摘 要：通过对高中生数学学习现状的调查分析,发现传统的数学教学只注重数学教材的知识编排顺序，缺少从整体上把握内容的有效方法，对学生的认知发展没有起到很好的促进作用；教学中传授给学生的知识大多是零散不系统的；同时对学生的学法指导重视不够。而且，学生对数学知识的认识存在着偏差，不善于总结、归纳，使他们的学习处于被动状态，不利于他们能力的提高。
认知学习理论指出，数学学习的过程即是新的学习内容与学生原有的数学认知结构相互作用，形成新的数学认知结构的过程。因此，教师的教学活动的出发点应该是学生已有的认知结构，落脚点应该是使学生构建尽量良好的数学认知结构。
针对上述情况，本文从当代认知学习理论和系统论出发，阐述了整体教学,数学认知结构理论以及整体教学在优化数学认知结构中的作用。在此基础上提出了整体教学所遵循的四条原则（整体性原则，结构化原则，建构性原则和归纳整理原则），课堂教学基本程序及三条教学策略（创设良好问题情景；在整体结构下进行重点知识讲解；在整体结构下建立知识链，指导学生对知识进行总结归纳）。并进行了实验研究，通过对实验所得数据的综合分析，验证了文中所提出策略的有效性,并得出下列结论：
整体教学加强了学生认知的灵活性，表现为解题思路开阔，解题方法多样。能够从整体入手，将几何、代数相关知识有机结合。学生整体认知结构的关联性很强，检索知识迅速敏捷。学生认知结构的完备性得到优化，分析综合问题的思路清晰明了，解决问题的能力得到了提高。
【关 键 词】 整体教学 数学认知结构 教学策略
Abstract：Through investigating and analyzing students’ study of math in high school, we find that traditional mathematic teaching only pays attention to the arrange of knowledge in mathematic teaching material while neglects available methods of grasping knowledge as a whole, and as a result, it has not accelerated the development of student’s cognition well. The knowledge taught by teachers is mostly not systemic; and the teaching doesn’t pay attention to directing students’ study methods. Furthermore, most of students’ study in a passive way because they have cognitive warps on mathematics knowledge , and are not good at summarizing and concluding what they’ve learned. So it is not good for advancing their abilities.
Cognitive learning theory points out that mathematics learning process is a process of forming new mathematics cognitive structure through combining new learning content and student’s intrinsic mathematics cognitive structure. So teaching should begin with students’ intrinsic cognitive structure then student can form good mathematics cognitive structure.
In view of what we’ve mentioned above, the paper expounded theories of holistic teaching, mathematics cognitive structure and the use of holistic teaching in optimizing mathematics cognitive structure. Based on it the paper brought up four principles that holistic teaching should follow (holistic principle, structure principle, construction principle and summing up principle), basic procedures and three teaching policies of classroom teaching (set up proper question scenes; explain important knowledge under holistic structure; build chains of knowledge and direct students to conclude knowledge under holistic structure). A lot of experiments have been done to support what is mentioned above. Through interactively analyzing experimental datas. It turned out that the policies brought up in the paper is available and the conclusion is as follows:
Holistic teaching strengthened the flexibility of students’ cognition .It shows that the thinking of solving problems is opened, and the methods became varied. Students combine knowledge of geometry and algebra as a whole. The association of students’ holistically cognitive structure is strong and students can search knowledge rapidly and smartly. The maturity of student’s cognitive structure is optimized; the thinking of analyzing integrated problems becomes clearer and the ability of solving problems is improved.
【 Key Words 】 Integer teaching； Mathematical cognitive structure； Teaching policy
1 问题的提出
1.1 优化学生数学认知结构的必要性
1.1.1 时代发展的要求
在当今科学技术突飞猛进发展、知识更新日益频繁和加快的时代，需要人们具有创新性学习能力，终身学习的能力和学会学习以求应变的能力。因此，教育工作的重心不仅是教给学习者固定的知识，而是转向塑造学习者新型的人格，学校教育的根本任务则在于使学习者学会如何学习、如何劳作、如何与他人共同生活以及如何生存。学习者应当能灵活运用各种学习方式，形成适合自己的学习套路，成为一个善学者；而要培养出一个个的善学者，教师应当形成一套相对稳定的、独具风格的和关注学生发展的教学方法。
