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初中数学课程标准解读心得体会 篇1

2022年4月21日，教育部颁布了2022新课程标准，将于今年9月1日起实行。暑假期间，在周林茜优秀教学能手工作站的指导下，我结合史宁中教授的课标解读，对2022新课标进行了认真的学习，使我获益匪浅。

On April 21, 2022, the Ministry of Education issued the 2022 new curriculum standard, which will be implemented on September 1 this year. During the summer vacation, under the guidance of Zhou Linxi's excellent teaching expert workstation, I carefully studied the 2022 new curriculum standard in combination with Professor Shi Ningzhong's interpretation of the curriculum standard, which has greatly benefited me.

一、2022年新课标出台的意义

1、 The significance of the new curriculum standard in 2022

党的十九大强调，“落实立德树人根本任务，发展素质教育”。习近平总书记提出培养民族复兴大任时代新人的新要求，中央作出关于义务教育深化教育教学改革和“双减”工作决策部署要求。并且现阶段教育发展对人才培养提到糊了新要求、新挑战。加之2011版课标在实行过程中还存在一些与新形势新要求不适应的地方，这些因素都使新课标颁布成了必然要求。

The 19th National Congress of the Communist Party of China emphasized that "we should implement the fundamental task of building morality and cultivating people, and develop quality education". At the present stage, the development of education has raised new requirements and challenges for talent cultivation. In addition, during the implementation of the 2011 curriculum standard, there are still some places that are not suitable for the new situation and new requirements. These factors have made the promulgation of the new curriculum standard an inevitable requirement.

二、2022新课标“新”在何处

2、 Where is the "new" of 2022 new curriculum standard

2022新课标在以下方面做出了调整：

The 2022 new curriculum standard has made adjustments in the following aspects:

1、明确界定了数学核心素养内涵，2022版新课标新增了核心素养这个概念：会用数学的眼光观察现实世界，会用数学的思维思考现实世界，会用数学的语言表示现实世界。

1. The connotation of mathematical core literacy is clearly defined, and the 2022 new curriculum standard adds the concept of core literacy: be able to observe the real world with mathematical eyes, think about the real world with mathematical thinking, and express the real world with mathematical language.

2、调整细化了学段的划分，2011版的课标中小学是分为两个学段的，而2022版新课标分为了三个学段。

2. The adjustment has refined the division of learning periods. The curriculum standard of 2011 edition is divided into two learning periods for primary and secondary schools, while the new curriculum standard of 2022 edition is divided into three learning periods.

3、结构化整合课程内容，学段目标在知识技能方面难度有所下降，把一些知识的学习转移到了初中，但是在问题解决方面的难度则大幅度提。

3. Structured and integrated curriculum content, the difficulty of learning phase objectives in knowledge and skills has decreased, and some knowledge learning has been transferred to junior high school, but the difficulty in problem solving has been greatly improved.

4、趋向多学科融合，注重实际运用。

4. It tends to be multidisciplinary and focuses on practical application.

5、增加学业质量标准，形成新的教学评价，2022版的新课标对于学习内容的评价有了明确规定，建议直接给出了教学评价建议和学业考试水平建议。

5. Increase the academic quality standards to form a new teaching evaluation. The new curriculum standard of 2022 has clear provisions on the evaluation of learning content, and the suggestions directly give suggestions on teaching evaluation and academic examination level.

三、《新课标》学习后对今后教学的几点思考

3、 Reflections on the future teaching after learning the new curriculum standard

1、教学中必须以初中阶段学生核心素养为导向

1. The teaching must be guided by the core quality of the junior middle school students

2022新课标明确界定了数学核心素养内涵：会用数学的眼光观察现实世界，会用数学的思维思考现实世界，会用数学的语言表示现实世界。这就要求我们在备课时整体去思考：在这节课的教学中，我是要让学生用数学的眼光去看问题还是让学生用数学思维去思考问题，或者是用数学的语言去表达问题。进而再去考虑，我在整节课的教学中用什么样的方式方法去实现这个核心素养目标。当然，有时候我们一节课无法达成这一目标，那么我们及应该思考，在这一章节中如何实现，或者在这一学期的教学中如何实现。

The 2022 new curriculum standard clearly defines the connotation of mathematical core literacy: be able to observe the real world with mathematical eyes, think about the real world with mathematical thinking, and express the real world with mathematical language. This requires us to think as a whole when preparing for the lesson: in the teaching of this lesson, I want students to look at problems with mathematical eyes, or let students think about problems with mathematical thinking, or express problems with mathematical language. Then I will think about how I can achieve this core quality goal in the whole class. Of course, sometimes we can't achieve this goal in one class, so we should think about how to achieve it in this chapter or in this semester's teaching.

The 2022 new curriculum standard clearly defines the connotation of mathematical core literacy: be able to observe the real world with mathematical eyes, think about the real world with mathematical thinking, and express the real world with mathematical language. This requires us to think as a whole when preparing for the lesson: in the teaching of this lesson, I want students to look at problems with mathematical eyes, or let students think about problems with mathematical thinking, or express problems with mathematical language. Then I will think about how I can achieve this core quality goal in the whole class. Of course, sometimes we can't achieve this goal in one class, so we should think about how to achieve it in this chapter or in this semester's teaching.

2、教学中必须以新课标的要求为准则

2. Teaching must be guided by the requirements of the new curriculum standard

这就要求我们不仅要清楚新课标中哪些知识点的教学有变化，还必须要清楚每个知识点的教学要求。掌握了这些，我们在教学中才能清楚本节课的具体的教学目标是什么，重难点是什么，进而确定用什么样的教学方式，以及将这个知识点讲到什么样的层次。是了解还是理解，是熟记还是掌握？比如，之前的教学中涉及到的证明都是几何证明，而新课标要求中不仅涉及几何证明还加入了代数证明。这些问题都对我们的教学提出。

This requires us not only to know which knowledge points in the new curriculum have changed in teaching, but also to know the teaching requirements of each knowledge point. With this knowledge, we can know what the specific teaching objectives of this lesson are, what the key points and difficulties are, and then determine what kind of teaching methods to use and what level to talk about this knowledge point. Understand or understand, memorize or master? For example, the proofs involved in the previous teaching are all geometric proofs, while the requirements of the new curriculum standard not only involve geometric proofs but also add algebraic proofs. These questions are all put forward to our teaching.

3、教学中必须以核心素养的要求去评价

3. Teaching must be evaluated according to the requirements of core quality

2022新课标明确界定了数学核心素养内涵：会用数学的眼光观察现实世界，会用数学的思维思考现实世界，会用数学的语言表示现实世界。这就要求我们在备课时整体去思考：在这节课的教学中，我是要让学生用数学的眼光去看问题还是让学生用数学思维去思考问题，或者是用数学的语言去表达问题。进而再去考虑，我在整节课的教学中用什么样的方式方法去实现这个核心素养目标。当然，有时候我们一节课无法达成这一目标，那么我们及应该思考，在这一章节中如何实现，或者在这一学期的教学中如何实现。

The 2022 new curriculum standard clearly defines the connotation of mathematical core literacy: be able to observe the real world with mathematical eyes, think about the real world with mathematical thinking, and express the real world with mathematical language. This requires us to think as a whole when preparing for the lesson: in the teaching of this lesson, I want students to look at problems with mathematical eyes, or let students think about problems with mathematical thinking, or express problems with mathematical language. Then I will think about how I can achieve this core quality goal in the whole class. Of course, sometimes we can't achieve this goal in one class, so we should think about how to achieve it in this chapter or in this semester's teaching.

The 2022 new curriculum standard clearly defines the connotation of mathematical core literacy: be able to observe the real world with mathematical eyes, think about the real world with mathematical thinking, and express the real world with mathematical language. This requires us to think as a whole when preparing for the lesson: in the teaching of this lesson, I want students to look at problems with mathematical eyes, or let students think about problems with mathematical thinking, or express problems with mathematical language. Then I will think about how I can achieve this core quality goal in the whole class. Of course, sometimes we can't achieve this goal in one class, so we should think about how to achieve it in this chapter or in this semester's teaching.

总之，《新课标》的实施，给我们的教学指引了方向，也对我们的教育教学提出了新的更高的挑战，我们需要不断学习新课标的理念，创新实践新课标的要求，努力提升自身的专业素质和教育教学水平，为实现党的“落实立德树人根本任务，发展素质教育”的目标，尽自己的微薄之力。

In a word, the implementation of the New Curriculum Standards has guided our teaching and has posed new and higher challenges to our education and teaching. We need to constantly learn the concept of the new curriculum standards, innovate and practice the requirements of the new curriculum standards, strive to improve our professional quality and education and teaching level, and do our little to achieve the Party's goal of "implementing the fundamental task of cultivating morality and developing quality education".

初中数学新课标解读心得体会 篇2

我们的生活离不开数学，每天的日常生活中处处都有数学的影子，这是数学最基础的运用。数学课程也具有基础性、普及性和发展性，能通过对数学课程的学习，掌握适应现代生活及进一步学习必备的知识和技能。

Our life is inseparable from mathematics. Every day in our daily life, there is a shadow of mathematics everywhere, which is the most basic application of mathematics. Mathematics curriculum is also basic, universal and developmental. Through learning mathematics curriculum, students can master the necessary knowledge and skills to adapt to modern life and further study.

数学是一切自然科学的基础。比如计算飞船“摆脱”地球引力的速度，是数学；生产精密仪器的时候不断调整数据更精准，是数学；物理坐标需要数字记录，物体运动轨迹需要建立数学模型，是数学；化学反应的进行速度、反应程度，以及反应过程的吸热放热、化学方程式的表达，也需要数学。上至天文，下至地理，所有涉及到计算的自然科学，全都与数学有关，而这些自然学科又相互融合，不断发展，衍生出各行各业。足可见数学之用的广泛性。

Mathematics is the foundation of all natural sciences. For example, it is mathematics to calculate the speed of spaceship "getting rid of" the earth's gravity; When producing precision instruments, it is mathematics to constantly adjust the data more accurately; The physical coordinates need to be digitally recorded, and the object motion track needs to be modeled mathematically; The speed and degree of chemical reaction, the heat absorption and heat release in the reaction process, and the expression of chemical equations also need mathematics. From astronomy to geography, all the natural sciences involved in computing are related to mathematics, and these natural disciplines are integrated with each other, developing constantly, and deriving various industries. It shows the universality of mathematics.

2021年4月21日，教育部印发义务教育课程标准（2022年版），现就《义务教育数学课程标准（2022年版）》谈谈数学组老师的研读心得。

On April 21, 2021, the Ministry of Education printed and distributed the compulsory education curriculum standard (2022 edition). Now, we will talk about the research experience of mathematics teachers in the compulsory education mathematics curriculum standard (2022 edition).

一、数学何以重要

1、 Why Mathematics Is Important

数学，是每一个学生必学的一门学科，数学知识我们每天也在用。对大多数人来说，小学学到的数学知识亦足够，随着年级的升高，我们会发现所学的数学知识越来越抽象，似乎离我们的生活越来越远，而数学的尽头是“哲学”。这也正体现了数学“化繁为简”这一学科特点。数学通过对现实世界的抽象化，以符号式就能高度概括出事物之间的关系，以及必然联系，在形成人的理性思维、科学精神和促进个人智力发展中发挥着不可替代的作用。

Mathematics is a subject that every student must learn. We also use mathematical knowledge every day. For most people, the mathematical knowledge learned in primary school is also sufficient. As grades rise, we will find that the mathematical knowledge learned is more and more abstract, which seems to be farther and farther away from our life, and the end of mathematics is "philosophy". This is also a reflection of the characteristics of mathematics as a discipline of "simplifying complexity". By abstracting the real world, mathematics can highly summarize the relationship between things and their inevitable connections in symbolic form. It plays an irreplaceable role in forming people's rational thinking, scientific spirit and promoting the development of personal intelligence.

对于“数学是什么”，课标在一开始就给出了概括性的定义：数学是研究数量关系和空间形式的科学，是培养孩子理性思维的重要学科。数学不仅是运算和推理的工具，还是表达和交流的语言。数学承载着思想和文化，是人类文明的重要组成部分。数学素养是现代社会每一个公民应当具备的基本素养。而在小学阶段，数学教育承载着落实立德树人的根本任务，实施素质教育的功能。通过数学课程学习激发学习数学的兴趣，养成独立思考的习惯和合作交流的意愿；发展实践能力和创新精神，增强社会责任感，梳理正确的世界观、人生观、价值观。

As for "what is mathematics", the curriculum standard gave a general definition at the beginning: mathematics is a science that studies quantitative relations and spatial forms, and an important discipline to cultivate children's rational thinking. Mathematics is not only a tool for calculation and reasoning, but also a language for expression and communication. Mathematics is an important part of human civilization, bearing thoughts and culture. Mathematics literacy is the basic literacy that every citizen in modern society should have. At the primary school stage, mathematics education bears the basic task of establishing morality and cultivating people, and the function of implementing quality education. Stimulate the interest in learning mathematics through learning mathematics courses, develop the habit of independent thinking and the willingness to cooperate and communicate; Develop practical ability and innovation spirit, enhance social responsibility, and sort out correct world outlook, outlook on life and values.

二、课标哪里有“变”

2、 Where does the curriculum standard change

（一）确立核心素养在课程目标中的导向作用

（1） Establish the guiding role of core literacy in curriculum objectives

新课标一个最引人注目的变化就是确立核心素养在课程目标中的导向作用，把培养学科核心素养提到一个前所未有的高度。

One of the most striking changes of the new curriculum standard is to establish the guiding role of core literacy in the curriculum objectives, and raise the cultivation of core literacy to an unprecedented height.

首先，我们需要明晰“核心素养”是什么。数学课程要培养的学生核心素养，主要包括三个方面，见图1；小学阶段数学核心素养的表现，见图2。

First of all, we need to clarify what the "core literacy" is. The core quality of students to be cultivated in mathematics curriculum mainly includes three aspects, as shown in Figure 1; See Figure 2 for the performance of mathematical core literacy in primary school.

图1核心素养的内涵

Figure 1 Connotation of Core Literacy

若用隐喻的方式来形容数学核心素养的“三会”，可以这样理解：“会用数学的眼光观察现实世界”，即用数与量，图与形来观察现实世界。如一瓶水，用语文的眼光观察是“水”字的结构和笔顺这些语文元素，用数学的眼光观察是瓶子的容积和水的体积这些数学元素。

If we use metaphor to describe the "three abilities" of the core mathematical literacy, we can understand it as follows: "ability to observe the real world with mathematical eyes", that is, to observe the real world with numbers and quantities, figures and shapes. Such as a bottle of water, the structure and stroke order of the word "water" are Chinese elements when viewed from a Chinese perspective, and the volume of the bottle and the volume of water are mathematical elements when viewed from a mathematical perspective.

“会用数学的思维思考现实世界”，即将问题简化、抽象化，使得方法和思维可迁移运用到其他学科乃至生活中。如我们日常整理房间，就蕴含着数学中的归纳与分类的方法与思想。“会用数学的语言表达现实世界”，数学语言是连接着数学思维与现实世界的媒介，数学语言的特点是简洁、清晰、符号化。如我们学习的数，＋-x÷＞＜=，字母表示数，解决问题的算式等，就是教孩子用数学语言表达现实世界及其与事物的关系。

"Think about the real world with mathematical thinking", that is, simplify and abstract problems, so that methods and thinking can be transferred to other disciplines and even life. For example, when we tidy the room daily, it contains the methods and ideas of induction and classification in mathematics. "Be able to express the real world in mathematical language". Mathematical language is the medium connecting mathematical thinking and the real world. Mathematical language is characterized by simplicity, clarity and symbolization. For example, the number we learn,+- X ÷ ＞＜=, the letter represents the number, the problem solving formula, etc., is to teach children to express the real world and its relationship with things in mathematical language.

图2核心素养的主要表现

Figure 2 Main Performance of Core Literacy

新课标中的课程目标以学生发展为本，以核心素养为导向，进一步强调使学生获得数学基础知识、基本技能、基本思想和基本活动经验（简称“四基”），发展运用数学知识与方法去发现、提出、分析和解决问题的能力（简称“四能”），形成正确的情感、态度和价值观。课程目标的素养导向，有利于转变将知识、技能的获得等同于学生发展的目标取向，引领教学实践及教学评价从核心素养视角来促进和观察学生的全面发展。用核心素养来表述课程目标，让课标“目中有人”。此举以“立”带“破”，让教师在教授“有用”之知识中贯穿“大用”之学识。

The curriculum objective in the new curriculum standard is based on the development of students and guided by core literacy. It further emphasizes that students should acquire basic mathematical knowledge, basic skills, basic ideas and basic activity experience ("four basics" for short), develop the ability to use mathematical knowledge and methods to discover, propose, analyze and solve problems ("four abilities" for short), and form correct emotions, attitudes and values. The quality orientation of curriculum objectives is conducive to changing the goal orientation that equates the acquisition of knowledge and skills with the development of students, leading teaching practice and teaching evaluation to promote and observe the overall development of students from the perspective of core quality. Use the core quality to express the curriculum objectives, so that the curriculum is "targeted". This move leads to "breaking" by "standing", so that teachers can teach "useful" knowledge through "great" knowledge.

（二）设计体现结构化特征的课程内容

（2） Design course content reflecting structural characteristics

在新课标的课程内容板块，首先映入眼帘的是小学由原来的两个学段调整为三个学段（见图3），且每个学段都有学业目标和评价标准。

In the course content section of the new curriculum standard, the first thing that came into view was the adjustment of the primary school from the original two study periods to three study periods (see Figure 3), and each study period had academic goals and evaluation criteria.

此外，各学段的主题变化较大。课程内容的结构化体现了学习内容的整体性，反映了学科本质的一致性、表现学生学习的阶段性。课程内容结构化，必然要求要以结构化的方式来组织教学内容，如以主题、项目、任务来组织结构化的课程内容，这也是我校目前各学科对于新课改的落地举措。

In addition, the themes of each learning period vary greatly. The structure of the course content reflects the integrity of the learning content, reflects the consistency of the nature of the subject, and shows the stages of students' learning. Structured curriculum content inevitably requires the organization of teaching content in a structured way, such as the organization of structured curriculum content with themes, projects and tasks. This is also the implementation of the new curriculum reform in various disciplines of our school.

正如许多专家所指出的，内容结构化并不意味着可以忽视或无视知识点，而是要在知识结构中去重新认识和定位知识点的意义与价值，要在学生的主动活动中实现知识点的教育价值。

As many experts have pointed out, content structure does not mean that knowledge points can be ignored or ignored, but that the significance and value of knowledge points should be re recognized and positioned in the knowledge structure, and the educational value of knowledge points should be realized in students' active activities.

（三）学业质量的评价方式更加丰富数学学习活动的实践性与丰富性对数学学业质量的评价方式提出了更多的需求，除了常用的的纸笔测试以外，表现性评价、增值性评价、过程性评价等方式的应用也更加综合和贴近学生发展实际。我校在对学生的综合评价中就加入了表现性评价的新型方式，还引入了多元主体评价，自主评价等操作方法，反馈更全面客观，导向更加明确科学，更加综合且真实地为每一位学生画像，引领学生的核心素养全面发展（见图4）。

（3） The evaluation method of academic quality has enriched the practicality and richness of mathematical learning activities, which puts forward more demands for the evaluation method of mathematical academic quality. In addition to the commonly used paper and pencil tests, the application of performance evaluation, value-added evaluation, process evaluation and other methods has become more comprehensive and close to the actual development of students. In the comprehensive evaluation of students, our school has added a new way of performance evaluation, and also introduced multiple subject evaluation, independent evaluation and other operating methods. The feedback is more comprehensive and objective, the orientation is more clear and scientific, and each student is more comprehensively and truly depicted, leading to the comprehensive development of students' core literacy (see Figure 4).

三、我们如何应“变”

3、 How should we "change"

从课标文本来看，学生素养发展，贯穿课标全文本，隐含在课程内容及教学实践中，体现在课程学习结果的具体描述中。要促成素养落地，需要更多教育协同方的共同努力。

From the text of the curriculum standard, the development of students' quality runs through the whole text of the curriculum standard, is implied in the curriculum content and teaching practice, and is reflected in the specific description of the learning results of the curriculum. To facilitate the implementation of literacy, more education partners need to work together.

（一）数学要整体性和一致性学习在数与代数中，新课标把原来的四个主题变为了“数与运算”和“数量关系”两个主题，把负数、方程、反比例移到了初中，这是不是意味着小学数学更轻松了？这个改动，按照史宁中教授的说法，其实是“更注重数学学习的整体性和一致性”的体现。他认为，数学的学习必须要能“串起来”，也就是孩子学到的知识要能有迁移。1。要呈现有结构的概念

（1） Mathematics should be studied in a holistic and consistent way. In number and algebra, the new curriculum has changed the original four topics into two topics: "number and operation" and "quantity relationship", and moved negative numbers, equations, and inverse examples to junior high school. Does this mean that primary school mathematics is easier? According to Professor Shi Ningzhong, this change is actually a reflection of "paying more attention to the integrity and consistency of mathematics learning". He believes that mathematics learning must be able to "string together", that is, the knowledge that children learn must be able to transfer. 1。 To present a structured concept

给孩子一个新概念，不仅要讲是什么，更要讲怎么比较，要有概念之间的区别和联系，能让孩子学会从一个知识点迁移到另一知识点，还能渐渐通过理解把这些知识点串起来。2。要能将方法学以致用教孩子的方法要让孩子觉得“有用”“好用”，在过去的小学数学中，用字母表示数的内容很少，并没有让孩子形成代数思想。课标提出加强孩子的代数思维，就是用字母一般性代表数，让孩子建立初步的“符号意识”，为以后学习方程打下基础。让孩子学会用抽象符号表示对象，会是将来数学学习的重点。中国教育学会副会长史宁中教授提出了孩子学代数的两个层次：两匹马→□□上面这个式子代表了感性具体→感性一般，叫做简约阶段。

To give children a new concept, we should not only talk about what it is, but also how to compare it. We should have the differences and connections between concepts, so that children can learn to move from one knowledge point to another, and can gradually connect these knowledge points through understanding. 2。 The method of teaching children should be "useful" and "easy to use". In primary school mathematics in the past, there was very little content of using letters to express numbers, which did not let children form algebraic ideas. The curriculum standard proposes to strengthen children's algebraic thinking, that is, to use letters to represent general numbers, so that children can establish a preliminary "symbol awareness" and lay a foundation for later learning equations. Let children learn to use abstract symbols to represent objects, which will be the focus of future mathematics learning. Professor Shi Ningzhong, Vice President of the Chinese Education Society, proposed two levels for children to learn algebra: two horses → □ □ The above formula represents the perceptual concrete → perceptual general, which is called the simplicity stage.

这个式子代表了感性一般→理性具体，叫做符号阶段。

This formula represents the general perceptual → specific rational, which is called the symbolic stage.

让孩子学会用抽象的符号表示对象，会是将来数学的重点。

Let children learn to express objects with abstract symbols, which will be the focus of mathematics in the future.

比如，孩子需要学会用符号表示对象的性质：

For example, children need to learn to use symbols to express the nature of objects:

当n是正整数的时候，2n是偶数。

When N is a positive integer, 2N is even.

还要学会用符号来表示对象的关系：

Also learn to use symbols to express the relationship of objects:

小明的爸爸比小明大30岁，如果小明a岁，爸爸b岁，那就可以写成：b=a+30

Xiao Ming's father is 30 years older than Xiao Ming. If Xiao Ming is A years old and his father is B years old, it can be written as: B=A+30

还可以用符号表示对象的规律：

You can also use symbols to represent the rules of objects:

一辆汽车以平均每小时60公里的速度行驶，t小时后行驶了s公里。可以写成：s=60t

A car runs at an average speed of 60 kilometers per hour, and it travels for S kilometers after T hours. It can be written as: S=60T

用符号表示对象的性质、关系和规律，是每个孩子都要培养的数学思维。未来也会从低年级开始渗透，比如让孩子接触这种式子：5-□□=2←→5=2+□□

Using symbols to express the nature, relationship and law of objects is a mathematical thinking that every child should cultivate. In the future, it will also infiltrate from the lower grades, for example, let children contact this formula: 5 - □□=2 ←→ 5=2+□□

用符号表示对象的性质、关系和规律，是每个孩子都应该培养的数学思维，如何引导孩子把一个个具象的内容，转化成抽象的符号，不仅仅是老师的任务，家长也可以在生活中多举例，以帮助孩子完成思维转换。

The use of symbols to express the nature, relationship and law of objects is a mathematical thinking that every child should cultivate. How to guide children to transform concrete content into abstract symbols is not only a teacher's task, but also parents can give more examples in life to help children complete the transformation of thinking.

3、更加注重跨学科的实践数学与其他学科的融合点比较多，比如语文课本里的曹冲称象，也能跨进数学课例，孩子通过重现曹冲称象的故事，能够自己探索“总量等于分量之和”这样的数学概念。通过综合与实践这个主题是希望把数学知识与日常生活联系得更紧密，让孩子们学会用数学的眼光看生活和传统文化。（二）更加重视对高阶思维的发展对比2011年课标中4-6年级的要求，能看到新课标对孩子的思维能力的要求是有所提高的。数学知识的学习量变少，但是对于数学知识的概念和性质的理解却更为重要，更关注概念+性质的理解。以往的数学题目可以靠背，考的是记忆层面。如：三角形内角和等于什么？但是未来的题目，将会更侧重考察孩子的数学思维层面，如：如果它不是直角三角形，那么它至多有几个钝角？也就是说，以后的题目将会更灵活，而不是让孩子简单地套公式，就能得出答案。所以新课标提出，要让孩子学会用推理的方式得到答案，重视推演的过程，是非常有必要的。经过小学数学学习，孩子们能探索出数与运算的一致性，形成符号意识、运算能力和推理意识，以形成更加高阶的思维方式；并能运用基本的数量关系，以及几何直观、逻辑推理和其他学科知识、方法，分析与解决问题，形成模型意识和初步的创新意识。

3. More attention is paid to the integration of interdisciplinary practical mathematics and other disciplines. For example, Cao Chong's image weighing in Chinese textbooks can also be used in mathematics lessons. Children can explore the mathematical concept of "total amount equals the sum of components" by reproducing the story of Cao Chong's image weighing. Through the theme of synthesis and practice, we hope to connect mathematics knowledge with daily life more closely, so that children can learn to look at life and traditional culture from the perspective of mathematics. （2） We pay more attention to the development of higher-order thinking. Compared with the requirements of grades 4-6 in the 2011 curriculum standard, we can see that the requirements of the new curriculum standard on children's thinking ability have been improved. The learning amount of mathematical knowledge is less, but the understanding of the concept and nature of mathematical knowledge is more important, paying more attention to the understanding of concept+nature. The past math problems can be back-to-back, and the test is memory level. For example, what is the sum of the internal angles of a triangle? But future questions will focus more on children's mathematical thinking. For example, if it is not a right triangle, how many obtuse angles does it have at most? That is to say, the questions in the future will be more flexible, instead of letting children simply use formulas to get answers. Therefore, the new curriculum standard proposes that it is necessary for children to learn to get answers by reasoning and attach importance to the process of deduction. After learning mathematics in primary school, children can explore the consistency between number and operation, form symbol consciousness, operation ability and reasoning consciousness, and form a higher level thinking mode; And be able to use basic quantitative relations, geometric intuition, logical reasoning and other disciplines' knowledge and methods to analyze and solve problems, and form model awareness and preliminary innovation awareness.

生活处处皆数学。我们也可以尝试在孩子提出的问题中寻找数学规律，引导他们进一步思考，为什么测核酸要10个人一组、为什么买彩票很难中奖、为什么井盖是圆形的……这些都是我们身边的数学。数学之“用”不仅仅是书本知识与应试技能，“聚焦核心，面向未来”是对数学新课标研读的总结。背公式、刷题的时代已一去不复返，知识最为重要的力量是对人身心潜能的激发和学习机制的改造，是对人性、人的精神世界的涵养，这时候，知识的内涵也从书本上的概念、原理、公式变成人在社会现实互动中的视野、立场和方法，变成了面对问题时的智慧与胆识，此时的知识才真正成为了个体力量，也就是真正的核心素养落地。数学之“大用”不仅在于启智增慧，更要能立德树人，把育人蓝图变成现实，培育一代又一代有理想、有本领、有担当的时代新人，为实现中华民族伟大复兴作出新的、更大的贡献！

Mathematics is everywhere in life. We can also try to find mathematical rules in the questions raised by children to guide them to further think about why it takes 10 people to test nucleic acid, why it is difficult to win the lottery, why the manhole cover is round... These are the mathematics around us. The "use" of mathematics is not only the book knowledge and examination skills, but also the summary of the study of the new curriculum standard of mathematics "focus on the core and face the future". The era of memorizing formulas and writing questions has gone forever. The most important power of knowledge is to stimulate people's physical and mental potential and transform the learning mechanism. It is also the cultivation of human nature and the spiritual world of people. At this time, the connotation of knowledge has changed from the concepts, principles and formulas on books to the vision, position and methods of people in social reality interaction, to the wisdom and courage when facing problems. At this time, knowledge has really become an individual power, That is to say, the implementation of the real core quality. The "great use" of mathematics is not only to enlighten and increase wisdom, but also to cultivate virtue, turn the blueprint of education into reality, cultivate new generation after generation of people with ideals, skills and responsibilities, and make new and greater contributions to the great rejuvenation of the Chinese nation!

初中数学课程标准解读心得体会 篇3

2022年4月颁布新课标后，我认认真真进行了阅读。新课标指出，学生是数学学习的主人，教师是数学学习的组织者、引导者与合作者，并要求教师实现角色转变，由传统的以讲授为主导的教学转变为提倡以探索和引导发现的教学。

After the new curriculum standard was issued in April 2022, I read it seriously. The new curriculum standard points out that students are the masters of mathematics learning, and teachers are organizers, guides and collaborators of mathematics learning, and requires teachers to realize the role change, from traditional teaching oriented teaching to teaching advocating exploration and guidance.

数学素养是现代社会每个公民应该具备的基本素养。数学教育既要使学生掌握现代化和学习中所需要的数学知识与技能，更要发挥数学在培养理性思维和创新能力方面不可替代的作用，因此，数学课程应致力于实现义务教育阶段的培养目标，要向全体学生，适应学生个性化发展的需要，使得人人都能获得良好的数学教育，不同的人在数学上得到不同的发展，作为一名初中数学教师要遵循新课标，上好每节课。

Mathematics literacy is the basic literacy that every citizen should have in modern society. Mathematics education should not only enable students to master the mathematical knowledge and skills needed in modernization and learning, but also give play to the irreplaceable role of mathematics in cultivating rational thinking and innovative ability. Therefore, mathematics curriculum should be committed to achieving the training objectives of compulsory education, adapt to the needs of students' personalized development, and enable everyone to obtain good mathematics education, Different people get different development in mathematics. As a mathematics teacher in junior high school, we should follow the new curriculum standards and teach each lesson well.

教师不再是课堂教学的主体，课堂不再是以教师为主体的单边的教学活动，是师生双向交流，交往互动，相互沟通，相互补充的过程；是学生围绕着教师设计的课堂这条主线，思维高速运转，不断发展，不断成熟的过程。在这过程中，学生应有能力的提高，数学思想方法的形成，成就感的喜悦，创新思维火花的迸射。

Teachers are no longer the main body of classroom teaching. Classroom is no longer a unilateral teaching activity with teachers as the main body. It is a process of two-way communication, interaction, mutual communication and mutual supplement between teachers and students; It is a process in which students revolve around the main line of the classroom designed by teachers, and their thinking runs at a high speed, develops and matures continuously. In this process, students should improve their ability, form mathematical thinking methods, feel the joy of achievement, and spark innovative thinking.

课堂教学要建立合理的科学的评价体系，既要关注学生的数学学习结果，也要关注他们学习的过程满分作文网；既要关注学生数学学习的水平，也要关注他们在学习活动中表现出的情感，态度的变化，关注学生个性与潜能的发展，调动学生学习的积极性。

Classroom teaching should establish a reasonable and scientific evaluation system, which should not only focus on students' mathematical learning results, but also on their learning process; We should not only pay attention to the level of students' mathematics learning, but also pay attention to the changes of their emotions and attitudes in learning activities, pay attention to the development of students' personality and potential, and mobilize students' enthusiasm for learning.

数学教学要关注个体差异，促使发展，不同的人在数学上得到不同的发展。数学教学同样也要让每个学生都有所收获，既要保证学困生能学得进去，要保证基础学生的整体发展，更不能压抑尖子生的个性及特长，教师要因材施教，因势利导，要通过多种途径及方法满足他们的学习需要，发展他们的数学才能。

Mathematics teaching should pay attention to individual differences and promote development. Different people have different development in mathematics. Mathematics teaching should also let each student gain something. It is necessary to ensure that students with learning difficulties can learn it, to ensure the overall development of basic students, and not to suppress the personality and expertise of top students. Teachers should teach students in accordance with their aptitude and guide them according to the situation. They should meet their learning needs and develop their mathematical talents through various ways and methods.

课程下的课堂教学，应是通过师生互动、生生之间的互动，共同发展的课堂。它既注重了知识的形成过程，注重了学生的情感体验和能力的培养。对新课改，课堂上要放下“架”，让学生喜欢你，充分发扬教学民主，尊重学生的人格，努力形成新型的、平等和谐的师生关系。因此，我们在教学中对教材的处理、教学过程的设计以及评价的方式都要以学生的发展为中心，以提升学生的全面发展为宗旨，这才是课改的最终目标。

The classroom teaching under the curriculum should be a class that develops together through the interaction between teachers and students and between students. It not only pays attention to the formation process of knowledge, but also pays attention to the emotional experience and ability training of students. For the new curriculum reform, we should put down the "shelf" in the classroom, let students like you, fully promote teaching democracy, respect students' personality, and strive to form a new, equal and harmonious teacher-student relationship. Therefore, the treatment of teaching materials, the design of teaching process and the way of evaluation in our teaching should be centered on the development of students, and the purpose is to promote the all-round development of students, which is the ultimate goal of the curriculum reform.

在今后的数学教学中，认真上好每节课，使得我的每个学生在每节数学课上都能有所收获，既学到数学知识，又获得能力的提高，思维的发展，数学思想的形成，发展学生的数学素养。

In the mathematics teaching in the future, every class should be carefully taught, so that each of my students can gain something in each mathematics class. They can not only learn mathematical knowledge, but also obtain the improvement of ability, the development of thinking, the formation of mathematical thinking, and the development of students' mathematical literacy.

初中数学课程标准解读心得体会 篇4

2022年4月，教育界发生了一件大事，那就是教育部颁布了《义务教育数学课程标准（2022年版）》。这是继2011年颁布的《义务教育数学课程标准》之后，时隔11年，教育的又一次重大变革。为了更好的帮助一线教师理解新课标，曹培英教授、史宁中教授先后通过线上活动，开展了《小学数学教学改进研究》、《义务教育数学课程标准修订总体情况介绍》专题讲座，让我们感受到新课程标准中的时代气息。下面就谈谈自己的几点感受：

In April 2022, a major event occurred in the education sector, that is, the Ministry of Education promulgated the Mathematics Curriculum Standards for Compulsory Education (2022 Edition). This is another major change in education after the 2011 Compulsory Education Mathematics Curriculum Standard. In order to better help front-line teachers understand the new curriculum standard, Professor Cao Peiying and Professor Shi Ningzhong successively carried out special lectures on "Research on the Improvement of Primary School Mathematics Teaching" and "Introduction to the Overall Revision of the Mathematical Curriculum Standard for Compulsory Education" through online activities, so that we can feel the flavor of the times in the new curriculum standard. Here are some of my feelings:

一、落实“立德树人”的根本任务

1、 Implement the fundamental task of "establishing morality and cultivating people"

习近平总书记多次强调，要全面贯彻党的教育方针，遵循教育教学规律，落实立德树人的根本任务，发展素质教育。义务教育课程规定了教育目标、教育内容和教学基本要求，体现国家意志，在立德树人中发挥关键作用。为了适应新的时代要求，与时俱进，《义务教育数学课程标准（2022年版）》应运而生。

Compulsory education curriculum stipulates educational objectives, educational contents and basic teaching requirements, reflects the will of the country, and plays a key role in establishing morality and cultivating people. In order to meet the requirements of the new era and keep pace with the times, the Mathematics Curriculum Standards for Compulsory Education (2022 Edition) came into being.

二、“综合与实践”被赋予具体内容

2、 "Synthesis and practice" is given specific content

综合与实践是小学数学学习的重要领域，在新课程标准中提出：小学的综合实践活动以“主题式学习”为主，初中可以尝试“项目式学习”。在主题式学习中，常见的量将以跨学科的内容形式设计在“综合与实践”中。比如：购物活动：认识人民币“元、角、分”；时间在哪里：认识时、分、秒；年、月、日的秘密：认识年、月、日等。

Synthesis and practice is an important field of mathematics learning in primary schools. In the new curriculum standard, it is proposed that comprehensive practical activities in primary schools are mainly "thematic learning", and junior high schools can try "project-based learning". In thematic learning, common quantities will be designed in the form of interdisciplinary content in "synthesis and practice". For example: shopping activities: knowing RMB "yuan, jiao, fen"; Where is the time: knowing hours, minutes and seconds; The secret of the year, month and day: know the year, month and day.

这让我想到在今年5月19日举行的包河区小学数学二片教学研讨线上活动中，来自屯溪路小学的欧阳老师给我们展示的《人民币使用手册》一课，欧阳老师采用的就是项目式学习，通过“量与计量领域”、“电子支付社会背景”和“国家主权”三个方面设计项目学习的内容：不扫码，7元可以怎么付？关于人民币，你都知道什么？关于人民币，你还想了解什么？《人民币使用手册》要包含哪些内容？如何制作“我会认”？整节课孩子们乐在其中，整个教学过程孩子们兴趣盎然，充分感受到了数学与生活的密切联系，数学学习的现实意义和应用价值，也在孩子们幼小的心灵中播下了国家主权的种子。由于课堂上的时间有限，所以重点探究了100元人民币。课后老师分时间段做了具体任务安排，让孩子们继续探究其他面值的人民币，并给它们做介绍，进一步丰富孩子们对人民币的认识。

This reminds me that in the online activity of Baohe District Primary School Mathematics II Teaching Seminar held on May 19 this year, Ouyang, a teacher from Tunxi Road Primary School, showed us the lesson "RMB User's Manual". Ouyang, a teacher, used project-based learning to design the content of project-based learning through three aspects: "quantity and measurement field", "social background of electronic payment" and "national sovereignty": how can I pay 7 yuan without scanning the code? What do you know about RMB? What else do you want to know about RMB? What should be included in the RMB User Manual? How to make "I can recognize"? The children enjoyed the whole lesson. The whole teaching process was full of interest. They fully felt the close connection between mathematics and life. The practical significance and application value of mathematics learning also sowed the seeds of national sovereignty in children's young minds. Due to the limited time in class, we focused on RMB 100. After class, the teacher made specific task arrangements in different periods, asking the children to continue to explore other denominations of RMB, and introduced them to further enrich the children's understanding of RMB.

三、传统文化中的数学

3、 Mathematics in Traditional Culture

2022版的新课程标准，特别注重传统文化的加入，培养学生的文化自信。比如：以“曹冲称象”的故事为依托，认识克、千克、吨、等量的等量相等、总量等于分量和；度量衡的故事、圆周率的故事等。史教授指出：要注意数学文化与其他学科的不同，要用数学的眼光去观察、数学的思维去思考、数学的语言去表达传统文化的知识。

The new curriculum standard of the 2022 edition pays special attention to the addition of traditional culture to cultivate students' cultural self-confidence. For example, based on the story of "Cao Chong Weighs Elephants", we should know that grams, kilograms, tons, equal quantities are equal, and total quantities are equal to the sum of quantities; A story of weights and measures, pi, etc. Professor Shi pointed out that we should pay attention to the difference between mathematical culture and other disciplines, and use mathematical vision to observe, mathematical thinking to think, and mathematical language to express the knowledge of traditional culture.

回想起2019年执教的《圆的认识》一课，课的最后，我呈现了古希腊数学家毕达哥拉斯的一句话：圆是一切平面图形中最美的图形。我的师傅刘主任评课时就指出：我国古代的教育家墨子就曾说过：圆，一中同长也。说的多好，外国数学家是从感官上感受圆的美，而我们的老祖先是从本质上揭示圆为什么这么美。不仅如此，刘辉的割圆术、祖冲之计算的圆周率等等，无不彰显我们的祖先对于圆探究的成果，这就是传统文化在数学中的渗透，这就是文化自信。我想，如何在数学课上更好的呈现数学史和中华传统文化，是我们每一位一线数学教师都应该去思考、去实践的。

Recalling the lesson "Understanding Circles" taught in 2019, at the end of the lesson, I presented the words of Pythagoras, an ancient Greek mathematician: Circle is the most beautiful figure in all plane figures. My teacher, Director Liu, pointed out when commenting on the class that Mozi, an ancient educator of our country, once said, "Round is equal to long.". Well said, foreign mathematicians felt the beauty of the circle from their senses, while our ancestors revealed why the circle was so beautiful in essence. Not only that, Liu Hui's circle cutting technique and Zu Chongzhi's calculation of pi all show our ancestors' achievements in circle exploration. This is the penetration of traditional culture in mathematics, and this is cultural self-confidence. I think that every front-line mathematics teacher should think and practice how to better present the history of mathematics and traditional Chinese culture in mathematics class.

2022年新课标已颁布数月有余，其中还有很多内容需要我不断地、反复地去研读，比如：方程移到初中、百分数移入“统计与概率”、增加了尺规作图和计数单位的内容等等。

The new curriculum standard for 2022 has been issued for more than a few months, and there are still many contents that I need to study repeatedly, such as: equation moved to junior high school, percentage moved to "statistics and probability", ruler drawing and counting unit added, etc.

不禁想起楚大夫屈原的一句话：路漫漫其修远兮，吾将上下而求索。虽然前路漫漫，但我必将砥砺前行，而新课标就是前行路上的那盏明灯，指引着我的数学教育之路。

I can't help thinking of the words of Qu Yuan, the doctor of Chu: The road is long and the road is long. Although there is a long way to go, I will forge ahead, and the new curriculum standard is the light on the way, guiding my math education.

初中数学课程标准解读心得体会 篇5

《义务教育数学课程标准（2022年版）》自公布以来，短时间成为数学同行们交流的热点话题。课程标准是教师教学的指挥棒，深入学习和领会课程标准的精髓，会让自身教学不走错路，少走弯路。通过一段时间的自学，自身对新课标也有些许体会和感悟，与同行们分享一下我的心得：

Since the publication of Mathematics Curriculum Standards for Compulsory Education (2022 Edition), it has become a hot topic of communication among mathematics peers in a short time. Curriculum standards are the baton of teachers' teaching. In depth learning and understanding the essence of curriculum standards will enable their own teaching not to take the wrong path, and less detours. After a period of self-study, I also have some experience and understanding of the new curriculum standard, and share my experience with peers:

一、夯实老内容，领会新导向

1、 Consolidate the old content and understand the new guidance

通过学习不仅夯实和重温了课程标准的老内容，更是解读了2022版新课标的新增内容和导向。课程标准从2001年出版到2011年出版，再到今年的2022年出版，基本上每十年改一次。今年新出版的新课标的指导思想中的基本理念和结构特征，与2011年版的还是有不少的变化。在基本理念中体现了“逐步形成适应终身发展需求的核心素养”，要设计体现结构化特征的课程内容，重点对内容进行结构化的整合。在探索激励学习和改进教学的评价中，要通过学业质量的标准的构建，融合“四基”“四能”和核心素养的具体表现，形成阶段性评价主要依据。

Through learning, we not only consolidated and reviewed the old content of the curriculum standard, but also interpreted the new content and guidance of the new curriculum standard 2022. The curriculum standards were published from 2001 to 2011, and then to 2022 this year. They are basically changed every ten years. The basic concepts and structural features in the guiding ideology of the new curriculum standards newly published this year are still quite different from those in the 2011 edition. In the basic concept, "gradually form the core quality to adapt to the needs of lifelong development" is reflected. It is necessary to design the curriculum content that reflects the structural characteristics, focusing on the structural integration of the content. In the evaluation of exploring and encouraging learning and improving teaching, we should integrate the specific performance of "four basics", "four abilities" and core accomplishments through the construction of the standards of academic quality to form the main basis for staged evaluation.

二、理论与实践相结合

2、 Combination of theory and practice

发现新课标并不是高不可及的“高大上”的标准，结合实践来解释主题结构化的意义，结构化突显内容的关联性，有助于知识与方法迁移，促进核心素养形成。强调内容结构化就是对学习内容的整体理解，对学生学习的整体把握，从基于单元的整体分析，对关键内容的深度探究，再通过核心概念的感悟，和知识与方法的迁移，促进学生整体发展，逐步形成核心素养。特别介绍了具有整体设计思路与内容结构化有密切关联的教学设计的理念和框架，强调了深度学习和单元整体教学可作为实现课程内容结构化的路径。

It is found that the new curriculum standard is not an unattainable "high and lofty" standard, and the meaning of topic structure is explained by combining practice. The structure highlights the relevance of content, which is conducive to the transfer of knowledge and methods and the formation of core literacy. Emphasize that content structure is the overall understanding of learning content, the overall grasp of students' learning, from the overall unit based analysis, the in-depth exploration of key content, and then through the perception of core concepts, and the transfer of knowledge and methods, to promote the overall development of students and gradually form core literacy. It particularly introduces the concept and framework of instructional design, which is closely related to the overall design idea and content structure, and emphasizes that deep learning and unit overall teaching can be used as the path to realize the curriculum content structure.

三、新名词的理解要结合教学实际

3、 Understanding of new nouns should be combined with teaching practice

我们老师往往纠结于专业术语的新名词，困惑于他人对教学的初步结论。比如什么是“整合思想”，就是改变过于注重以课时为单位的教学设计，推进单元整体教学设计，体现数学知识之间的内在逻辑关系，以及学习内容与核心素养表现的关联。在小学阶段，更多的体现的是培养学生的“意识和感受”，在初中阶段，更多的培养的是其“能力与观念”。

Our teachers often get entangled in new terms of professional terms and confused with others' preliminary conclusions about teaching. For example, what is "integration thinking" is to change the teaching design that pays too much attention to class hours, promote the overall unit teaching design, reflect the internal logical relationship between mathematical knowledge, and the relationship between learning content and core quality performance. In the primary school stage, what is more reflected is the cultivation of students' "consciousness and feelings". In the junior middle school stage, what is more developed is their "ability and concept".

四、学习过程中对问题的思考

4、 Thinking about problems in the learning process

如何在教学中更好地把握数学课程体现核心素养”和“如何深入理解课程标准的新要求”这样的系列问题会在我们学习课标时总在头脑中思考。通过思考感悟颇多：

A series of questions such as how to better grasp the core quality of mathematics curriculum in teaching and how to deeply understand the new requirements of curriculum standards will always be in our mind when we study the curriculum standards. Through thinking, we have gained a lot of insights:

1、社会文明的发展，影响和牵引着数学文明发展，要把数学与社会发展紧密相连。

1. The development of social civilization affects and pulls the development of mathematical civilization, and mathematics should be closely linked with social development.

2、不能叫用字母表示数，应该称为用字母表示关系、性质和规律。

2. Instead of using letters to express numbers, we should call it using letters to express relations, properties and laws.

3、“学科实践”指的就是我们教学实践，是实际教学中我们该怎么做。

3. "Discipline practice" refers to our teaching practice and how we should do in actual teaching.

4、对学生的计算思维的培养如何落实？事实上，就是要培养学生有逻辑地思考问题。

4. How to implement the cultivation of students' computational thinking? In fact, it is necessary to train students to think logically.

5、“会用数学的眼光观察世界，会用数学的思维思考世界，会用数学的语言表达世界”的“三会”目标里，不光要看世界外在的，还要将问题数学化、抽象化，来解决实际问题，它都是与现实世界相关联的，也就是说外在和内在的相结合。其具体表现更多的是内在的，例如：数感、量感和计算能力等等。

5. In the "three meetings" goal of "being able to observe the world with mathematical eyes, think about the world with mathematical thinking, and express the world with mathematical language", we should not only look at the outside of the world, but also mathematically and abstractly solve practical problems. It is all related to the real world, that is, the combination of the outside and the inside. Its specific performance is more intrinsic, such as: number sense, quantity sense and computing ability.

通过本次自学课标使我更能深刻的理解课标，让我去思考背后的教育价值和核心概念，促进我要能够质疑问难、反思自我、勇于探索、深入学习，从而掌握新课标核心思想的脉络，把握新时代教育思想的脉搏，凝心聚力再前行！

Through this self-study curriculum standard, I can better understand the curriculum standard, let me think about the educational value and core concepts behind it, and promote me to be able to ask questions, reflect on myself, be brave to explore, and learn in depth, so as to grasp the context of the core ideas of the new curriculum standard, grasp the pulse of the education ideas of the new era, and forge ahead with cohesion!

初中数学课程标准解读心得体会 篇6

学习新课程标准，在教学工作中给我提出了极大的挑战，作为一名一线的普通教师，接受课改新理念，感受课改新思维，使用课改新教材，至始至终将课改的精神贯穿于我的教学之中。经过努力，渐渐地从陌生走向了熟悉，从战战兢兢走向了从容应对。对我来说，新课改是一场对话，一座平台，更是一把迈向成功教育的钥匙。

Learning the new curriculum standards has posed a great challenge to me in my teaching work. As a front-line ordinary teacher, I accept the new ideas of curriculum reform, feel the new thinking of curriculum reform, use the new textbooks of curriculum reform, and always put the spirit of curriculum reform into my teaching. Through efforts, gradually from unfamiliar to familiar, from trembling to calm. For me, the new curriculum reform is a dialogue, a platform and a key to successful education.

回顾初中数学教学这二十几年走过的路，作为一名教师我庆幸，赶上了新课程改革，走进了新课程改革背景下的初中数学教学。在这一过程中，我真切地看到了自己成长的轨迹，真切地感受到了新课程改革给我们的孩子、学校和教师带来的活力和变化。“为了每一个学生的健康发展”是新课程改革的核心理念。但同时，新课程改革中暴露出的一系列的问题，也是让我们老师们要深思的。可喜的是，我们参与一线教学工作的老师已经能够理性地看待新课程改革，开始用批评与反思赋予课堂教学以新的生机，构建教学真的精彩。随着课改实践的不断深入，让我们发现了一个个充满生命活力的初中数学课堂。让我体会最深的是：课堂上师生之间的平等对话、共同参与和探究发展。以下我就围绕这几点谈谈自己学习新课程标准的体会：

Looking back on the past 20 years of mathematics teaching in junior high school, as a teacher, I am lucky to catch up with the new curriculum reform and enter the junior high school mathematics teaching under the background of the new curriculum reform. In this process, I really saw the track of my growth and felt the vitality and changes brought to our children, schools and teachers by the new curriculum reform. "For the healthy development of every student" is the core idea of the new curriculum reform. But at the same time, a series of problems exposed in the new curriculum reform also make our teachers think deeply. Fortunately, our teachers involved in the front-line teaching work have been able to look at the new curriculum reform rationally, and began to give new vitality to classroom teaching with criticism and reflection, so as to build a truly wonderful teaching. With the deepening of the practice of curriculum reform, we have found a number of junior high school math classes full of vitality. What makes me feel most deeply is the equal dialogue, joint participation and exploration and development between teachers and students in the classroom. I will talk about my experience of learning the new curriculum standards around these points:

一、平等对话是课堂教学的基础

1、 Equal dialogue is the foundation of classroom teaching

新课程要求转变教师角色，转变教学行为。教师不是绝对的权威，而是与学生平等的交流者，是学生的合作者。教学中教师的态度是否和蔼、亲切、有鼓动性，对学生是否民主、尊重、有亲和力，对教学过程有十分重要的影响。教师首先是学生学习的伙伴，同时才是学生学习的指导者，所以要走下讲台，走到学生中间，拉近与学生的距离，真正地俯下身子，和学生心贴着心，听听他们心中的疑惑，了解他们的喜怒好恶，帮助解决他们想努力解决的问题。为学生创造宽松、愉悦的教学氛围。给孩子真正的欣赏，就要给学生以心理的支持，创造良好的学习气氛，激发他们的表现欲望，因为“即使在最丑的孩子身上，也有新鲜的东西，无穷的希望。”在教学中，我们要做的是积极地看，积极地听，设身处地感觉学生的所作所为，所思所想。随时掌握课堂中的各种情况，根据这些情况考虑指导学生学习的方法，尤其是尊重学生个性，鼓励他们发表感受，谈自己的见解。

The new curriculum requires changing teachers' roles and teaching behaviors. Teachers are not absolute authority, but equal communicators and cooperators with students. Whether the teacher's attitude in teaching is kind, cordial and inspiring, whether the students are democratic, respectful and amiable, has a very important impact on the teaching process. Teachers are the partners of students' learning and the guides of students' learning at the same time, so they should step down from the platform, walk among students, close the distance with students, really lean down, and be close to students' hearts, listen to their doubts, understand their likes and dislikes, and help solve the problems they want to solve. Create a relaxed and pleasant teaching atmosphere for students. To give children real appreciation, it is necessary to give students psychological support, create a good learning atmosphere and stimulate their desire for performance, because "even the ugliest children have something new and endless hope." In teaching, what we should do is to look actively, listen actively, and feel what the students are doing, thinking and thinking. Keep abreast of various situations in the classroom, consider ways to guide students' learning according to these situations, especially respect students' personality, encourage them to express their feelings and talk about their own opinions.

二、共同参与是课堂教学的灵魂

2、 Joint participation is the soul of classroom teaching

“参与”是课堂教学的灵魂，教学的真正含义是教师教学生如何学习。因此，要使学生学会学习，就要从课堂教学改革入手，构建和谐平等的师生关系，使学生主体精神得到发挥、主体人格不断完善、养成主动学习的习惯，促进学生积极地、主动地、创造性地去掌握新的学习方式。在课堂教学中调动全体学生的学习积极性，使他们主动参与、全面参与、全程参与，兴趣盎然地学习、生动活泼地发展，是课堂教学的灵魂。学生的思维状态如何，直接影响学习的效率。教师一定要根据学生已有的生活经验，创设鲜明生动的情景，激活学生思维的兴奋点，真正使学生动脑、动口、动手，学思结合，乐于参与。在学生的学习过程中，学生永远是学习的主体，教师要为他们创设探究的氛围，组织他们在参与中学习，在活动中领悟，在创新中发展。能激发学生强烈的学习需要与兴趣的教学，能使学生获得积极的、深层次体验的教学，能给学生足够自主的空间、足够活动的机会的教学，能真正做到“以参与求体验，以创新求发展”的教学，才能有效促进学生的发展。

"Participation" is the soul of classroom teaching. The real meaning of teaching is that teachers teach students how to learn. Therefore, in order to make students learn to learn, we should start with the reform of classroom teaching, build a harmonious and equal relationship between teachers and students, give play to the students' subjective spirit, constantly improve their subjective personality, develop the habit of active learning, and promote students to actively, actively and creatively master new learning methods. In classroom teaching, it is the soul of classroom teaching to mobilize all students' learning enthusiasm, make them actively participate, fully participate, participate in the whole process, learn with interest, and develop lively. The state of students' thinking directly affects the efficiency of learning. Teachers must create vivid scenes based on the students' existing life experience, activate the excitement of students' thinking, and truly enable students to use their brains, mouths, hands, and learn and think together, and be willing to participate. In the learning process of students, students are always the subject of learning. Teachers should create an atmosphere of inquiry for them, organize them to learn in participation, comprehend in activities, and develop in innovation. Teaching that can stimulate students' strong learning needs and interests, enable students to obtain active and in-depth experience of teaching, provide students with enough independent space and enough opportunities for activities, and truly achieve the teaching of "participation for experience, innovation for development", can effectively promote students' development.

三、探究发展是课堂教学的精髓

3、 Exploring development is the essence of classroom teaching

在课堂教学中，要有意识地让学生在自主学习、交流合作中，逐步提高独立探究的意识，增强与人合作的需求感。从而学会学习、学会做事、学会做人，学会与人交往和合作。这是课堂教学研究的主攻方向。《数学课程标准》指出：“积极倡导自主、合作、探究的学习方式，必须根据学生身心发展和数学学习的特点，关注学生的个体差异和不同的需求，爱护学生的好奇心和求知欲，充分激发学生的主动意识和进取的精神。”我认为，应抓住“学生主体性的发展”和“探究精神、实践能力的培养”，着眼于学生的可持续发展，使学生成为具有综合素质的人才。这就极其需要拓宽教育教学的视野，数学中进行探究学习，对培养自主学习能力有极大的促进作用。数学中探究学习，是学生在实践中获取知识、方法、情感体验的过程。可以是学生感悟学习过程，领悟学习方法的过程。“探究”更重要的还不是结果，而是探究过程本身，然后获取探究的乐趣，培养学生主动探究的意识。探究性学习的目的在于改变学生由单纯地接受教师传授知识为探究学习方式，为学生构建开放的学习环境，提供多渠道获取知识，并将学到知识加以综合应用于实践的机会，促进他们形成积极的学习态度和良好的学习策略，培养创新精神和实践能力，发展学生个性。

In classroom teaching, students should consciously improve their awareness of independent inquiry and the need to cooperate with others in independent learning, communication and cooperation. Thus learn to learn, learn to do things, learn to behave, learn to communicate and cooperate with people. This is the main direction of classroom teaching research. The Mathematics Curriculum Standard points out: "Actively advocate the learning method of autonomy, cooperation and inquiry. We must pay attention to the individual differences and different needs of students according to the physical and mental development of students and the characteristics of mathematics learning, care for students' curiosity and thirst for knowledge, and fully stimulate students' initiative and enterprising spirit." I believe that we should focus on "the development of students' subjectivity" and "the cultivation of exploration spirit and practical ability", focus on the sustainable development of students, and make students become talents with comprehensive quality. It is extremely necessary to broaden the vision of education and teaching. Inquiry learning in mathematics can greatly promote the cultivation of autonomous learning ability. Inquiry learning in mathematics is a process in which students acquire knowledge, methods and emotional experience in practice. It can be the process of students' perception of learning process and learning methods. What is more important about "inquiry" is not the result, but the inquiry process itself, and then get the fun of inquiry, and cultivate students' awareness of active inquiry. The purpose of inquiry learning is to change students' way of inquiry learning from simply accepting knowledge imparted by teachers, to build an open learning environment for students, to provide multi-channel access to knowledge, and to integrate the learned knowledge into practice, to promote them to form a positive learning attitude and good learning strategies, to cultivate innovative spirit and practical ability, and to develop students' personality.

“随风潜入夜，润物细无声”，对孩子的教育不是一朝一夕的事情，需要我们的老师细心、耐心地教导、引领。但我相信随着新课程改革的不断深入，教学理念、教学手段的不断更新，会出现了更多让人们感到高兴的事情。我们的数学教学课堂才会真正地发出金子一般的光彩。

"Sneak into the night with the wind, moisten things silently". The education of children is not an overnight thing. Our teachers need to carefully and patiently teach and guide. But I believe that with the continuous deepening of the new curriculum reform and the continuous updating of teaching concepts and teaching methods, more things will come out that make people happy. Only in this way can our mathematics teaching classroom really shine like gold.

初中数学新课标解读心得体会 篇7

聚焦核心概念落实核心素养

——《义务教育数学课程标准（2022年版）》内容结构化分析

《义务教育数学课程标准（2022年版）》（以下简称《标准》）在课程理念、目标、内容等方面都有明显变化，明确落实立德树人的根本任务，体现了数学学科育人价值的课程理念，确定了核心素养导向的课程目标。课程内容的结构化是课程修订的重要理念，在这一理念下数学课程内容的结构和具体内容都有调整，理解和把握课程内容的结构化特征有助于准确把握《标准》，并有效落实于教学实践。

一、《标准》内容结构化的特征分析

为体现核心素养导向的课程目标，根据课程内容结构化整合的理念，《标准》在内容结构上进行了调整，在“数与代数”“图形与几何”“统计与概率”“综合与实践”四个领域下整合或调整了学习主题。

小学由原来的两个学段调整为三个学段，各学段的主题变化较大。初中阶段的主题变化不大，某些表述有所调整，如事件的概率改成随机事件的概率。“综合与实践”领域虽没有内容主题，但变化较大的是以跨学科主题学习为主，并将部分知识内容融入其中。

（一）内容结构化体现了学习内容的整体性

课程内容的结构化通过主题整合的方式呈现，体现了学习内容的整体性。

在“数与代数”领域，小学三个学段的主题由原来的“数的认识”“数的运算”“常见的量”“探索规律”“式与方程”“正比例、反比例”六个整合为“数与运算”和“数量关系”两个。这不只是形式上的变化，更是从学科本质和学生学习视角对相关内容的统整，更好地体现了学科内容的本质特征和学生学习的需要。“数与运算”主题将数的认识和数的运算两个核心内容进行整合，将数与运算作为一个整体进行组织，体现二者之间的密切关联。小学阶段的运算都是数的运算，包括整数、小数、分数运算。数与运算不可分，数的认识包含数的抽象表达、数的大小比较等，自然数从小到大就是一个累加的过程，从1开始每增加一个后继（+1）就得到一个新的数，其中蕴含了加的运算，数的大小比较也与运算密切相关。运算的重点在于理解算理、掌握算法，算理的理解最终都要追溯到数的意义。如加法运算，整数和小数的加法是相同数位上的数相加，分数的加法是相同分母的分数直接相加，也就是分数单位相同的分数相加，即分母不变、分子相加。整数、小数、分数的加法计算都可以理解为相同计数单位的个数相加。将数与运算整合成一个主题，有助于从整体上理解数和运算，为学生从整体上把握和理解数学知识与方法，形成数感、符号意识、运算能力、推理意识等核心素养提供基础。“数量关系”主题突出了问题解决的内容载体和问题解决能力培养。常见的数量关系、式与方程、正比例、反比例和探索规律等内容得到整合（方程移到第四学段），这些内容的本质都是数量关系。从数量关系的视角理解和把握这些内容的教学，有助于从整体上认识这些内容的核心概念。数量关系的重点在于用数和符号对现实情境中数量之间的关系和规律进行表达，凸显用数学模型解决现实情境中的问题。在数量关系主题下，包含了用四则运算的意义解决实际问题，理解和运用常见的数量关系解决问题，从数量关系的角度理解字母表示关系和规律、比和比例等内容。初中第四学段的“数与式”也是数与运算的延伸，本质上是数的认识扩展，以及数与式的运算。“方程与不等式”“函数”两个主题要求学生较为系统地学习数量关系，并进一步学习变量之间的数量关系，探索事物的变化规律。从这个意义上说，义务教育阶段的“数与运算”和“数与式”构成了一个统整的主题；“数量关系”和“方程与不等式”“函数”构成了一个统整的主题。

在“图形与几何”领域，小学三个学段的主题整合为“图形的认识与测量”“图形的位置与运动”。图形的认识重点是图形特征的探索与描述，图形的测量是对图形大小的度量，图形的认识与图形测量需要从整体上把握。图形的认识是对物体形状的抽象图形进行表示，重点是认识图形的特征。图形特征的认识与图形的测量有密切关系，如长方形相对的边相等这一特征，需要通过测量确认其正确性。图形的测量离不开对图形的认识，图形测量的过程与结果都与具体图形的特征密切相关。探索图形的周长、面积、体积的问题，一定要与具体的图形建立联系，对图形特征的把握直接影响图形测量的学习。如学生在学习长方形面积时，在一个长和宽都是整厘米的长方形中，摆满面积单位（1平方厘米的小正方形），面积单位的个数就是其面积。这样的操作之所以可行，与长方形的四个角都是直角有关。探讨平行四边形面积就没有这么简单，直接摆小正方形就行不通，要将平行四边形转化成长方形才可以。图形的认识和测量的整合，凸显了两个主题内容之间的内在联系，有助于学生从整体上理解和掌握这些内容，并使学生形成知识与方法的迁移。图形的位置与图形的运动也是有密切关系的内容。在小学，图形的位置重点是用一对有序数对描述一个点的位置（距离和方向也可以看作一对数），图形的运动主要是图形的平移、旋转和轴对称。要认识到图形运动本质上是图形上点的位置的变化，这种变化主要是平移或旋转，确定图形运动前的位置与运动后的位置的关系，了解其中的变化和不变，也就是点的位置的变或不变，所以图形的运动与图形的位置有密切的关系。初中第四学段“图形的性质”是“图形的认识与测量”的延伸，学生要以抽象的方式进一步探索小学阶段涉及的图形，从基本事实出发推导图形的几何性质和定理，理解和掌握尺规作图的基本原理和方法。“图形的变化”和“图形与坐标”是小学阶段“图形的位置与运动”的延伸，学生要进一步学习图形在轴对称、旋转和平移时的变化规律和变化中的不变量，以及用代数的方法表达图形的特征，体现数形结合。义务教育阶段图形与几何的相关主题构成一个整体。

在“统计与概率”领域，小学三个学段的主题调整为“数据分类”“数据的收集、整理与表达”和“随机现象发生的可能性”三个，重点强调数据的处理。收集、整理与表达是数据处理的主要方式，更有助于学生数据意识的形成。原课标中的“分类”调整为“数据分类”，与“数据的收集、整理与表达”一致，二者构成一个整体，都是以数据为研究对象，前者是后者必要的准备。学生可以从整体上理解统计离不开数据，二者都是用恰当的方法处理数据，从而逐步形成数据意识。初中第四学段的主题“抽样与数据分析”和“随机事件的概率”是小学三个学段主题的延伸，五个主题构成一个整体。

“综合与实践”领域强调解决实际问题和跨学科主题学习，以主题式学习和项目式学习的方式设计与组织。义务教育阶段对这一领域进行了整体设计，同样构成一个整体。

（二）内容结构化反映学科本质的一致性

内容结构化通过学习主题的重组实现，四个领域下的主题不仅体现了内容的整体性，还反映了主题内学科本质的一致性。学科本质一致性以主题的核心概念为统领，以一个或几个核心概念贯穿整个主题，在不同学段表现的水平不同，但本质特征具有一致性，指向的核心素养也具有一致性。以“数与代数”领域为例，对于“数与运算”主题，“数的意义与表达”“加的意义”“相等”“运算律”等是核心概念（大概念、大观念或关键概念），其中最重要的概念是“数的意义与表达”，整数、小数、分数的认识与运算都与相应数的意义与表达密切相关。“数的认识”中从整数到分数、小数，都是从数量到数的抽象，核心的概念就是其意义和用抽象符号表达的方式。自然数表达为“十进制计数法”，用0、1……9这十个符号和以十为基底的位值制表达所有的数，如235表达的是2个“百”、3个“十”和5个“一”，分数和小数也是用抽象的方式表达。“数的运算”中，算理和算法的理解最终都追溯到数的意义，同样具有一致性。在“数与运算”主题下，几乎所有的问题都可以用这样一个或几个核心概念去理解，这样少量的几个核心概念反映了这一主题的学科本质。在对该主题内容持续的学习过程中，学生会不断利用这些概念并通过迁移解决新的问题，相关的核心素养“数感”“符号意识”“推理意识”“运算能力”不断得到发展。初中第四学段的“数与式”是小学阶段“数与运算”主题的延续，数的认识拓展到有理数。运算不仅包括数的运算，还拓展到式的运算，但主题的学科本质是一致的，几个核心概念也贯穿在主题内容之中，学生核心素养的发展也具有一致性。

对主题学科本质的分析，特别是主题核心概念的确定，是值得研究的重要话题。上面仅是对“数与运算”主题学科本质一致性的简要分析。对“数量关系”“图形的认识与测量”“图形的位置与运动”“数据的收集、整理与表达”等主题学科本质一致性的理解，以及相关核心概念的提炼，需要在教学实践中不断探索。

（三）内容结构化表现学生学习的阶段性

根据学生发展年龄特征和学习循序渐进的需要，义务教育阶段课程内容各学习主题以螺旋式上升的方式被安排在四个学段。不同学段提出了相应的水平要求，表现了学生学习的阶段性特征，这体现在各主题不同学段的“内容要求”“学业要求”和“学段目标”之中。以“数与代数”领域“数量关系”主题为例，在小学三个学段表述为“数量关系”，初中第四学段的“方程与不等式”和“函数”则是小学阶段数量关系的延伸和发展，在体现内容的整体性和学科本质一致性的同时，四个学段内容的选择和设计呈现明显的阶段性。对比第三学段“数量关系”主题和第四学段“方程与不等式”主题的部分学业要求，就可以发现它们的阶段性特征（见表1）。

从数量关系的角度看，两个主题的学科本质具有一致性，但有明显的阶段性特征。例如，关于等式的基本性质，第三学段的要求是“在具体问题中感受等式的基本性质”，第四学段则是“掌握等式的基本性质”；关于代数思维，第三学段的要求是“在具体情境中，用字母或含有字母的式子表示数量之间的关系、性质和规律”，第四学段则是“根据具体问题中的数量关系列出方程，理解方程的意义”。了解各主题的阶段性要求，不仅对特定学段内容的理解和教学要求有重要意义，而且有助于教师了解同样主题在不同学段的特征，从而分析学生的学习基础和未来学习的需求。阶段性特征也体现在同一主题下对不同学段核心素养的要求上。例如，“数量关系”和“方程与不等式”主题，第三学段重点强调几何直观、模型意识（在内容要求中）和初步的应用意识，第四学段强调建立模型观念。

二、课程内容结构化的现实意义

《标准》强调，课程内容的组织“重点是对内容进行结构化整合，探索发展学生核心素养的路径”，这是本次课程修订的重要理念。义务教育数学课程的结构化特征，在内容设计上体现了整体性、一致性和阶段性。为什么要对内容进行结构化整合？内容结构化有什么现实意义？下面对此作一些简要分析。

课程内容组织有多种模式，遵循学科的逻辑、学生发展的逻辑抑或解决社会问题的取向，不同设计理念构成不同样态的课程结构。课程内容的结构化是综合考虑各方面因素进行的课程组织方式。重视学科结构，是以学科逻辑为主线，以有助于学生理解和促进学生发展为目标的课程设计理念。“学科结构的学说对于课程的规划和组织具有指导作用和实际影响。内容的连贯与综合、教学方法和学习方式都与所采用的结构概念联系着。”许多教育学者对其有明确的论述，如布鲁纳在《教育过程》一书中对学科结构的价值、意义和方法作了系统阐述，施瓦布强调学科内容结构在课程教学设计中的作用。纵观学科结构研究的理论，结合本次课程修订提倡的理念，数学课程内容的结构化具有以下几个方面的意义。

（一）有助于更好地理解和掌握学科的基本原理

课程内容的结构化，目的在于体现学习内容之间的关联，使学生更好地理解一个学科的基本原理，进而促进其对学习内容的掌握和能力的发展。将学科内容恰当地组织起来，进而形成适应学生理解和迁移的知识结构，避免学生简单孤立地学习知识与方法，使其在学习过程中建立起合理的结构体系，这是课程内容结构化的基本理念。布鲁纳认为，“简单地说，学习结构就是学习事物是怎样相互关联的”。例如，在数学中，“代数学就是把已知数同未知数用方程式连接起来，使得未知数成为可知的一种方法。解这些方程式所包含的三个基本法则，是交换律、分配律和结合律。学生一旦掌握了这三个基本法则所体现的思想，他就能认识到，要解的‘新’方程式完全不是新的，它不过是一个熟悉的题目的变形罢了。就迁移来说，一个学生是否知道这些运算法的正式名称，比起他是否能够应用它们来，是次要的”。学习内容的这种关联是通过学科的核心概念实现的，在结构化的内容体系中，知识之间不是孤立的互不相干的，学科知识之间是相互关联的，打通知识之间关联的钥匙就是学科的基本原理。布鲁纳强调教学要注重基本观念的运用，认为“一门课程在它的教学过程中，应反复回到这些基本观念，以这些观念为基础，直至学生掌握了与这些观念相适应的一整套体系为止”。学科结构化的目的是使学习者了解所学内容的关联，而不是对个别知识的掌握。学习者从内容的关联中体会其中的核心概念（或基本观念），并将这些核心概念在其后的学习中反复运用和强化。施瓦布对学科结构也有类似的观点，认为“学科结构是部分地由规定的概念体系所构成”“不同的学科具有极其不同的概念结构”。近年来有关学科的大概念、大观念，学科核心概念的进阶等方面的研究重点，都与学科结构的理念一脉相承。

前面分析的《标准》内容结构整体性特征体现了这样的理念，一个主题内知识与方法之间构成一个整体，这些内容通过核心概念建立起联系，使具体内容的学习不再单一而碎片化，而是强调在具体内容中体现基本原理的核心概念的理解和运用。例如，数与运算中“数的意义与表达”“相等”“运算律”等是核心概念，这些核心概念是学习相关内容的关键，在学习具体内容时，学习者将不断地回到这些核心概念，从而在整体上理解掌握相关的内容。

（二）有助于实现知识与方法的迁移

内容结构化使得零散的内容通过核心概念建立关联。核心概念（关键概念、大概念、大观念）可以把主题内零散的内容联系起来，促进知识与方法的迁移。“核心概念是可以把领域或主题内，甚至跨越不同领域、不同主题的更为基本的概念、方法和问题联系起来的具有支配性的概念，是促进有意义的、联系紧密的知识的一个实用而强大的工具。例如，‘等分’这个核心概念（一个整体可以被分为大小相等的几个部分）为儿童发明用于公平分配物品的非正式方法提供了概念基础，等分（类比公平分配的非正式的形式）就为理解包括除法、分数、度量和平均分在内的正式概念奠定了基础。”内容结构化可以通过核心概念更好地理解和掌握一类内容中基本的概念和方法。核心概念帮助学生更好地理解和强化更多的知识与方法，并将其运用于新场景的学习之中，实现知识与方法的迁移。学生学到的是以核心概念为线索的一套学科内容体系，而不是简单的零碎的知识和技能。在布鲁纳有关学科结构的理论中，人们所熟知的“任何学科的基本原理都可以用某种形式教任何年龄的任何人”的观点，听起来似乎有些极端，但从内容结构化的视角理解，这里的基本原理并不是形式化的术语表达的抽象的学科概念，而是支撑某一类知识体系的核心概念，这些核心概念的表现形式可以处于不同层次和不同水平。对于不同年龄的学生，可以用恰当的方式使他们在不同水平上认识其表达方式，如数学中的“相等”是一个核心概念，对于用“=”来表达相等的关系就有不同水平，有研究将其分为“机械的操作型，灵活的操作型，基础的关系型，互相比较型”等不同水平。《义务教育课程方案（2022年版）》提出的“加强课程内容的内在联系，突出课程内容结构化，探索主题、项目、任务等内容组织方式”正是反映了课程设计的结构化理念。早在20世纪90年代，北京的特级教师马芯兰就以结构化的思想梳理了小学数学的核心概念，并以核心概念为线索，“由十几个最基本的概念为知识的核心，把小学中的主要数学知识联系了起来。‘和’这个概念则是知识的核心的核心。在学生学习‘10以内数的认识’时就开始以渗透的手段逐步建立‘和’的概念，通过渗透‘和’的概念学习‘10以内数的认识’‘加、减计算’‘理解加减关系’‘加减求未知数’‘简单应用题的结构’”。马芯兰通过数学内容的结构化，以核心概念为线索构建学习内容体系，对“数与代数”领域中的540多个概念之间的从属关系进行了深入研究，将起决定作用的十几个核心概念提炼出来，形成了一个完整的知识结构体系。用较少的时间使学生理解核心概念，可提高小学数学教学质量和效率，通过知识与方法的迁移实现小学数学教学减负增效。

近年来有许多关于“大概念”及其在学科课程教学中作用的研究，促进人们深入地思考其理论与实践。“广义的大概念指的是，在认知结构化思想指导下的课程设计方式，是为避免课程内容零散庞杂，用居于学科基本结构的核心概念或若干居于课程核心位置的抽象概念整合相关知识、原理、技能、活动等课程内容要素，形成有关联的课程内容组块。狭义的大概念同样是出于课程结构化的目的，同时强调学生对核心概念本质的理解，特指对不同层级核心概念理解后的推论性表达。”这里提到的“大概念”“核心概念”都与课程的结构化密切相关，只有在具有结构化特征的学科内容主题中，核心概念才有可能得到凸显，发挥引领、深化的作用，带来持续发展。

以核心概念为线索的课程内容结构化，有助于课程实施者更好地把握课程内容本质，在分析和提炼学习主题核心概念的基础上，理解具体学习内容的学科本质，使学生深刻理解和掌握学习内容，并在此基础上实现知识与方法的迁移，从而促进学生核心素养的形成。结构化的课程内容可以促进课堂教学的改革，实现“用少量主题的深度覆盖去替换学科领域中对所有主题的表面覆盖，这些少量主题使得学科中的关键概念得以理解”。这样的教学设计之所以能够实现少量主题的深度覆盖替换所有主题的表面覆盖，是因为利用知识与方法的迁移，而在迁移中发挥作用的则是“关键概念”，这里的关键概念与核心概念是一致的。

（三）有助于准确把握核心概念的进阶

学习进阶的研究是针对学科的核心概念或大概念展开的，在物理、化学、生物等科学类学科中有大量的研究。数学学科的学习进阶研究在国外由来已久。尽管数学学科学习进阶研究与科学领域的有所不同，但在本质上具有共同的特征。国内对于数学学科学习进阶的研究虽然刚刚起步，但也有学者对数与代数、统计与概率等主题中核心概念的进阶有系列的研究。学习进阶研究重点关注四个必备的要素：大概念及对大概念的解析；界定清晰的各进阶层级；检验学生所处水平的测评工具；促进学生发展的教学干预手段。从某种意义上说，学习进阶的研究可以看作布鲁纳学科结构理论的延续与教学实践的支持。布鲁纳认为，教授学科基本结构有四个重要意义：一是懂得基本原理，使得学科更容易理解；二是使学习的内容更容易记忆；三是更容易实现知识和方法的迁移；四是缩小高级知识与低级知识之间的差别。这些关于学科结构重要性的观点，与学习进阶的基本要素有异曲同工之处。就学科内容结构化的现实意义而言，我们还需在上述学科结构的四个意义的基础上增加一条，就是结构化的内容对于学生形成核心素养的重要意义。以核心概念为主线的结构化学习主题，有助于课程实施者从学习进阶的视角整体理解学生不同阶段的学习内容，明确每一个阶段完成的学习任务所达成相关核心概念的阶段性水平。随着学习进程的递进，学习内容不断扩展，相关核心概念的水平不断提升，从而使学生的核心素养逐步形成。结构化的内容会使学生的学习变得更轻松，更持久，“一个人越是具有学科结构的观念，就越能毫不疲乏地完成内容充实和时间较长的学习情节”。在这样的学习过程中，学习建立积极的情感体验，而持久的学习经历也有助于活动经验的积累和核心素养的形成。内容结构化，凸显学习主题的整体性和一致性，并通过主题中起重要作用的核心概念来实现。

内容结构化的阶段性特征凸显学习进阶的进程，学习进阶的阶段性特征通过关键内容的教学体现出来。课程内容的结构化提供了以核心概念为线索的促进学习进阶的路径，透过关键内容的深度学习实现核心概念的理解与进阶。以“数与运算”主题为例，“数的意义与表示”可以看作一个核心概念，其核心要义是如何从数量抽象为数，如何将数用符号表达出来。在义务教育阶段的四个学段中，学生学习有关数的内容时都与这个概念建立关联。第一学段认识20以内的数、百以内的数、万以内的数；第二学段认识十进制计数法，初步认识分数和小数；第三学段认识分数和小数的意义，自然数的性质（奇数与偶数、质数与合数）；第四阶段认识有理数。每一个阶段虽然认识具体的数不同，但其学科本质都指向核心概念“数的意义与表示”，都是用抽象的符号和计数单位表达数。例如，35表示的是3个十（十位），5个一（个位）；35表示的是3个1/5（分数单位）；-35表示与35相反的量。每一种抽象的符号表达，都与具体的数量关联。如何建立起这种关联，学生在不同阶段对于这种关联的理解水平如何，以及如何引导学生理解与掌握这种关联，都需要通过结构化的学习内容来实现。把握其中的核心概念，并在学生学习进阶过程中实现内容与方法的迁移，进而促进学生核心素养的发展，是整体提升教学质量的关键。课程内容的结构化为实现教学方式的变革提供了可能。

三、内容结构化带来的挑战与契机

课程内容结构化对课程实施提出了新的要求，同时也为教科书编写和教学改进等提供了契机。内容结构化体现了内容统整的理念，避免了知识的碎片化。在内容要求和学业要求中，将关联密切的知识内容统整，体现了核心概念为主线的内容一致性。内容结构化为教育者引导学生从整体上深刻理解主题的内容和方法，促进学生能力的发展和核心素养的形成提供了条件。在教学活动中，要充分考虑学科的核心概念，从体现核心概念的关键内容入手，促进学生对其学科本质的理解，形成知识与方法的迁移，逐步发展学生的核心素养。

（一）内容编排以主题的核心概念为线索

《标准》对领域下的主题进行了整合，凸显了数学学科的本质，体现了主题内容的一致性，为教科书编写和教学设计提供了更多选择和组织的空间。

首先，主题的整合将带来教科书呈现上的变化。《标准》除“综合与实践”领域外，小学阶段和初中阶段分别列出七个和八个学习主题，如“数与代数”领域包括“数与运算”“数量关系”“数与式”“方程与不等式”“函数”五个主题。每个主题都构成一个整体，其中蕴含了反映主题学科本质的核心概念，这些核心概念在不同学段具有一致性和阶段性。例如，小学的“数与运算”主题和初中的“数与式”主题具有共同特征，其学科本质具有一致性，“数的意义和表示”“相等”“运算律”等作为统领的核心概念体现在不同学段的相关内容之中，而在不同学段又具有阶段性特征，抽象的程度不同，表征的水平就有所不同。教科书的呈现既要考虑将其作为一个整体进行设计与组织，也要体现其阶段特征。对于“数与运算”主题，现有的教材大多是将数的认识和数的运算分成不同的单元进行设计。有教材将“100以内数的认识”和“100以内数的加减法”安排在一下和二上的不同单元。依据《标准》对“数与运算”主题的整体理解，可以考虑将100以内数的认识和加减法运算安排在同一单元，使学生在理解数的意义的同时，探索100以内加减法的算理和算法，从而在整体上理解和掌握这个内容。数与运算的结合，不仅促进学生对算理和算法的理解掌握，反过来也可以帮助学生从运算的角度进一步理解数的意义，有助于学生数感、符号意识、运算能力、推理意识等核心素养的形成。当然，并不是所有的数与运算内容都要采取整合的方式来编排，即使分成不同的单元进行组织和设计，也可以用整体的观点理解相关内容，以把握数与运算的关联。“图形与几何”领域将“图形的认识”与“图形的测量”主题整合为“图形的认识与测量”主题，强调图形的认识与测量关联，从整体上认识图形与测量。与其相关的核心概念可能包括“图形的特征”“图形大小的度量”等。几何中的测量都是对图形的测量，图形测量的本质是确定图形的大小，从一维、二维到三维，分别用长度、面积、体积表达。对一个图形完整的认识，包括对其特征（如长方形的边和角及其关系）的认识，也包括对这个图形的周长、面积等度量的认识。例如，三角形的两边之和大于第三边，可以从边的长度的测量视角进行探索。将图形的认识与测量整合成一个主题，为图形与几何的学习提供了更广阔的空间，不仅可以把周长和面积这样的测量问题整合起来进行分析和理解，也可以尝试将图形的认识与测量问题整合起来进行教材的组织和教学设计。

其次，具体内容主题归属的变化有助于课程实施者准确理解其学科本质。《标准》对一些内容调整了主题归属，如“用字母表示数”和“百分数”由原来“数的认识”主题下分别调整到“数量关系”和“数据的收集、整理与表达”主题下。用字母表示数在以往的标准和教学中只是作为数的进一步抽象，数是数量的抽象，字母又是对数的更一般的表达，是更高层次的抽象。《标准》将用字母表示数调整到“数量关系”主题下，重点将用字母表示数理解为事物之间关系和规律的一般性表达，其内容要求是“在具体情境中，探索用字母表示事物的关系、性质和规律的方法，感悟用字母表示的一般性”，学业要求为“能在具体情境中，用字母或含有字母的式子表示数量之间的关系、性质和规律，感悟用字母表示具有一般性”。从数量关系角度来理解字母表示数的学科本质，其教学的重点和意义与以往相比就会产生变化，从某种意义上弥补了小学阶段不学简易方程带来的缺失，有助于发展学生初步的代数思维。“百分数”的内容移到“数据的收集、整理和表达”这个主题下，凸显了百分数的统计意义。以往百分数在“数的认识”主题下，学生更多是从数的意义理解百分数，将百分数看作特殊的分数。但百分数主要用于解决实际问题，从统计意义上理解百分数更能清晰地了解其来龙去脉。百分数的内容要求是“结合具体情境，探索百分数的意义，能解决与百分数有关的简单实际问题，感受百分数的统计意义”。这些内容主题归属的变化，有助于课程实施者准确理解具体内容的本质，为合理的教学设计创造条件。

（二）内容分析凸显学科本质的整体特征

分析学习内容是合理进行教学设计和课堂实施的前提，其重点在于对学科内容的整体理解。课程内容结构化为整体上理解相关内容的学科本质提供了线索，有助于确定一类学习内容的核心概念、关键内容和重点难点。以“小数除法”为例，在现行某版本的教材中，这个内容单元和相关的前后知识安排如表2所示。

学习内容的单元分析一般是将单元作为整体，分析这个单元内容的本质及其不同内容之间的关系，确定单元的重点和难点等。从主题视角看单元内容的本质及其关联，并且将本单元内容与前后相关的单元内容建立联系，会对其本质有更清晰的认识和理解。“小数除法”这个单元的主题是“数与运算”，主要内容是小数除法的计算方法。从教材内容的具体分析可以看出，前三个内容是不同类型的小数除法，体现这个内容的核心概念是“计数单位个数‘累加’”。从计算方法的角度确定哪个具体内容（例题）是重点，有助于学生理解小数除法的算理和算法。而后三个内容“近似计算”“循环小数”“混合运算”不属于计算方法，近似计算和混合运算都与问题的情境有直接关系，从某种意义上讲涉及问题解决能力，其核心概念与计算方法不同。《标准》在第二学段“数与代数”领域对“数量关系”主题有“能在简单的实际情境中，运用四则混合运算解决问题”的学业要求。而循环小数在本质上是数的认识的扩展，之所以在小数除法单元中呈现，原因之一就是解决类似1÷3这样的问题时出现了循环小数，其重点不是除法的问题，是数的表示的拓展，是如何表达循环小数和循环小数在具体情境中怎样取舍的问题，其核心概念是“数的意义与表达”。这两类问题虽然不是该单元的重点，但与小数除法的计算有关，可以看作小数除法的应用，其本质是问题解决和数的表达。施教者在对内容进行纵向整体分析时还要了解前后单元的相关内容。从表2可以看到，四年级与小数除法相关的内容有整数除法、运算律和小数的意义等，五下进一步学习的分数除法，与整数除法和小数除法的算理相关。数的运算的重点在于理解算理、掌握算法，与算理直接相关的核心概念是“计数单位的‘累加’”，这一核心概念在四年级和五下都会在不同的运算单元中重复出现。从这个意义上讲，这些相关内容在学科本质上具有一致性。将能够突出地体现核心概念一致性的内容作为关键内容组织教学，有助于实现知识和方法的迁移，使这些相关内容在整体上形成一个“大单元”。内容结构化有助于从整体上把握内容的关联，清晰地梳理数的运算内容的线索，以及不同阶段“数与运算”主题之间的联系。将对主题学科本质的整体理解运用到具体的内容分析之中，有助于深刻理解具体学习内容的核心概念，以及单元内容的重点和关键内容的确定。

（三）教学活动突出关键内容的单元整体设计

内容结构化促进课堂教学改进的持续研究，从关键内容入手的单元整体教学设计是实现核心素养导向目标的重要路径。《标准》结构化的内容设计在领域下以主题的形式呈现，具体内容要求呈现学科知识与核心素养两条线索。主题的整合更加凸显学科内容的本质特征，以及相关内容之间的联系。通过教学内容的纵向分析，可以从整体上把握学习内容的发展脉络、学科本质的一致性特征以及内容之间的关联，同时把握一个主题内容重点体现的核心概念以及蕴含的核心素养。教学设计与组织应当采用单元整体教学设计的思路，从整体的视角分析内容本质和学生学情，聚焦核心概念，确定核心素养导向的学习目标，针对单元中的关键内容设计与实施体现深度学习的教学活动。下面以小数除法为例，借助表2作简要分析。

首先，基于自然单元内容的整体分析，形成以核心概念为线索的反映该单元与前后相关单元之间联系的内容的整体理解。以教材的自然单元为形，以单元和单元之间内容本质与核心概念为魂，从自然单元入手进行内容分析，既容易操作，又可以从自然单元分析中将学习内容延伸、拓展，实现对学习内容的整体理解。表2显示“小数除法”单元的核心内容是“数与运算”主题中的小数除法，其重点是理解算理、掌握算法。小数除法的算理和算法与整数除法有密切关系，需要追溯到整数除法，特别是有余数除法的教学，教学设计时有必要考虑唤起学生这方面的认知，特别是核心概念“计数单位个数‘累加’”的运用。小数意义的理解对于小数除法算理的理解不可缺少，教学中应采用恰当的方式帮助学生运用小数意义理解算理。除了这个主题外，第四至第六三个内容又涉及数的认识和问题解决等，教学中应与相关的核心概念关联，采取不同的教学策略。

其次，确定单元中的关键内容。关键内容是能更好地体现所学内容的学科本质和核心概念的内容，并且蕴含着相关的核心素养。表2中第一至第三个内容是不同类型的小数除法问题，这些内容中能较为集中地体现小数除法的算理和算法的内容可以作为教学的关键内容。从该单元的教材安排看，第一个内容是小数除以整数，可以理解教材的编者将这个内容作为关键内容的设计思路。这样的设计不无道理，这个内容直指小数除法运算，学生直接面对的是小数除法，要解决的问题就是被除数是小数时怎样计算，可借助这个问题理解小数除法的算理和算法。吴正宪基于多年的教学经验，在对内容进行整体分析基础上，将第二个内容“整数除以整数商是小数”作为关键内容，通过具体的问题情境引导学生探索和理解小数除法的算理和算法：“4个人吃饭，付给服务员97元，这顿饭他们要AA制”，让学生根据这个情境提出问题和解决问题。问题本身并不难，但在进行运算时发现97÷4=24……1，这是一个有余数的除法。在AA制的情境中，需要将余下的1继续除，在整数除法的范围内无法解决这个问题。“余下的1怎么分”引起学生学习过程的认知冲突。这个问题的解决直接引出小数除法计算算理的深度探索。将小数除法与以往学习的有余数的除法联系起来，运用学生学习的前概念，可以引起学生进一步探索和思考。更重要的是，从有余数的除法引入可以唤起学生相关的核心概念——计数单位个数“累加”与细分，并让学生将其运用于新的问题解决之中。当以“一”为单位的1不够除以4的时候，将其变成以十分之一为单位的10个0。1，就可以除以4，商是2（2个0。1），接下来的计算都是这个方法的推理。这个例题作为学习这类内容的关键内容，对于深刻理解算理、掌握算法起画龙点睛的作用。

最后，设计有效的教学活动。基于学生的基础和前概念，组织围绕关键内容的学习活动，有助于促进学生整体发展。关键内容体现学科本质，指向学生的核心素养。有效教学活动的组织需要基于学生现有的知识基础和对当前学习内容的理解水平以及存在的困惑，提出引发学生思考的问题，并采用多样性的策略与方法，引导学生独立思考、质疑问难、合作交流，在解决问题过程中深度理解所学内容，形成和发展核心素养。在小数除法教学中，师生围绕“余下的1怎样分”的问题展开教学活动，学生经过独立思考，给出不同的解决方法，再对有代表性的方法进行讨论、质疑、交流，最后实现问题解决，在理解算理、掌握算法的同时，学生的推理意识、运算能力、几何直观等核心素养获得发展。

课程内容结构化是深化基础教育课程改革的重要理念，在中小学数学课程与教学改革中应引起充分的重视。伴随着《标准》的颁布与实施，围绕课程内容结构化的理解及其引起的深化教学改革的探索将成为重要的研究话题。

初中数学课程标准解读心得体会 篇8

最近利用课余时间学习了初中数学新课标，有一定的心得体会。初中数学是义务阶段的一门主要课程，数学来源于生活，又服务于生活，很多的知识结构均是由现实生活中的实际问题抽象而来，并利用该知识解决数学问题，这也是我们常常说的提出问题、分析问题到解决问题的过程，从而更好的使学生形成理性思维达到提高能力的目的，具体有以下体会：

Recently, I learned the new curriculum of junior high school mathematics in my spare time, and I have some experience. Mathematics in junior high school is a major course in the compulsory stage. Mathematics comes from life and serves life. Many knowledge structures are abstracted from the actual problems in real life, and use this knowledge to solve mathematical problems. This is also the process of posing problems, analyzing problems and solving problems, which we often say, so as to better enable students to form rational thinking to improve their ability. The specific experience is as follows:

一、授课过程中一节课的知识点要少而精，重点问题重点讲解，使学生能吃透读懂，对知识的讲解要追本求源，把课本教材知识放在首位，同时还要积极的调动学生学习的积极性，让学生对知识进行提炼和总结，没有学生的主动参与就不是一节成功的课，新课标倡导学生自主学习，合作学习和探究学习，这些都是以学生的主动参与为前提的。

1、 In the course of teaching, the knowledge points of a lesson should be few and precise. The key problems should be explained with emphasis to enable students to understand and understand. The explanation of knowledge should be based on the source, and the knowledge of textbooks and textbooks should be put in the first place. At the same time, the enthusiasm of students should be actively mobilized to refine and summarize knowledge. Without students' active participation, it is not a successful lesson. The new curriculum standard advocates students' independent learning, cooperative learning and inquiry learning, These are all based on the active participation of students.

二、在教学活动中，教师要当好组织者。教师要充分信任学生，相信学生完成学习的能力，把机会交给学生，俯下身子看学生的学习，平等参与学生的研究，把课堂放给学生，给学生充足的时间与空间尝试并合作探究，让学生表现自己，树立自信心，培养学生的专研精神。

2、 In teaching activities, teachers should be good organizers. Teachers should fully trust students, believe in their ability to complete learning, give students the opportunity, look down at their learning, participate in students' research on an equal basis, give students enough time and space to try and cooperate with them, let students express themselves, build self-confidence, and cultivate their professional research spirit.

三、初中教师在新课标中的角色是：课程价值的思考者、学科专业的播种者、学生发展的促进者，合作探究的协作者，资源保障的服务者，终生发展的示范者。

3、 The role of junior middle school teachers in the new curriculum standard is: the thinker of curriculum value, the seeder of disciplines and majors, the promoter of student development, the collaborator of cooperative exploration, the service provider of resource security, and the demonstration of lifelong development.

四、新课标的新变化有以下五个方面的新变化：深化课程教育导向；优化课程标准结构；提高了学业质量标准；增强了指导性；变革育人方式，突出实践。

4、 The new changes of the new curriculum standards include the following five aspects: deepening the guidance of curriculum education; Optimizing the structure of curriculum standards; Improve the academic quality standards; Enhanced guidance; Change the way of educating people and highlight practice.

总之，我们在教学中对教材的处理、教学过程的设计以及评价的方式都要以学生发展为中心以提高全面发展为宗旨，这才是我对学习新课标的最终体会。

In a word, we should focus on the development of students and improve the all-round development in the way of teaching materials processing, teaching process design and evaluation, which is my final experience of learning the new curriculum standard.

初中数学课程标准解读心得体会 篇9

2022年4月，教育部发布了义务教育课程方案和课程标准（2022年版），通过研读，使我受益匪浅。谈一点自己粗浅的感悟。

In April 2022, the Ministry of Education released the compulsory education curriculum plan and curriculum standards (2022 version), which benefited me a lot through study. Talk about a little bit of my humble feelings.

新知识的学习是数学教学中比重最大也是非常重要的环节。在新知识的学习中，要关注初中数学课程中的核心内容，以及蕴含在核心内容中的数学思想方法，进而才能设计出培养学生数学学科核心素养的教学设计。那么，初中数学课程的核心内容有什么特征呢？

The learning of new knowledge is the most important part in mathematics teaching. In the learning of new knowledge, we should pay attention to the core content of junior high school mathematics curriculum, as well as the mathematical thinking methods contained in the core content, and then we can design a teaching design to cultivate the core quality of students' mathematics discipline. So, what are the characteristics of the core content of junior high school mathematics curriculum?

第一，从数学知识的角度看，必须是对今后进一步的数学学习和课堂之内的数学应用来说都重要的内容。

First, from the perspective of mathematical knowledge, it must be an important content for further mathematical learning and mathematical application in the classroom in the future.

第二，它们在数学课程和教材中处于重要的、不可或缺的基础和主干地位。

Second, they are in an important and indispensable foundation and backbone position in mathematics courses and textbooks.

第三，必须能将以前学过的数学知识和以后将要学习的数学知识有机地联系起来。

Third, we must be able to organically link the mathematical knowledge we have learned before with the mathematical knowledge we will learn later.

例如，在初中的“数与代数”领域中，数及其运算、字母（式）及其运算都是数学的核心内容，整体来看，这可以看成一个大单元，当然，也可以分开来看成两个中单元，它们自始至终贯穿于整个初中的数学课程，对于这样的核心内容，我们在理解课程内容时应该从以下几个方面去把握。

For example, in the field of "number and algebra" in junior high school, number and its operation, letter (formula) and its operation are the core content of mathematics. On the whole, it can be seen as a big unit, and of course, it can be seen separately as two middle units, which run through the whole junior high school mathematics curriculum from beginning to end. For such core content, we should grasp from the following aspects when understanding the curriculum content.

（1）要帮助学生搞清楚运算的对象，在初中阶段运算对象主要有两个：一个是数，包括小学学过的自然数，分数和初中拓展的有理数，无理数组成的实数，让学生了解在这些不断扩大的数的范围过程中，是运算在追求可逆性和封闭性的结果。另外一个运算的对象就是表示数的字母（式），各种代数式的概念和运算也可以类比数的概念和运算进行迁移。

(1) To help students understand the objects of operation, there are two main objects of operation in junior high school: one is numbers, including natural numbers learned in primary school, scores and rational numbers expanded in junior high school, and real numbers composed of irrational numbers, so that students can understand that in the process of expanding the range of these numbers, operations are the result of the pursuit of reversibility and closure. Another object of operation is the letter (formula) representing the number. The concepts and operations of various algebraic expressions can also be transferred by analogy with the concepts and operations of number.

（2）要不断理解和认识运算的背景和意义如为什么要做加法，为什么要做减法，为什么要做乘法或除法。等等。只有不断理解运算的含义，才有可能灵活运用这些运算来帮助解决问题。

(2) We should constantly understand and understand the background and significance of operations, such as why we need to add, why we need to subtract, and why we need to multiply or divide. wait. Only by constantly understanding the meaning of operations can we flexibly use these operations to help solve problems.

（3）要理解运算法则。不仅要教给学生运算的法则，而且要帮助学生去体会制定这些法则的意义和合理性。理解运算法则实际上就是运算中进行逻辑推理的基础。

(3) Understand the algorithm. We should not only teach students the rules of operation, but also help them understand the significance and rationality of formulating these rules. Understanding the operation rules is actually the basis of logical reasoning in the operation.

（4）要在解决实际问题中恰当运用运算，或者能够找到更为简洁的运算途径。

(4) It is necessary to properly use the operation in solving practical problems, or find a more concise way of operation.

（5）要能够理解除精确的运算外，还有估算或逼近的概念，学生应该具有估算的意识和能力。

(5) Students should be able to understand the concept of estimation or approximation in addition to accurate calculation. Students should have the awareness and ability of estimation.

对于这样的核心内容，我们在有了整体认识的基础后，就可以在具体实施中进行单元主题设计了。例如，在“有理数及其运算”的单元教学设计中，可以在充分考虑了本单元内容的学科本质和地位的基础上，将本单元的内容放在更大的范围（数、字母及其运算）内进行考虑，实现对课程内容的整体认识和把握，关注学生数学素养的提升，以期实现深度学习。

For such core content, we can design the unit theme in the specific implementation after we have the overall understanding. For example, in the unit teaching design of "rational number and its operation", the content of this unit can be considered in a wider range (number, letter and its operation) on the basis of fully considering the subject nature and status of the content of this unit, so as to realize the overall understanding and grasp of the course content, pay attention to the improvement of students' mathematical literacy, and achieve in-depth learning.