Under the impact of the new round of curriculum reform, our original mathematics classroom teaching gradually shows its impatience and powerlessness in promoting students' sustainable development. In this case, we urgently want to find a key to solve this problem.

In the past, mathematics classes paid more attention to the study of book knowledge, and the content of teaching materials and teachers' knowledge were limited, so students passively accepted this limited teaching content. As everyone knows, we completely ignore the extensive teaching content contained in students, society and life. When we use new teaching materials and want to solve this phenomenon, we should focus on "the study of mathematics small projects".

Our organizational form is "class teaching system". This highly closed organizational form makes it easy for students in the same class to form almost similar study habits after years of living and studying together. This is contrary to the basic starting point of mathematics curriculum standard "promoting students' all-round, sustained and harmonious development and realizing different development of different people in mathematics". "Small topic research" is the study of social and life problems completed by students. The flexibility of the organizational form of small-scale research is one of the effective methods we can find so far to make up for the above shortcomings.

The most important value for students to learn mathematics is to "know the connection between mathematics and life" and "think". And students can practice a pair of eyes that are good at discovering by conducting small-scale research. These eyes can not only see the problems related to mathematics in life, but also be good at finding problems in research, which makes continuous thinking an indispensable life element in the process of students' research on small topics. This kind of research fully embodies the dual value of mathematics.

First, the basic framework of mathematical research

Small subject research is not a patent of mathematics, and other disciplines also exist. Therefore, it is absolutely unnecessary for us to find another way for the research mode of mathematics small topics. In the process of repeated practice and continuous improvement of small topic research, we have determined its relatively fixed basic framework.

Its basic process is: the emergence of problems-the formation of research groups-the formulation of activity plans-the implementation of activity plans-reporting and communication.

Second, the concrete implementation of the research on small mathematics topics

(A) the emergence of the problem

The process of topic selection is the first learning activity for students to find problems, ask questions and establish research topics after they step into the door of research-based learning, and it is the starting point for strengthening students' problem consciousness and cultivating innovative spirit.

How to generate problems in 1

Path 1: Teachers develop teaching material resources.

There are many small topics in our textbooks. Therefore, in the initial stage of small-scale research, it is a convenient way for teachers to develop resources and set topics in combination with the content of teaching materials to ensure that the selected topics have research value and practical implementation. For example, our teacher has designed many creative small topics in combination with math textbooks. Did you send a greeting card? How big is a hundred million? I've grown taller? Nutritional lunch and so on.

Path 2: What students extract from life.

The premise of students' refining must be that after learning a small topic, students gradually develop the thinking habit of "learning mathematics to see life and thinking about mathematics in life". Students observe life from a different perspective than adults, and their inspiration is more vivid. The thinking they cause in life may become the goal of their small research. For example, large shopping malls often engage in promotional activities, and students and parents will encounter such questions when shopping together: Can they really use the promotional activities of shopping malls? When the students raised this question, the teacher immediately realized that it was a good question worth studying, and after consulting with the students, he formed a special topic: "Buy one hundred and get one hundred free-the secret of the merchant", and conducted a small special study on this topic. Students have a strong interest and strong operability. Some students also found that some large supermarkets provide buses to pick up and drop off customers for free, so can supermarkets still make a profit? Students with this question, after everyone's induction, formed a research topic: supermarket commodity survey. Under the critical observation of students, the research scope of small topics has been broadened, such as: sports and height, mathematical problems in botanical gardens, consumption ratio of non-staple food varieties, learning to ride, etc.

Path 3: Common problems that plague students.

The closer you get to students, the problems that often bother them. Students must try their best to solve it. This kind of problem naturally becomes the content of students' small topic research. Schools often hold sports competitions, and children especially hope to win in the activities. Faced with failure, they are eager to find the reason and turn defeat into victory, so the topic of "winning tug of war" came into being. How to finish homework quickly and with high quality? Efficient homework completion method has become a difficult problem they want to pursue. There are also small topics such as "the time and quality of Chinese character practice" and "learning in aerobics", which not only let students experience the happiness of scientific research, but also help them solve their lingering worries.

2 the process of the problem

No matter how the problem arises, the process from the problem to the establishment of the discipline can basically be represented by the following flow chart:

Cannot be deleted

Many problems can be easily solved at once.

Dependent related merger project

Valuable reservation

In other words, this part of the problems that have been sorted out and merged are often the most valuable for research. Its feasibility lies in students' ability to participate in the research, but it will be difficult. This is most suitable for the cultivation of students' research ability and thinking quality.

(B) the formation of the research group

In the process of students' research on small topics, a lot of content needs to be completed in cooperation. The members of the research group are usually closely related, and everyone has a tacit understanding, which is very beneficial to speed up the research and promote the process of research work. Of course, in the process of research, students should learn to communicate with others and cultivate their spirit of cooperation with anyone. Therefore, the principle of forming a research group can vary from person to person, and the policy can be relaxed appropriately.

(3) Make an activity plan

The formulation of the activity plan includes the title of the subject, the research purpose, the list of members of the research group and their division of labor, research methods, relevant instructors, implementation steps, presentation and reporting methods, etc. Its formulation provides a planning guide for the next stage of implementation.

We take buy one hundred and get one hundred free as an example, focusing on the following parts: research purpose, research methods and implementation steps.

1, research purpose:

In order to carry out more targeted practical activities, it is particularly critical to determine the purpose of the activities. After much deliberation, we have decided as follows:

(1), using the percentage of mathematical knowledge to analyze and study mathematical problems in life.

(2) Through investigation and practice, cultivate students' practical ability and communication ability. Cultivate a sense of cooperation. Use mathematical methods such as analysis and comparison to solve practical problems in life and understand the practical significance of mathematical knowledge.

2. Research methods: According to the characteristics of this activity, in the form of group cooperation, social surveys and interviews were used to collect data, and the data were analyzed in the group to form research results.

3. Specific implementation steps:

(1), social survey (actual survey data of shopping malls), poster collection (compared with actual survey),

(2) Interview (visiting customers and parents to understand consumer psychology)

(3) Summarize the situation and analyze the data (sort out and analyze the situation in the group)

(4) research report form (novel and convincing)

(5) Achievement promotion (show the research results to the whole class in groups and learn from the experience of other groups to improve the research results of this group)

According to the method, the group will divide the work and implement the task to everyone.

(4) implement the programme of activities

With a clear guide to action, there is a law to follow in the implementation stage of the problem. In the process of implementing the activity plan, we follow the following principles:

1 principle of monitoring at any time

After the plan is formulated, it is likely that it will not only be imperfect, but also deviate from the general direction. The teacher's guidance must be followed up. Teachers and students find the crux of the problem, seek suitable ways to discuss it repeatedly, foresee the gains and losses, and make repairs.

For example, in the small project of "accessing the network", students collected some data about our country in economy, education, military affairs, agriculture and other aspects through a series of research activities such as determining several aspects of research, division of labor, and then consulting materials in groups. However, this subject has neglected its "mathematical characteristics" in the process of marching. Students just rewrite big data, and the data list does not bring mathematical thinking. At this time, we need to modify the activity plan. How to make activities reflect the value and significance of mathematics? After re-adjustment by teachers and students, it was finally revised as "going into the network to see the changes". Use relevant mathematical knowledge (number operation and statistics) and mathematical thinking methods (analogy, synthesis and analysis) to present the great changes of the motherland in recent years in various ways such as tables and comparative data. Some students choose different statistical forms in the report, some students compare the data before and after, and some students present the problems they found with mathematical vision and mathematical thinking in the form of a list. With this change, students will sort out and analyze the collected data and explore deeper problems in mathematical knowledge and methods.

2 cooperation * * * the principle of knowledge

When making the activity plan, we arranged the division of labor among the members of the research group. For example, in the activities of beautifying the campus, the students in charge of the research site don't mean that they don't have to do anything else as long as they find a place to study. But responsible for the outcome. In addition, everyone put forward their own views in the study. Do you agree or disagree? Why? What's your own opinion? Everyone should have the opinion of participation. In other words, the division of labor is only a task that you are mainly responsible for and personally accomplish, and cooperation should run through the research process.

Our research on small topics can't be just for research, and our research should have high research value. Under the principles of "monitoring at any time" and "cooperation and knowledge", our practice should enable students to achieve the following goals:

1 Understand the purpose of society

Each of us is realizing our personal life goals and ideals under the background of social life. Therefore, through every little thing, every activity, we can understand the society bit by bit, that is, the process of making students mature and really grow up over time. For example, in the study of Little Butler, students learned that the family, as the smallest unit of society, wanted to survive based on society, which initially branded the students' sense of survival.

2 Understand the purpose of mathematics

What is the importance of learning mathematics? Students will naturally realize the importance of mathematics in the process of learning small questions. In the study of any small mathematical topic or part of non-mathematical topics, the research methods and conclusions need the support of mathematical knowledge. Therefore, students who have participated in small-scale research on mathematics not only have strong ability to apply mathematical knowledge, but also study mathematics more actively than those who have not participated in small-scale research.

3 Know your own purpose

In a questionnaire survey, there is such a question "What is the purpose of your study?" Among the answers, 65% are for teachers' praise and parents' happiness, 22% are for becoming a scientist when they grow up, and the rest account for 13%. This survey shows that students are not sure about their growth goals. Why is this the result? Because students don't know themselves at all. Just in a passive state. But after a small-scale study, we found that this situation has been greatly improved. In the process of research, students know what I am good at and what knowledge I need urgently, and begin to ask themselves to take the initiative to learn. In the process of this change, we have achieved the goal of knowing ourselves.

(5) Reporting and communication

In the stage of communication and reporting, the first thing to do is to report selectively. Because in the research stage of the project, the amount of information obtained by students through various channels such as surveys, interviews and the Internet must be considerable. When reporting, we should convey the research results to the whole class in the form of a group, with a focused introduction, not covering everything. Second, we should pay attention to the communication and reporting process of experimental research. First of all, the research content of students' sports may have been studied by predecessors, or it may have considerable scientific and technological content, but students can't reach this height for the time being. In that case, shouldn't we study this kind of topic? That's not true. Because students carry out small-scale research in order to experience the scientific research process, understand the scientific research methods and learn to study and solve problems. Even if the students' research results are not typical, it doesn't matter if they fail completely. Therefore, the focus of communication is what methods students use to carry out research, what they have learned in the research, or what puzzles they have encountered, as well as problems that cannot be solved at present.

It should also be noted that all small research projects can't come to an end after classroom communication. Some topics may have other undiscovered research value, and students can continue their studies after class. For example, when students are doing research on "going into the network to see changes", there is such a message that students have consulted: China's cashmere production ranks first in the world. However, after investigating this data, students have aroused new thinking: What is the relationship between cashmere production and environmental protection? What other topics are worth studying from this data? Therefore, it has caused new and valuable problems that need further study. In this way, the research behavior will always run through every class and after class, so that the research of small topics can penetrate into every corner of students' study and life, and the research atmosphere can permeate among students.

Third, new problems and thinking

In the process of small project research, we feel the changes of students. First of all, students' ability to observe life has been enhanced, especially their ability to look at life from a mathematical perspective. From the articles written by students in math diary, and from the mathematical tabloids after students' practical activities, we are delighted to see that students can consciously record and reflect when they consciously use their mathematical knowledge, which is more valuable. Secondly, it can improve students' mathematical thinking methods.

But behind the joy, we also see new problems, which have to make us calm down, stop and think seriously.

(A) the limitations of the problem

Most of the topics we study are extensions of textbook knowledge, which are common problems in students' life, while few studies are done on individual problems that are not often involved and valuable to life (such as applied mathematics in various industries).

(B) superficial research

In the research of small topics, due to the limitation of students' existing knowledge and experience, teachers' professional skills are superficial and the research methods are single, which makes it impossible to continue the research of some topics.

(C) the evaluation is not timely

The implementation stage of students' small project research is mostly carried out after class, and sometimes the instructor can accompany them all the time. However, there will also be conflicts between students' research time and teachers' working time, which will lead to untimely guidance and evaluation, and secondary rework will occur from time to time.

In the process of small-scale research, we deeply realize that students are the discoverers of problems in the process of practical activities and the practitioners of in-depth research. They are not only the subject of small-scale research implementation, but also the subject of thinking. Therefore, the process of small-scale research is the process of infinite energy generation, and the research has brought us surprising changes, which makes us have to continue sincerely.