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What generalizations do students achieve with respect to trigonometric functions in the transition from angles in degrees to real numbers?
The Journal of Mathematical Behavior Pub Date : 2020-06-01 , DOI: 10.1016/j.jmathb.2020.100778 Erdem Çekmez
The Journal of Mathematical Behavior Pub Date : 2020-06-01 , DOI: 10.1016/j.jmathb.2020.100778 Erdem Çekmez
Abstract The aim of this study is to examine prospective mathematics teachers’ generalizations of trigonometric functions from the unit circle to the Cartesian coordinate system. The researcher developed a test that aimed to reveal students’ generalizations, as well as the possible differences between them. The test was administered to 30 students who were near completion of their university degree program. The findings showed that the students were unable to establish the link between the unit circle and the Cartesian coordinate representation system; and therefore, they were not able to interpret the outputs of trigonometric functions with input of a real number that is not a multiple of π. The researcher also found that the students had developed certain misconceptions regarding the properties of trigonometric functions. To improve the teaching of trigonometric functions an instructional sequence and an alternative definition for trigonometric functions is proposed.
中文翻译:
在从度角到实数的过渡过程中,学生对三角函数得到了哪些概括?
摘要 本研究的目的是考察未来数学教师对三角函数从单位圆到笛卡尔坐标系的推广。研究人员开发了一项测试,旨在揭示学生的概括以及他们之间可能存在的差异。该测试是针对 30 名即将完成大学学位课程的学生进行的。结果表明,学生无法建立单位圆和笛卡尔坐标表示系统之间的联系;因此,他们无法解释输入不是 π 倍数的实数的三角函数的输出。研究人员还发现,学生们对三角函数的性质产生了某些误解。
更新日期:2020-06-01
中文翻译:
在从度角到实数的过渡过程中,学生对三角函数得到了哪些概括?
摘要 本研究的目的是考察未来数学教师对三角函数从单位圆到笛卡尔坐标系的推广。研究人员开发了一项测试,旨在揭示学生的概括以及他们之间可能存在的差异。该测试是针对 30 名即将完成大学学位课程的学生进行的。结果表明,学生无法建立单位圆和笛卡尔坐标表示系统之间的联系;因此,他们无法解释输入不是 π 倍数的实数的三角函数的输出。研究人员还发现,学生们对三角函数的性质产生了某些误解。