도함수의 성질에 관련한 학생들의 사고에 대하여
On the students’ thinking of the properties of derivatives
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Mathematical concept exists in the structural form, not in the independent form. The purpose of this studyis to consider the network which students actually have for the mathematical concept structure related to theproperties of derivatives. First, we analyzed the properties of derivatives in ‘Mathematics II’ and showed themathematical concept structure of the relations among derivatives, functions, and primitive functions as anetwork. Also, we investigated the understanding of high school students for the mathematical conceptstructure between derivatives and functions, and the structure between functions and second order derivativeswhen the functional formula is not given, and only the graph is given. The results showed that studentsmainly focus on the relation of ‘function-derivatives’, the thinking process for direction of derivative and thethinking style for algebra. On this basis, we suggest the educational implication that is necessary for studentsto build the network properly.
Abstract
Mathematical concept exists in the structural form, not in the independent form. The purpose of this studyis to consider the network which students actually have for the mathematical concept structure related to theproperties of derivatives. First, we analyzed the properties of derivatives in ‘Mathematics II’ and showed themathematical concept structure of the relations among derivatives, functions, and primitive functions as anetwork. Also, we investigated the understanding of high school students for the mathematical conceptstructure between derivatives and functions, and the structure between functions and second order derivativeswhen the functional formula is not given, and only the graph is given. The results showed that studentsmainly focus on the relation of ‘function-derivatives’, the thinking process for direction of derivative and thethinking style for algebra. On this basis, we suggest the educational implication that is necessary for studentsto build the network properly.
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