Exploring gifted students’ perception of mathematical problems

Abstract

There are students who exhibit exceptional mathematical abilities and devote themselves to thinking of mathematics in unusual manners. In this paper, to reveal their engagement in mathematics and derive suggestions from them for mathematics education, I have focused on their perception of mathematical problems. Reviewing previous studies focusing on mathematical giftedness and the learning of mathematics, it was suggested that gifted students tended to perceive mathematical problems analytically and grasp deep structure of them. And also, it was suggested that such a feature characterizes gifted students’ engagement in mathematics as follows. First, perceiving deep structure of mathematical problems enables students to perform highly in problem-solving. Second, focusing on deep structure of mathematical problems encourage students’ mathematical inquiry and generating creative ideas. To exemplify the latter one, I showed the conceivable process of mathematical inquiry focusing on the relationships between Pascal’s triangle and binomial theorem.