Abstract
The purpose of this paper is to explore how the mathematical content knowledge on the derivative of the exponential function is demonstrated in analysis courses, compared to the school mathematics where is introduced without rigorous justification. We analyzed structures of justifications of in analysis textbooks used in department of mathematics education at college of education in South Korea, and compared the structures with learning trajectories in school mathematics. As a result, there were four major types of the justifications and one of them fills the gap in the learning trajectories in the high school calculus textbooks. This result suggests the necessity of understanding mathematics content knowledge for pre-service teacher education in connection with school mathematics.
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