【作者】 陈峰；

【导师】 房之华；

【作者基本信息】 苏州大学 ， 学科教学（专业学位）， 2015， 硕士

【摘要】 圆锥曲线是高考中的重点和难点,是高中解析几何的核心内容,具有承上启下重要的作用.在这一章节,学生借助平面坐标系实现代数与几何、方程和曲线的相互转化,能够充分感受到数形结合的魅力所在.高中生学好圆锥曲线有利于塑造自身开拓、灵活、创新的思维模式.然而由于很多圆锥曲线问题的题意比较复杂,相对于其他章节,对学生的运算能力也提出了更高的要求,容易在分析和运算上形成学习障碍.那么学生在学习圆锥曲线的过程中,究竟有哪些具体的学习障碍?作为教师又应该如何应对这些学习障碍?本文将通过调查和分析高中生学习圆锥曲线中的认知水平与学习障碍,尝试探寻有利于排除学习障碍的教学方案.研究采用了定性与定量相结合的方法,以苏州市工业园区苏州大学附属中学高三理科的211名学生作为研究对象,借助SOLO分类法编制了测试题,划分了学生的解答,并结合调查问卷和访谈的结果调查了高中生在学习圆锥曲线过程中存在的学习障碍,主要有以下几点:(1)学生学习圆锥曲线的信心不足,普遍存在畏难情绪;(2)学生没有养成提前预习和及时复习的良好习惯,课堂听课方式被动;(3)学生对圆锥曲线的定义重视程度不足,做题时缺乏运用定义的意识;(4)学生基本运算能力不足,欠缺简化运算的方法和技巧;(5)学生头脑中缺乏数学思想方法的储备,做题时很难灵活运用.针对调查中发现的圆锥曲线学习障碍,本文提出以下应对策略:(1)关注学生的学习情感,通过培养学生的学习兴趣、提升学习信心、加强师生交流帮助学生克服对圆锥曲线的恐惧心理;(2)通过体验基础知识的生成过程、注意讲练结合、辨明圆锥曲线各定义之间的区别和联系,使学生遵循循序渐进、螺旋上升的认知规律,牢固掌握圆锥曲线的基础知识,学会合理运用定义;(3)通过规范学生的运算过程、采用课堂限时训练、培养良好的运算习惯、积累简化运算的方法提升学生的运算能力;(4)圆锥曲线解题中几种常见的数学思想方法有数形结合、化归、分类讨论、归纳猜想,本文根据上述数学思想方法的各自特点,制定了相应的训练措施,并提倡教师在平时的圆锥曲线教学中渗透以上数学思想方法;(5)使学生明确自己的学习目标,制定合理的学习计划,引导学生用好笔记本和纠错本,做到及时巩固,学会自我监控,通过提升学生的元认知水平,提高学生的自主能力,改善学习方式.更多还原

【Abstract】 Conical section is the emphasis and difficulty in the college entrance examination, is the core content of high school in analytic geometry, has the essential important role. In this section, the students with the help of a plane coordinate system to realize the mutual transformation between algebra and geometry, equation and curve, can fully feel the number form combining charm. High school students learn conic to shape their own development, flexibility, innovative thinking mode. However, because a lot of conic question the question is more complex, relative to other chapters, to student’s operation ability also put forward higher request, easy in analysis and calculation on learning disabilities. So students in the learning process of conic, exactly what specific learning disability? As a teacher should learn how to deal with these obstacles? This article through the investigation and analysis of high school students cognitive level and learning disabilities in the learning conic, trying to explore to rule out the teaching plan of learning disabilities. Research adopted the combination of qualitative and quantitative methods, with three of the affiliated high school of suzhou industrial park of suzhou university science department 211 students as the research object, with the help of a SOLO taxonomy created test, divides the students’ answers, and combined with the results of questionnaire and interview survey that exist in the high school students in the learning process of conic learning disabilities, mainly include the following:(1) the students’ lack of confidence, the conic widespread fear;(2) the students have no students to form good habits, and prepare in advance and timely review of classes with passive;(3) the student to the definition of a conic degree is insufficient, lack of the consciousness of using the definition, to solve the problem.(4) the students lack basic operation ability is insufficient, simplify the operation methods and techniques;(5) the students lack reserves, the method of mathematical thinking in the mind is difficult to apply to solve the problem.In view of the conic learning disabilities in the survey found, this paper puts forward the following strategies:(1) pay attention to student’s learning emotion, by cultivating the students’ interest in learning, enhance learning confidence, strengthen the communication between teachers and students to help students overcome their fear of conic;(2) through the experience knowledge generation process, pay attention to speaking practice combination, discern the difference between the definition and conical, causes the student to follow step by step, has risen in a spiral of cognitive law, firmly grasp the basic knowledge of conic, and learn to reasonable use definition;(3) through the specification of the operation process, uses the classroom students training, cultivate good habits of operation, accumulation of simplified computing method to promote students’ operation ability;(4) the conic problem solving mathematical thinking method of several common in several form combining, transforming, classification, discussion, inductive hypothesis, this paper, based on the characteristics of the mathematics thinking method, formulate the corresponding training measures, and promote the teachers in the usual teaching of conic penetration above mathematical thinking method;(5) make the students to clear their own learning goals, formulate reasonable plan and guide the student to use his notebook and error correction, achieve timely consolidated, self-monitoring, by enhancing the students’ metacognitive level, improve the students’ independent ability and improve learning.更多还原