Genetic Teaching Research Of The Hyperbola

Conic section is one of important parts of high school mathematics curriculum,and it is the key content in college entrance examination each year. Learning conic is important for students to understand the thinking of analytic geometry:using the method of algebraic for geometry problems. The middle portion is located hyperbolic conic learning after elliptical, parabolic before. Because of the complex and nature of graphic formulas of trival are usually the most difficult part to grasp conic. Although the new curriculum reform, has reduced the intensity of the hyperbolic investigation, but does not change the present situation of student learning difficulties hyperbolic, it is necessary to carry out research and teaching improvement of hyperbola.Knowledge Learning is initially come from concept, the extent of conceptual understanding is often the basis for other parts of learning. So introducing the concept of hyperbolic and derivation of equations should be given focus. The introducing the concept of hyperbolic and derivation of equations in existing textbooks basically comes from the analogy of elliptical, although this approach is relatively simple and it also reflects one kind of important mathematical thinking---analogy, however compare to occurred teaching thought, it has the following disadvantages:(1) does not account for why we need to study hyperbolic, and research method is very unitary, in fact, using of zipper is difficult to really draw a smooth hyperbolic, it is difficult to stimulate students’ learning interest;(2) introducing of hyperbolic is rather abrupt, almost directly "throw" to the students, and lacks exploration and communication in the classroom, so students hardly feel the formation process of hyperbola.Therefore, this study is focused on the formation process of conic, especially hyperbola, to analyzes the relationship between the original concept of hyperbolic and concept given on the today’s textbooks, as well as compare a variety of classic hyperbolic standard equation derivation method in the history, combined with today’s high school math textbooks used in several major Version for hyperbolic equations derived concepts and treatment. Then, based on the occurrence of pedagogical theory required to reconstruct the history of hyperbolic and designed based on two kinds of methods to derive the history of mathematics and the standard way of introducing the concept of hyperbolic equations, ways and then given the comparison with textbook, received good feedback.This paper adopted a variety of research methods---literature study, questionnaires and teacher interviews, conducted for hyperbolic instructional design. Through literature study which identified the research questions, through questionnaires master degree students to understand the extent and the receiving mode and introduced the concept of hyperbolic equations to derive the way the textbooks given for hyperbolic, and then investigated for teachers and students based on the history of mathematics and introduced the concept of hyperbolic equations given derivation of instructional design selection bias. Finally, in-depth interviews with teachers discussed the comments and suggestions of the teachers on instructional design, derive the following conclusions:(1) stage hyperbolic teaching out of real life, and no unique mathematical methods (analog only oval), resulting in a lack of student interest in learning hyperbolic.(2) As students do not have much of a hyperbolic visual impression, the introduction of a single textbook approach will result in a one-sided understanding of the students, and therefore should be hyperbolic to establish the concept of teaching a different perspective.(3) For high school students "flat truncated cone on the top section of a hyperbolic " or " hyperbolic optical properties of the application " has a very good understanding, so they are able to accept the introduction of the concept of hyperbolic way.(4) in introducing the concept of hyperbolic equations, and the derivation of the standard choice of teaching methods, teachers and students complete opposite preference in the textbook way teachers and students are favored in instructional design based on mathematical history. The reason is considered the starting point of each is different, teachers pay more attention to the efficiency of teaching, teaching students to make them even more hope to generate interest in learning.(5) Despite writing more emphasis on teaching the concept of logical order, rather than the concept of historical sequence generated, but for suitable teaching theme, through the reconstruction of history, so that students go through the process of development of mathematical knowledge occurs, make mathematics learning to become "re-creation " would be a good way of teaching.Based on the above conclusion, we draw inspiration teaching, along with the history of mathematics, there are four hyperbolic based instructional design.