For the gifted mathematics student, early mastery of concepts and skills in the mathematics curriculum usually results in getting more of the same work and/or moving through the curriculum at a faster pace. Testing, grades, and pacing overshadow the essential role of creativity involved in doing mathematics. Talent development requires creative applications in the exploration of mathematics problems. Traditional teaching methods involving demonstration and practice using closed problems with predetermined answers insufficiently prepare students in mathematics. Students leave school with adequate computational skills but lack the ability to apply these skills in meaningful ways. Teaching mathematics without providing for creativity denies all students, especially gifted and talented students, the opportunity to appreciate the beauty of mathematics and fails to provide the gifted student an opportunity to fully develop his or her talents. In this article, a review of literature defines mathematical creativity, develops an understanding of the creative student of mathematics, and discusses the issues and implications for the teaching of mathematics.

The identification of creative potential in mathematics poses many challenges. Much of the research into the identification of mathematical creativity has focused on the development of measurement instruments. Scoring of these instruments is time consuming and subject to scorer interpretation, limiting their use. This study sought a simpler means to obtain indicators of creative potential in mathematics. Existing instruments were used to explore the relationship between mathematical creativity and mathematical achievement, attitude towards mathematics, self-perception of creative ability, gender, and teacher perception of mathematical talent and creative ability. Data were gathered from 89 7th graders in a suburban Connecticut school. The regression model predicted 35% of the variance in mathematical creativity scores. Mathematical achievement was the strongest predictor accounting for 23% of the variance. Student attitudes towards mathematics, self-perception of their own creative abilities, and gender contributed the remaining 12% of variance. Interpretation of the relative importance of the independent variables was complicated by correlations among them.

Spatial ability has been valued as a talent domain and as an assessment form that reduces cultural, linguistic, and socioeconomic status biases, yet little is known of the spatial ability of students in gifted programs compared with those in general education. Spatial ability is considered an important indicator of potential talent in the domains of science, technology, engineering, and mathematics (STEM). This study explored undergraduate students’ spatial ability, focusing on mental rotation, by investigating the relationships of three variables with performance on a spatial ability test, in terms of test scores and test completion time. A three-way analysis of variance revealed statistically significant main effects of gifted program participation, choice of academic major, and gender, suggesting that students who participated in a gifted program, who majored in a STEM discipline, or who were male outperformed their counterparts on a measure of spatial ability when the other conditions were equivalent. No interaction effects existed among the three variables, indicating that none of them functioned as a moderator of students’ performance on the spatial ability assessment. However, when spatial ability was considered as a mediating variable in a path model, gender had the largest total effect on the probability of students majoring in a STEM area. In addition, the more time students spent on the spatial ability test, the better they tended to perform, which is a finding inconsistent with current literature.

The fields of gifted and engineering education share many common interests, and their students share many common attributes. Infusing and making engineering implicit in the K-6 education programs creates opportunities to develop concepts, skills, and habits of the mind that are valuable in all disciplines while providing opportunities to discover and develop talent in the science, technology, engineering, and mathematics (STEM) disciplines.