High School Conic Cognitive Level Of Development

Conics is a difficult section in the Analytic Geometry for senior high school students. It involves geometry and algebra from the view of content, and includes the representation of shape, the transition from the representation of shape to the representation of number and the further representation of number.Guided by the SOLO (Structure of the Observed Learning Outcome) taxonomy,we design the tests based on the Curriculum Standards of Mathematics for Conics. Then we analyze the cognitive level and its development in the process of conies study for senior high school students using the methods of testing and interview and discussion.We analyze the cognitive level and its development in the process of conies study from the dimensions of samples, types of classes and the gender differences. Combining SOLO taxonomy with the Wittrock's Theory of Generative Learning, the cognitive characteristics of different categories of cognitive level, the common problems and their reasons are discussed, also the relevant suggestions to teaching of mathematics are also given .The conclusions of this thesis are the following:(1) The cognitive level of most students is M₁ level in the first unistructural(U)-multistructural(M)-relational(R) cycle within the concrete symbolic mode, and the following level for other students is R₁ level. Hence, the cognitive level and its development for senior high school students is M₁â†'R₁, then R₁â†'U₂. This things happens in the female and male students except the proportion at M₁ level and R₁ level.(2) In the transition of M₁ level to R₁ level, most students show high ability in the transition of the representation of shape to the representation of number, and certain ability of the representation of number, but not enough. The male students perform better than the female students in the above aspects. Senior high school students have certain ability in the transition of R₁ level to U₂ level, but low. The male students perform a little better than the female students. (3) The main problems in the transition of M₁â†'R₁ for the students of M₁ level are no understanding the knowledge better, memorizing too much, incomplete transition of the geometric problems to the algebraic ones and lacking of the representation of number. Emphasizing the concrete stuffs when answering the question is another problem. The reasons for these problems are mainly the "level concise" in the cognition, relying too much on the auxiliary function of the representation of shape on the representation of number and lacking enough ability of the further representation of number.The problems in the transition of M₂â†'R₂ for the students of R₁ level are almost the same as the students of M₁ level, however, the reasons are mainly the "level concise" in the transition of M₁â†'R₁ and the methods of transition is not brief and flexible, the incomplete transition of R₁â†'M₁ and lacking the ability of the representation of number.Moreover, there is a big difference on the cognitive levels and cognitive characteristics among different persons. One aim of teaching is to foster the transition of the students' cognitive levels based on the above factors.