Overcoming a Pitfall of Circularity in Research on Problem Solving by Mathematically Gifted Schoolchildren

A considerable portion of research on mathematical giftedness seeks to compare between problem-solving experiences of gifted and average-ability schoolchildren. In some comparative studies, either quantitative or qualitative, some of the identified differences can be (implicitly) embedded in the study design. In light of the evaluation criteria adopted from research on general intellectual abilities and problem-solving competences, such studies bear a danger of falling into the pitfall of circularity. The goal of this article is to discuss three ways of overcoming this pitfall. The discussion converges to methodological implications for evaluating past research and conducting further research on problem solving by mathematically gifted schoolchildren.