Study On The Cognitive Level Of Complex Numbers In High School Students

With the advancement of science and technology,the importance of complex numbers theory has become increasingly prominent.It not only has great significance for the development of mathematics itself,but also makes great contributions in many scientific fields.Currently,there is little research on high school students’ cognitive levels of complex numbers,and the SOLO classification theory is a qualitative evaluation method that focuses on students’ learning processes and quality.Based on the SOLO classification theory,the author of this paper investigated the cognitive level of high school students’ understanding of complex numbers through the following two questions.The first one is what is the situation of high school students’ cognitive level of complex numbers under the SOLO theory? What are the difficulties in learning complex numbers? And the second question is what are the main factors affecting high school students’ cognitive levels and difficulties in learning complex numbers? The following conclusions were drawn through the research:1.The cognitive level of high school students’ understanding of complex numbers is examined in this study.(1)From the perspective of test papers,most students have reached the highest SOLO level,i.e.the associative structure level,in the dimensions of complex number concepts and operations.The cognitive level of complex number operations is the highest.In the dimension of comprehensive application of complex numbers,only 11% of students have reached the highest SOLO level,i.e.the abstract extension level.(2)From the perspective of interviews,most students do not understand the origin,purpose,and significance of complex numbers,and their enthusiasm for learning complex numbers is low.(3)In terms of different grades,the overall cognitive level of complex numbers in the third grade is higher than that in the second grade.(4)In terms of the difficulties of learning complex numbers,students have an inadequate understanding of complex number knowledge and struggle to integrate it with other knowledge.As a result,they lack confidence in learning complex numbers.2.The main factors affecting high school students’ cognitive level of complex numbers are identified in this study.These factors include:(1)a lack of in-depth understanding of complex number knowledge;(2)a lack of mathematical thinking that combines numbers and geometry;(3)the influence of learning attitudes and confidence;(4)the influence of teachers’ teaching concepts and methods;and(5)the influence of teachers’ own knowledge literacy and teaching abilities.Based on the research conclusions above,the author proposed relevant teaching suggestions to improve high school students’ cognitive level of complex numbers,with the aim of inspiring and assisting teachers in their teaching endeavors.