This systematic review aimed to explore the cognitive characteristics of mathematically gifted individuals. Screening 497 studies, we obtained 22 empirical research that particularly explored cognitive characteristics of mathematically gifted individuals. We presented our findings under two major themes: domain-specific and domain-general abilities. Research that investigated domain-specific abilities suggested that problem-solving, mathematical creativity, and mathematical reasoning were essential characteristics of mathematical giftedness whereas some domain-general abilities including, perceptual abilities, visual-spatial ability, memory, and reasoning were found to contribute to mathematical giftedness. We also noted several within-group variations, suggesting a complex interaction of cognitive traits. Our results call for brand new frameworks on mathematical giftedness as the findings provide unique domain-specific characteristics that are different from what were provided by renowned models in the field. We also provided implications that encourage differentiated learning practices to meet the academic needs of mathematically gifted individuals.

This paper explores the dual nature of "institutional" and "partial" meanings associated with mathematical entities in an educational setting. The institutional meaning represents the formal understanding endorsed by the mathematical community, while the partial meaning pertains to the limited and evolving comprehension that students possess. Through a theoretical perspective, this research examines how students’ progress from partial knowledge toward institutional knowledge, emphasizing the importance of the teacher’s role and the educational context in facilitating this transition. The conclusion suggests that the shift to institutional knowledge relies heavily on effective pedagogical mediation and social interaction, which are essential for students to fully grasp mathematical objects.

Due to the ongoing difficulties in teaching mathematics, especially geometry, in Nigerian schools, new teaching methods are needed to improve student performance. This quasi-experimental research examined how the Know-Want-Learn (KWL) method impacts the geometry performance of upper-basic students in Kaduna North, Nigeria. Two questions were posed for research, and two void hypotheses were examined. The study included 98 students selected from a population of 6300 upper-basic students in Kaduna North. They were split into two groups: an experimental group (n=50) that was taught using the KWL strategy, and a control group (n=48) that received instruction using traditional methods. The researcher created a 28-question multiple-choice Geometry Performance Test (GPT) with a reliability coefficient of 0.86, as determined by Cronbach's alpha. Students were tested before and after to determine how well they performed in geometry. The results showed that the experimental group performed significantly better than the control group, with an average score of 23.52 in the post-test, compared to 14.69. ANCOVA analysis revealed a significant impact of the KWL technique on students' achievement (F=242.518, p<.001), explaining 74.5% of the variability (partial η² = .745). Additionally, there were no significant differences between male (M = 19.40, SD = 5.304) and female (M = 18.93, SD = 5.045) students in the experimental group, t(96) = 0.444, p = 0.658.These results indicate that the KWL approach promotes a more profound comprehension and involvement in geometry, and utilizing it could enhance mathematics teaching in Nigerian schools with equality across genders. It is advised to use the KWL strategy for teaching geometry in co-ed and single-sex schools and to organize teacher training sessions and seminars to encourage its adoption by math educators.