【作者】 赵宇；

【导师】 孔凡哲；

【作者基本信息】 东北师范大学 ， 课程与教学论， 2008， 硕士

【摘要】 空间向量引入立体几何是数学课程改革的重点之一。其中改革的难点和焦点在于:空间向量应该放在一个什么样的位置?传统的立体几何又应该放在一个什么样的位置?如何在立体几何的教学和学习中,正确处理好空间向量的位置问题。本研究主要采用问卷调查法、访谈法、文献分析法和比较分析法,对东北地区三所学校的六个班级学生以及若干教师进行调查,集中研究空间向量对立体几何教与学产生的影响,包括对教学内容、教学方法、学生数学思维能力三方面的影响。自2007年3月开始,笔者查阅了有关空间向量与立体几何课程、教学方面的大量文献,在此基础上,对《全日制普通高级中学数学教学大纲》与《普通高中数学课程标准(实验)》关于空间向量内容的要求,进行了比较研究。同时,对《全日制普通高级中学教科书(必修)第二册下(B)》与《普通高中课程标准试验教科书》关于立体几何与空间向量的课程内容安排,进行了文本对比分析。2008年3月,对东北地区三所学校(辽宁省实验中学、黑龙江省实验中学、大庆实验中学)高中二年级学生进行了问卷调查,并对这三所学校的部分教师进行了教师问卷与访谈。同时,于2008年4月份对调查的数据与文本分析的结果进行了比较系统的分析研究。调查结果的显示主要可以分为以下两点:第一,在现行的高中数学教材中,空间向量成为了一个独立的知识体系,增加了立体几何的教学内容,增加了教师教学的难度。同时,对学生来说,增加了一种新的解决立体几何习题的方法。问卷结果显示:实验班级有73%的学生采用向量法,平行班级有60%的学生采用向量法,其中均有一半的学生能够较好的使用向量法,学生可以在综合法与向量法中自由选择。因此,引入向量可以适当降低了学生学习立体几何的难度。第二,空间向量是立体几何的一个通法,学生只要通过向量坐标运算方式和代数式运算方式就能够解决立体几何习题,并且从多年的高考试题中可以看出,采用代数式运算方式解答的立体几何习题不多。因此,引入向量降低了学生使用综合法的几率,在一定程度上弱化了对学生空间想象能力训练的要求。笔者认为,这些问题经过妥善处理,都可以在高中数学课程实施过程中得到改善:第一,在教学过程中,注重空间向量与其它学科的联系,注意空间向量与平面向量的对比讲授,从而有效降低学生接受空间向量的难度,降低教师的教学难度。第二,在教学过程中,大量采用实物教学,让学生接触更多的实际物体,对于培养学生的空间想象能力十分有利。第三,在教学过程中,通过一题多解,精心编制或选择立体几何例题、习题等方式平衡向量法和综合法在学生思想中的地位,让学生在学习向量法的同时,不忽视综合法。更多还原

【Abstract】 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.更多还原