In this paper I describe aspects that seem to be exclusive for teaching mathematically gifted/promising students. First, I discuss the qualities of the mathematically gifted mind and suggest the use of the construct of mathematical potential for that of mathematical giftedness with reference to school students. Second, I assume that high quality teaching of mathematics in any classroom should be directed at the construction of deep and robust mathematical knowledge, development of conceptual understanding, and the promotion of a positive attitude toward the subject.
I argue that relative to a regular classroom, teaching mathematically gifted students (a) involves a higher (than regular) level of mathematical challenge, (b) requires from students a higher level of creative and critical thinking, (c) requires minor scaffolding, and (d) requires teacher sensitivity to the special needs of students, as well as greater attentiveness, flexibility, and reflectivity. To support these arguments, I present the voices of students and describe one mathematics lesson with mathematically promising students.
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