Abstract:

The changes and development of argumentative skills in the context of a deeper mathematical understanding are important aspects of mathematical teaching and learning, and especially in the support of gifted children. Various characteristics of primary school children’s arguments could have been worked out, but so far they have not been observed over a longer period in terms of changes (e.g. Koleza, Metaxas & Poli, 2017). In longitudinal studies on changes in the general cognitive development of children, the focus on mathematical argumentation products remains implicitly (e.g. Piaget, 2002). Nevertheless, these developmental psychological results, as well as the comparison of models characterizing giftedness in different ages, lead to the presumption that changes in argumentation products can be observed within the age span of nine and twelve years (Käpnick, 1998; Sjuts, 2017).

This longitudinal study documents the mathematical argumentation products of potentially mathematically gifted primary school children over a 12-month period. Within this period, 14 children worked on arithmetical reasoning tasks in individual interview settings. For each child, the study involves three interviews which span the children’s age from nine to ten years. The changes in the hereby formulated argumentation products are analyzed on the levels:
(1) Toulmin’s argument structure,
(2) content of the argument,
(3) independency of the argument, and
(4) validity of the argument.

For all categories, Cohens’ Kappa is between 0.66 and 0.72 which can be interpreted as a good intercoder reliability. In order to see which of the characteristics are stable or variable within one year, the starting point of the analysis is from a global perspective. In this, the analysis of the 56 tasks of each survey date is compared for all children over t1, t2 and t3. Afterwards, changes within the categories on the level of the individual children are classified in terms of the following cases:
(a) stable,
(b) variable with a tendency
(c) variable without a tendency.

The paper provides first insights into the hypothetical consistency and variability of the characteristics of the children’s arguments. The extended use of elements from the Toulmin scheme might be a general change in the argumentation products of these children within the observation period. Content seems to be depend on further aspects and influences apart from the sample’s development in this age span. The need for argumentation remains quantitatively stably within the observed period. Finally, the percentage of generally formulated elements changes with an increasing tendency overall categories, even on the individual level for this sample.

Keywords:

Mathematical Giftedness, Argumentation, Toulmin.