目前，新一轮的课程改革正在全国范围内展开，从内容、理念到实施都发生了深刻变化。数列是高中数学的重要内容，是培养学生观察、分析、推理、逻辑思维和探索创新能力的重要章节，处于数学知识和数学方法的汇合点，起着承前启后的作用。同时数列问题有利于考察学生的思维、运算、应用能力，倍受高考命题者的关注。因此，如何与时俱进的理解这部分内容，高效率、高质量的进行这部分内容的教学，具有直接而又现实的意义。通过文献检索发现目前对数列的研究主要集中于具体的数列及其性质，对数列教学的研究主要是具体内容的教学设计及相关教学方法，各种教辅用书及相关数学著作也有比较详尽的叙述，但这些研究或是只注重结论，适用范围窄小，或是概括性太强，缺乏针对性，对数列内容中蕴含的思想方法的论述缺乏系统性，数列的应用价值未能充分体现，对学生数列学习中的困难与障碍认识不够具体与深刻。同时，本文通过访谈、测验、问卷等研究方法，对我校数列教学与学习情况进行了细致的调查与分析，认为教学中主要存在如下问题：师资力量相对较弱，流动性大，教师负担重，教学理念较为陈旧；重难点的剖析不到位，学习方法指引欠缺；数学思想方法在数列教学中没有被足够重视和培养；数学应用意识未被充分渗透。而在学生方面则集中表现为如下问题：学生基础差，缺乏学习的兴趣与信心；不能很好的把握学习重点，突破难点；数学学习缺乏系统性，数学思想方法理解不到位；数学应用能力差，从而一些同学虽在数学上下了很大功夫，但学习效率不高，成绩并不理想。因此，本文首先对数列通项与求和的类型与方法进行了系统总结，并在对教学大纲、考试大纲、新课程标准进行了认真分析与比较的基础上，结合自己多年的实际教学经验，提出提高数列教学质量的以下措施：立足现实，抓好“双基”教学；技术整合，多种方式并用；强调联系，形成知识体系；注重实质，掌握思想方法；联系实际，体现数学价值。最后，根据上文的结论与措施，精心设计了一篇教学案例，以期对同行有所启示。当然，由于能力与精力有限，不足之处在所难免，本人也将再接再厉，为我国的教育事业做出自己的贡献。

At present the New Course Criteria is spreading in the whole country, which needs great change in contents, ideology and implementation. Sequence of number is one of the important contents in senior maths teaching. It’s an essential chapter, which can cultivate students’ observation, analysis, reasoning, exploration and innovation; it connects the former and the latter. It can estimate students’ thinking, operation and application. Therefore, it draws the examiners’close attention.Thus how to understand this part at the present time and teach it with high efficiency and quality is of practial meaning.The author made a thorough literature review, finding the present study on sequence of number mainly focuses on the exact one and its quality. Also, when teaching sequence of number, the teacher mainly emphasizes the design of exact contents and relative teaching methods. Moreover, there are some specific description of teaching books, assisting ones and concerned works. But all of these emphasize more conclusions, not application. Such resulted in either limited usage or too much summary. The difficulties that the students may meet in the study haven’t given enough attention.The study employs interviews, tests, questionaires, ect to carefully investigate and analyze its present teaching and learning in our school. The findings show the following problems: lack of qualified teachers, change of teachers’post at random, teachers’heavy load, stale teaching ideology, students’ poor learning foundation, lack of students’ interest and confidence in study, not enough analysis of important and difficult points, deficiency of guidance in strategies, not enough cultivation of maths thought in teaching of sequence of number, not enough teachers’penetration of maths application and students’poor application in practice. Although the students work hard at it, the efficiency is not high and the grade is not ideal.The author, first, gave a systematic summary of the type and way of general term of sequence and its sum , and then, in his own teaching combined with the practical situation of the school, compared and analyzed the textbook, carefully read the Teaching Guidance, Examination Guidance and New Curriculum Criteria.The study got the following conclusion: grasp the “doule base” on reality; employ different technique; emphasize relation between different parts and form knowledge net; pay close attention to maths essence and master methods; embody the maths value combined with reality.At last, the authour provided a teaching design according to the conclusion and measures. It’s hoped that the study can be a reference left to others. Of course, there may be some shortcomings in this paper due to the limited ability and energy. Anyway, the author will continue to work hard and devote more to the cause of the education.