Mechanisms underlying the association between perceived recurrence risk and negative emotions in patients with ischemic stroke: a cross-sectional study.

Mathematically gifted students are often expected to demonstrate high levels of mathematics achievement because they usually show strong interest in mathematics, rapid understanding of mathematical relationships, flexible reasoning, and advanced problem-solving ability. However, mathematical giftedness does not automatically lead to consistently high mathematics achievement. Some mathematically gifted students may have strong mathematical potential but still differ in how they organize mathematical knowledge, regulate their learning, apply learning strategies, and transform mathematical understanding into actual performance. Therefore, the education of mathematically gifted students should not focus only on the amount of mathematical knowledge they possess, but also on how they learn mathematics and how they connect mathematical knowledge with learning processes. Previous studies have provided important theoretical explanations of giftedness and mathematical giftedness. and emphasized that giftedness involves multiple abilities and potentials, including intellectual ability, creativity, motivation, and social and self-related characteristics. In the field of mathematics, suggested that mathematically gifted students often perceive the world through a mathematical perspective and are able to generalize mathematical relationships and operations quickly. Similarly, noted that mathematically gifted students may demonstrate advanced mathematical reasoning, flexible mental processes, and distinctive approaches to mathematical problem solving. Moreover, previous studies have described mathematically gifted students as learners who may complete mathematical tasks with unusual speed and accuracy, engage in mathematical thinking that differs qualitatively from that of their peers, identify relationships among mathematical concepts without direct instruction, and sometimes skip intermediate steps in problem solving (; ; ; ). These characteristics further suggest that mathematical giftedness should be understood not only in terms of high performance, but also in terms of distinctive mathematical thinking and learning processes. However, mathematical giftedness and mathematics achievement should not be regarded as identical. A student may possess mathematical giftedness without always achieving high mathematics scores, and high achievement in mathematics does not necessarily indicate mathematical giftedness. Recent research has further emphasized that mathematical giftedness is a multidimensional construct rather than a single form of high mathematical ability. , in a systematic review of empirical studies on the cognitive characteristics of mathematically gifted individuals, reported that mathematical giftedness involves both domain-specific abilities, such as mathematical reasoning, problem solving, and mathematical creativity, and domain-general abilities, such as memory, reasoning, and visual-spatial ability. also showed that research on mathematical giftedness has developed across educational and psychological traditions, but further empirical research is still needed to clarify how mathematically gifted students learn and develop their abilities. These recent studies suggest that mathematically gifted students should be examined not only in terms of cognitive characteristics, but also in relation to their learning processes and knowledge structures.