Examples and generalizations in mathematical reasoning – a study with potentially mathematically gifted children

  • 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.

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Author:Simone JablonskiORCiDGND, Matthias LudwigORCiDGND
Parent Title (English):Indonesian Mathematical Society journal on mathematics education : (IndoMS-JME)
Place of publication:Palembang
Document Type:Article
Date of Publication (online):2022/11/17
Date of first Publication:2022/11/17
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2023/09/08
Tag:Examples; Longitudinal Study; Mathematical Giftedness; Mathematical Reasoning; Typology
Page Number:26
First Page:605
Last Page:630
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:3 Sozialwissenschaften / 37 Bildung und Erziehung / 370 Bildung und Erziehung
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International