What are the characteristics of mathematical creativity? An empirical and theoretical investigation of mathematical creativity.

Abstract

The main research question in this research project was "what are the characteristics of mathematical creativity?" It was investigated both qualitatively and quantitatively and the findings are presented in four articles. In the first article, three high achieving students were given an unfamiliar trigonometric problem. The findings indicate strongly that the student’s way of thinking is strongly linked with imitative reasoning and only when received some form of guidance, were they able to display creative and flexible reasoning. In the second article, a theoretical model for optimizing creativity was investigated empirically using ANCOVA. Intrinsic motivation and an aesthetic sense of mathematics were found to be significant predictors of mathematical creativity. The data also revealed a strong relationship between mathematical achievement and mathematical creativity. The third article looked at differences in mathematical creativity between 8th grade students and 11th grade students. Older students were found to score significantly higher on the mathematical creativity test. A proposed explanation for this is that the older students have three more years of schooling and might have developed a stronger connectedness of their mathematical knowledge base. Article four is a commentary and synthesis of three articles on mathematical creativity, giftedness and ability. The synthesis revealed that mathematical creativity is strongly linked with mathematical ability, spatial cognitive style and high intelligence.