A Probe Into The Conceptual Representation Of High School Students On Complex Elements

Concept image is all mental pictures of a mathematical concept in students’ mind. It consists of pictures、symbolic forms、diagrams and graphs and so on. We can think that concept image is the most active psychological factors of learner. But in the study of mathematics education, mathematical concept image is still under development. So this article which takes complex unit as an example is to explore the concept image on complex unit of high school students. This study constitutes of 4 parts:(1) What are the students’ concept representations about the definition ofcomplex number?(2) What are the students’ concept representations about modulus of a complexnumber?(3) What are the students’ concept representations about the operation ofcomplex number?(4) What are the students’ concept representations about the plane of complexnumber?This article makes reference the articles on error types of complex unit. After choice, the author creates the questionnaire of concept image on complex unit of high school students. The study for which there are 80 high school students including two classes of different degree were tested takes it as research tool. The results show:First, for complex correlation concept, when students face the stimulus of imaginary unit, it appears in students’ brain is that itself of imaginary unit and partial algebra type. The proportion of them is more than half. The proportion of imaginary unit is up to 74% and partial algebra type is 51%.Second: the definition of complex, 94.5% of students can judge correctly the real part and imaginary part of a complex number. There are only 5.5% of students cannot do it that think the imaginary part is not only real and it includes imaginary unit. It shows that there is not strong concept image of the definition of complex for the only 5.5% of student.Third: modulus of a complex number, we find that 79% of the students are able to accurately identify the geometric meaning of complex modulus. But there are still 21% of the students cannot judge.Fourth: The most frequent error is over generalization of the real radical multiplication. On the whole, the correct rate of each item is around 70%、80%. It shows that there are still a small number of students cannot grasp the complex operation.Through this research, we can understand the concept image on complex unit of high school students. It also provides the basis for middle school teachers to understand students.