Concepts and Skills in High School Calculus: An Examination of a Special Case in Japan and the United States

An investigation of above-average high school calculus students from Japan and the United States in order to determine any differences in their conceptual understanding of calculus and their ability to use algebra to solve traditional calculus problems. We examined and interviewed 18 Calculus BC students in the United States and 26 Suugaku 3 (calculus) students in Japan. Each student completed two parts of a written examination. The first part (Part I) consisted of problems emphasizing conceptual understanding but requiring little or no algebraic computation. Problems on the second part (Part II) required sound algebraic skills in addition to good conceptual understanding. Following the examination, we interviewed each student in order to assess their mathematical and educational background, their college and career plans, their thinking on the examination problems, their understanding of concepts, and their computational and reasoning skills. We found little difference in the conceptual understanding of calculus between the two groups of students, but the Japanese students demonstrated much stronger algebra skills than their American counterparts. Accepted and edited under the editorship of Edward A. Silver.