A Survey On The Comprehension Level Of Complex Numbers Among High School Students

It is necessary to cultivate students with the core literacy of mathematics in the new era,which requires “taught for understanding”.As a significant concept,complex numbers are closely related to algebra and geometry,which contain rich educational value and have a positive effect on students' core accomplishment of mathematics.Mathematics curriculum,whatever domestic or abroad,had paid much attention to the understanding of complex numbers,but the domestic studies of interpreting level of complex numbers had been relatively weak.The main researches are based on experience speculatively,lack the support of empirical researches.This research takes this opportunity to establish the model of “Facets and Layers of Complex Numbers”.According to the ordinary high school mathematics curriculum standard,this paper conducts systematic research on the interpreting level of Cartesian form(referred to as the understanding of complex numbers)for students of grade two in senior high school.The questions are:(1)Generally what is the level of students to complex numbers' understanding? What is the level of understanding in different dimensions?(2)What are the influences of gender and school variables on the level of comprehension? What are the reasons that affect students' understanding level of complex numbers?(3)Based on students' understanding level of complex numbers,how to achieve a certain level of understanding?The main conclusions are:(1)As a whole,the understanding level of complex numbers shows a decreasing trend,and the performance in algebraic dimension is better than geometric dimension.In algebraic dimension,most of the students can reach the activity level and program level,but students' performance in object level is not good.Most students just remember the definition and classification of complex numbers,and fail to understand the essential characteristics accurately.In terms of geometric dimension,most of the students can reach the activity level and program level,but the object level is low.Most of the students are not familiar with the geometric meaning of complex numbers' operation and modulus.(2)The understanding level of students does not show gender discrimination;Different types of schools only have significant differences in the object level.The main factors that affect students' plural comprehension level include the curriculum standard,textbook,college entrance examination and teachers.(3)Based on the results,the corresponding suggestions are put forward from the perspective of teaching.Teaching advice: Teachers should pay close attention to the teaching of complex numbers.In the dimension of algebra,we can integrate the history of mathematics;reflect the process of extensions of numbers' systems;grasp the essential characteristics of complex numbers.In geometric dimension,we can construct complex geometric model by analogy;effectively make use of modern information technology;strengthen inquiry teaching,deepen students' understanding.