Abstract:

What characterizes a (potential) mathematical talent? Certainly, it is not a universal characteristic, but rather mathematics-specific characteristics that are attributed to these children. A prominent example in the German giftedness research is Käpnick's (1998) catalog of characteristics for the third and fourth grades, which lists, for example, special structuring abilities, the change of levels of representation, or mathematical creativity. Other catalogs, e.g., by Heinze (2005) or Sjuts (2017) use a similar approach: Mathematical giftedness is described - for a specific age group - by the association of mathematical activities and generic competencies.

For some characteristics there is agreement on their relevance for the diagnosis, selection, and support of (potentially) mathematically gifted children. For example, children's structuring abilities have been researched in detail (Ehrlich, 2013) and can be found in a large number of the parallel existing trait catalogs.

The situation is different for mathematical reasoning. This becomes especially clear if one examines the different feature catalogs for the occurrence of mathematical reasoning or sub-activities of it: Sometimes mathematical reasoning is listed as a trait (e.g., Heinze, 2005), while in other catalogs it is only listed in parts (Sjuts, 2017) or not at all (Käpnick, 1998). Fritzlar (2011) even formulates the hypothesis that mathematical reasoning is not an giftedness trait.

These different perspectives are taken as an opportunity in this article to focus more closely on mathematical reasoning in the context of mathematical giftedness. For this purpose, theoretical foundations and considerations are first presented, which are then supported and expanded by empirical findings from a qualitative study with 21 (potentially) mathematically gifted children. Finally, consequences for the diagnosis and support of mathematical giftedness are formulated.

The results show that the reasoning of the children differs in the completeness and generalization. Still, it can be hypothetically concluded that reasoning on a general level and creativity might be interrelated. This assumption might be used for the diagnosis and support of mathematical giftedness.

Keywords:

Giftedness, reasoning, creativity.