Mathematical creativity and mathematical giftedness in the primary school age range: an interview study on creating figural patterns

Abstract

Relationships between mathematical giftedness and mathematical creativity have been widely studied, but few studies are available for primary school age. For an investigation in this age group, it seems appropriate to use a content area that not only has high relevance for mathematics and special potentials for creativity, but also requires only a little knowledge and is easily accessible. We therefore investigated whether mathematically gifted primary school students differ from non-gifted ones in high creativity in dealing with mathematical patterns and structures. This question was explored in an interview study in which 24 third graders were asked to invent as many different figural patterns as possible, which enabled creative mathematical activity also by combining arithmetic and geometric aspects. A detailed qualitative analysis of the data revealed among other results several types of flexibility concerning the invention of patterns. The selection of students ensured that all participants performed well to very well in regular mathematics classes and that 14 of them could additionally be assumed to be mathematically gifted based on a specific test. This allowed a comparison of both subgroups. Results indicate a high correspondence between mathematical giftedness and mathematical creativity concerning the invention of figural patterns.

Relationships between general giftedness, expertise in mathematics, and mathematical creativity that associated with pattern generalization tasks in different representations

“…The systematic review of the empirical research on creativity in mathematics (education) revealed that MSTs are the most frequently used research tool for the evaluation of MC at the school level. Examples of such studies can be seen in Assmus and Fritzlar (2022) and Schoevers et al (2022).…”

“…In this special issue, two papers were devoted to the analysis of creativity associated with solving PG tasks. Assmus and Fritzlar (2022) investigate creativity related to the generation of diagrammatic patterns by students with varying levels of mathematical giftedness and demonstrate that mathematical expertise increases creativity. Singer and Voica (2022) demonstrate that PG itself is a creativitydirected activity as related to the pattern "creation."…”

“…Schoevers et al (2022) argued that creativity predicted student performance on geometrical problems generally and that creativity predicted student achievement on geometry problems requiring multiple solutions. Focusing on patterns, Assmus and Fritzlar (2022) argue that mathematical activity offers a variety of opportunities for creative development. They find several types of flexibility related to the invention of patterns and a high correspondence between mathematical giftedness and MC regarding the invention of figural patterns.…”

“…Generalization processing is important both for the advancement of mathematics as a scientific field (Sriraman, 2003, 2004 with reference to Piaget, 1971) and for the development of mathematical reasoning in mathematics education (Rivera, 2013). As such, generalization is a potentially creative process that can lead a person to discover something new to them (Assmus & Fritzlar, 2022). Researchers in mathematics education and beyond connect the ability to generalize with levels of intelligence (Sternberg, 1979) and mathematical competencies and mathematical giftedness (Assmus & Fritzlar, 2022; Krutetskii, 1976; Sriraman, 2003).…”

“…As such, generalization is a potentially creative process that can lead a person to discover something new to them (Assmus & Fritzlar, 2022). Researchers in mathematics education and beyond connect the ability to generalize with levels of intelligence (Sternberg, 1979) and mathematical competencies and mathematical giftedness (Assmus & Fritzlar, 2022; Krutetskii, 1976; Sriraman, 2003).…”