade 4; Grade 5; Grade 6; Foreign Countries; Longitudinal Studies; Germany + Suchen Sie Ihr Suchwort? Mathematical logics; Mathematische Logik; Denkfähigkeit; Mathematische Bildung; School year 03; 3. Schuljahr; Schuljahr 03; School year 04; 4. Schuljahr; Schuljahr 04; School year 05; 5. Schuljahr; Schuljahr 05; School year 06; 6. Schuljahr; Schuljahr 06; Ausland; Longitudinal study; Longitudinal method; Longitudinal methods; Längsschnittuntersuchung; Deutschland
Abstract	Mathematical arguments are central components of mathematics and play a role in certain types of modelling of potential mathematical giftedness. However, particular characteristics of arguments are interpreted differently in the context of mathematical giftedness. Some models of giftedness see no connection, whereas other models consider the formulation of complete and plausible arguments as a partial aspect of giftedness. Furthermore, longitudinal changes in argumentation characteristics remain open. This leads to the research focus of this article, which is to identify and describe the changes of argumentation products in potentially mathematically gifted children over a longer period. For this purpose, the argumentation products of children from third to sixth grade are collected throughout a longitudinal study and examined with respect to the use of examples and generalizations. The analysis of all products results in six different types of changes in the characteristics of the argumentation products identified over the survey period and case studies are used to illustrate student use of examples and generalizations of these types. This not only reveals the general importance of the use of examples in arguments. For one type, an increase in generalized arguments can be observed over the survey period. The article will conclude with a discussion of the role of argument characteristics in describing potential mathematical giftedness. (As Provided).
Anmerkungen	Indonesian Mathematical Society. Jl. Padang Selasa 524, Palembang, South Sumatra 30139, Indonesia. Tel: +618-127-106777; Fax: +627-113-20310; Web site: http://jme.ejournal.unsri.ac.id/index.php/jme
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01