The Research On Teaching And Learning Of Spatial Vector And Three-dimensional Geometry

The spatial vector introduction three-dimensional geometry is one of key which mathematics curriculum reforms. Reform difficulty and the focal point lie in: A what type should the spatial vector place the position? What type should the traditional Euclidean space geometry place the position? How in the Euclidean space geometry teaching and the study, processes the good spatial vector correctly the position.This research has mainly used the questionnaire survey procedure, the interview law, the literature analytic method and the comparison research text analytic method, carries on the investigation to the northeast area three school six class's and grade's students as well as certain teachers, the centralism research space vector teaches to the three-dimensional geometry with the influence which study produces, including to course content, teaching method, three-dimensional geometry exercise, student's mathematics power of thought and so on four aspect influences.Since March,2007,author read the related spatial vector and the three-dimensional geometry curriculum, the teaching aspect massive literature, in this foundation, to "Full-time Ordinary Senior middle school Mathematics Program of instruction" and "the Ordinary High school Mathematics Curriculum Standard (Experiment)" about the spatial vector content request, has conducted the comparison research, simultaneously, to "Full-time Ordinary Senior middle school Textbook (Compulsory) Second Volume of Under (B)" and "Ordinary High school Curriculum Standard Experiment Textbook" about three-dimensional geometry and spatial vector curriculum content arrangement, has carried on the text contrast analysis. In March, 2008, through to the northeast area three schools (Liaoning Province experiment middle school, Heilongjiang Province experiment middle school, Daqing Experiment Middle school) the high school second year students has carried on the questionnaire survey, and has carried on the teacher questionnaire and the interview to these three school partial teachers. And has conducted the quite systematic analysis research in April, 2008 to the investigation data and the text analysis result.The investigation result demonstration mainly may divide into following two points: First, in the present high school mathematics teaching material, the spatial vector has become an independent knowledge system, increased the three-dimensional geometry course content, increased the teacher teaching difficulty. At the same time, to the student, increases one new solution three-dimensional geometry exercise method, the questionnaire result had demonstrated that, The good class and grade has percent seventy three student to use the vector method, the parallel class and grade has 40% student to use the vector method, in which has a half student to be able the good use vector method. The student in may again synthesize method and the vector method the free choice, therefore, reduced the student to study the three-dimensional geometry the difficulty.Second, the spatial vector is three-dimensional geometry one passes the law, the student so long as can solve the three-dimensional geometry exercise through the vector coordinates operation way and the algebraic expression operation way, and may see from many year college entrance examination test question, uses the algebraic expression operation way explanation the three-dimensional geometry exercise not to be many. Therefore, reduced the student to use the synthesis method probability, attenuated to the student space imagination ability training.The author believed that, these questions may the high school mathematics curriculum implement in the process to be improved again; the concrete method is as follows: First, the teacher in the teaching process, the attention space vector with other discipline relation, for example in the physics strength, and, carries on the spatial vector and the plane vector the contrast to teach, thus achieved reduces the student to accept the spatial vector difficulty the goal, then reduces teacher's teaching difficulty.Second, the teacher in the teaching process, uses the object teaching massively, lets the student contact more actual objects, enhances to the student space imagination ability raise.Third, in the teaching process, through topic multi-solutions, careful way balance vector methods and so on establishment, choice three-dimensional geometry sample question, exercise and the synthesis method in the student thought status, lets the student during study vector method, do not have to neglect the synthesis method.