初中数学老师在制定教案的时候，要注意培养学生的主动提问能力(2)

总之，《标准》在重视培养学生数学知识和技能的同时，比《大纲》更注重每个学生的情感、态度、价值观和综合能力的发展，付出重视学生潜在个性的发掘和发展。为学生各方面的可持续发展奠定良好的基础。

1.3 结构体系对比

《教学大纲》和《标准》以各自独特的结构体系体现各自的指导思想。 《教学大纲》主要由教学目标和教学内容的确定和安排、教学中应注意的几个问题、教学内容等组成。标准由前言、课程目标、内容标准、课程内容四部分组成。实施建议。前言包括基本概念和设计思路；课程目标包括总体目标和学校目标（第三学期7~9年级为初中）；课程实施建议包括教学建议、评价建议、教材编写建议、课程资源开发利用建议等。

《大纲》有一个简短的序言，简要描述了数学学科的性质、价值和功能。这与《标准》相同，但《标准》也在序言中阐述了基本概念。详细阐述了设计思路，有利于教材编写者和教师从整体上把握“标准”。

为保证新数学课程的开发和顺利实施，《标准》花了大量篇幅对课程实施提出建议。在实施建议中，通过阐述与实例相结合的方式，具体阐明《标准》所倡导的基本概念的内涵，及其在教材编写、教学过程、评价指标等方面的具体表现，方便数学教育工作者整体把握数学课程。

1.4 课程内容对比

为了实现各自的课程目标，“教学大纲”和“标准”呈现各自的课程内容。 《教学大纲》的教学内容分为代数和几何两部分，《标准》安排了“数与代数”、“空间与图形”、“统计与概率”、“实践与综合应用”（第三初中学期安排学科学习）”4个平行学习区。

(1)与《纲要》相比，《标准》的内容设计体现了“九年一贯”的思想。《标准》将9年分为3个部分（第三部分） 7~9年级（即初中），更注重小学和初中数学内容的衔接，也说明每个学生在接受义务教育的整个过程中，所学的数学是密切相关的，应该具有普遍性和基本的性和发育性。

(2)通过《教学大纲》规定的教学内容的教学，强调学生要掌握扎实的数学基础知识。通过课程内容的学习，《标准》强调学生的数学活动，培养学生的数学意识、符号感、空间概念、统计概念、应用意识和推理能力。而这些“隐藏”的目标并不是相互孤立的，不能通过某一部分内容来实现，它们相互渗透到整个数学课程的内容中。例如几何教学是培养和培养学生推理能力的一种方式，但绝不是唯一的方式[3]。推理训练也可以在代数、统计学等领域进行。事实上，数学课程内容的每个分支都充满了推理。

(3)在以往数学大纲的基础上，《大纲》规定的教学内容有了很大的创新，但与《大纲》相比，课程内容发生了很大的变化，有是加强和削弱的方面。

在强化内容方面，《标准》更注重学生数感和符号感的培养，注重口语计算和估计，提倡算法多样化，重点引导学生认识必要性证明，了解证明的基本过程，加强对学生“有理有据”的培养，强化了3D空间几何的相关内容，为学生提供了大量“直觉思维”的素材。 《标准》大大加强了“统计与概率”的内容，首次将“统计”概念作为义务教育阶段数学课程的重要目标之一，而《教学大纲》仅涉及代数统计的初步内容，几乎没有概率的内容。）”部分，将本应处于隐性位置的这个领域与其他知识领域并列。这是对“标准”的创新。它不仅强调这一领域，而且有助于改变长期脱离现实，学生有机会综合运用数学知识和方法解决实际问题，探索数学规律，体验数学与现实的联系，培养学生独立探索和合作交流的能力。 《纲要》还提到“至少每学年要组织一次探索活动”，加强学生实践机会，有利于培养学生探索精神，为学生交流合作创造条件。

在弱化内容方面，《标准》在保持基本笔试计算训练的同时，进一步控制了计算难度和速度。比如初中有理数的混合计算不超过3步；公式的简单记忆被淡化，多项式的计算被减少。 ，乘法公式和分解要求；弱化二次函数的极值问题；不单独设置“应用题”单元，取消对应用题的人为分类等。例如“大纲”中的“一元线性方程的应用”、“一个系统的应用” 《标准》中未规定线性方程组”等；删去部首、无理方程、可转化为一元二次方程的分数方程（2个以上）、二元二次方程、三元线性方程等的运算； reduce the requirements for formalization of the argumentation process and proving skills, only requiring proof of the basic properties of basic figures (triangles, quadrilaterals), aiming to let students master the basic proof methods. The textual expression requirements for the relevant terms in the course content have also been reduced, and attention has been paid to "dilute the form".

(4) Both "Outline" and "Standard" focus on the use of historical mathematics materials to strengthen students' ideological and moral education. The "Outline" proposes to use historical materials on algebra and geometry to ideological education for students. Mathematicians’ research on the Pythagorean theorem" and other content; The Standard recommends arranging relevant mathematical background knowledge to enrich students’ overall understanding of mathematics development. It can be seen that the mathematics historical materials listed in the "standard" are not limited to the country, and they have the courage to look at the world.

(5)"Standard" pays more attention to the application of new technology. Although the "Outline" mentions the use of calculators, it is only used to solve some complex calculation problems, such as square root and cube, etc., while the standard "Advocate the close integration of modern information technology with course content, and encourage the use of calculators and computers as powerful tools for research and problem-solving, and enhance students' understanding of mathematics. It can be seen that modern information technology is mentioned in the "Standard" Higher status.

1.5 Comparison of evaluation concepts

The evaluation of students' mathematics learning is to fully understand students' mathematics learning conditions, motivate students to study hard, and promote teachers to improve teaching. This is the consensus of the "Syllabus" and the "Standard". However, due to the difference in the curriculum goals of the two, This leads to different evaluation concepts.

Although the "Syllabus" proposes to improve teaching testing and evaluation, it is mainly limited to performance testing and evaluation. It pays more attention to examinations, and examinations are limited to written tests. The purpose, content, methods and methods of mathematics learning evaluation have not been fully considered. Results presentation etc.

The "Standard" presents a brand-new evaluation concept: (1) When evaluating, it pays attention to the results of students’ learning, but also to their learning process, not only paying attention to the level of students’ math learning, but also paying attention to their performance in learning activities. The emotions, attitudes and personality tendencies that come out emphasize students’ exposure of the thinking process of “doing mathematics”; (2) advocates diversified evaluation methods and changes the single written test mode (even if the basic knowledge and skills are tested, it is also consistent with The actual background is combined with the problem-solving process, focusing on examining students’ understanding of the meaning of the knowledge itself and its application on the basis of understanding). It is recommended to organically combine various methods such as examinations, project activities, writing papers, activity reports, student files, etc. ;(3) The subject of evaluation also shows a diversified trend. It is no longer a single model of teacher evaluation, but a combination of self-evaluation, student mutual evaluation, teacher evaluation, parent evaluation, and social-related personnel evaluation, advocating the formation of a unified A scientific and reasonable evaluation mechanism; (4) The presentation of the evaluation results is no longer a simple score or grade, but a combination of quantitative and qualitative presentations, giving full attention to the personality development of students, and striving to make every student get A successful experience.