Abstract: There is strong societal pressure to place students in honors courses. Are students placed in honors courses truly gifted? This mixed-methods study examines beliefs and conceptual understandings of students enrolled in an honors precalculus mathematics class in a United States secondary school. Forty-five students were surveyed, classified into one of two groups, and then four students in each group were interviewed in-depth. Results found a dichotomy between students. One group was concerned with conceptual understanding, making connections, divergent thinking and multiple representation of mathematics. In the second group students were good exercise doers, calculating correct answers and memorizing procedures. Thus teachers need to differentiate lessons as much as possible to challenge all students to reach their full potential.

Key words: honors, gifted, advance placement, mathematics, diversity