Signs of Critical Reflection in Mathematical Experiential Learning Contexts

Abstract

In this article, we analyzed reflections of undergraduate students of Primary school education and also the reflections of gifted primary school children. The reflections were collected in those two subsamples separately, while learning Math in experiential way. For the suitability to observe critical reorganization of mathematical images, the scaling as a subject was chosen.

The process of learning in adults has a feature to encompass the critical reflection approach for the problem solving. The aim of our study was to shed light on differences and similarities between adults and gifted primary school children in mathematical reasoning.

We used the following methods: case study; observation; audio recordings; and qualitative analysis (i. e. content analysis). In whole study, 13 undergraduate students and 16 gifted children from III–IV grades took a part.

The results indicate that the main insights in the mathematical content were made while comparing measurements of different dimensions. The similarities between adults and children were found in how critical reorganization of mathematical images was done. The difference occurred in the extent of reasoning abstraction. Gifted children already at primary school years were able to formulate logical explanations into mathematical rules. However, for the children to make critical reflections, the experiential basis (practice) is obligatory. In contrast, adults used abstract reasoning even in experiential (practical) situations.