A Digital Approach to Talent Development With Mathematical Proof

Abstract

In the field of mathematics, proving is considered both the most crucial and the most challenging skill to acquire. The latter aspect is a likely reason why this topic is not emphasized in the (in this case, German) school curriculum. However, when it comes to fostering gifted children, extracurricular and challenging content is needed. Proving shows substantial overlap with the disciplines of reasoning and problem solving, which have often been successfully incorporated into fostering programs. And while some educators refrain from teaching proof to schoolchildren, even those who are gifted, others demand the integration of the topic into regular lessons for all age groups. This dissertation examines how gifted primary school children can be supported through an enrichment course designed to teach them the construction of mathematical proofs. The course was held as an asynchronous online course. Possible challenges associated with the format and topic were investigated in a pilot study of the course. The children participating in the study reported that they liked most parts of the course and were eager to engage with the content. They also identified parts that were too challenging from cognitive or technical perspectives. Following the study, a new test instrument was developed and validated to measure Proof Competency (PC) in children. This instrument was then used in an efficacy study of the revised course alongside motivational measures. This study did not find that the course had significant effects on PC, possibly due to the high number of non-finishers in the treatment group, which is typical for asynchronous online courses. Furthermore, the exceptionally high self-concept the children had before the course significantly declined. These findings led to the idea of a follow-up study to investigate how situational motivation evolves throughout the course. The outcomes revealed specific aspects of the course where additional scaffolding or facilitation could help prevent students from dropping out. Furthermore, embedding self-regulation training could be identified as a potential way to further enhance successful course participation.