A brief discussion on how to carry out "Research on Small Projects in Primary School Mathematics"
Under the impact of the new round of curriculum reform, our original mathematics classroom teaching has gradually revealed its role in promoting students' The impatience and weakness of sustainable development. In this situation, we are eager to find a key that can solve this confusion.
In the past, mathematics classes focused more on the learning of book knowledge. The content of the teaching materials and the teacher's knowledge were limited. Students will passively accept this limited teaching content. Little do we know that we have completely ignored the vast teaching content contained in students, society, and life. When we use new textbooks and try to solve this phenomenon, we focus our attention on "research on small mathematics topics".
Our organizational form adopts the "class teaching system". This highly closed organizational form makes it easy for students studying in the same class to form almost similar study habits after experiencing several years of living and studying together. This is contrary to the basic starting point of the mathematics curriculum standards of "promoting students' comprehensive, sustainable and harmonious development and realizing different people's different development in mathematics". "Small project research" is research on social and life issues completed by students. The flexibility of small project research organizational forms is one of the effective methods we have found so far to make up for the above shortcomings.
The most important value for students to learn mathematics is “understanding the connection between mathematics and life” and “thinking”. And students' research on small projects can help students develop a pair of eyes that are good at discovery. These eyes can not only see problems related to mathematics in life, but are also good at discovering problems in research. They make continuous thinking an indispensable life element in students' small project research process. Such research has fully demonstrated the dual value of mathematics.
1. The basic framework of small-topic research in mathematics
Small-topic research is not a patent of the mathematics discipline, it also exists in other disciplines. Therefore, there is absolutely no need for us to find another way to study small mathematical topics. In the process of repeated practice and continuous improvement of small project research, we determined its relatively fixed basic framework.
The basic process is: generation of problems - formation of research groups - formulation of activity plans - implementation of activity plans - reporting and communication.
2. Specific implementation of small-topic research in mathematics
(1) Generation of questions
The process of topic selection is that after students enter the gate of research-based learning, The first learning activity of discovering problems, raising questions and establishing research topics is the starting point for strengthening students' problem awareness and cultivating innovative spirit.
1 Way to generate questions
Path 1: Set by teachers to develop teaching material resources.
Our textbooks contain a large number of small topic research contents. Therefore, in the early stages of small topic research, in order to ensure that the selected topic has research value and is feasible to implement, it is a more convenient way for teachers to develop resources and set topic selection based on the content of the teaching materials. For example, our teachers designed many creative small topics based on mathematics textbooks. For example: "Have you ever sent a greeting card", "How big is 100 million", "I have grown taller", "Nutritious lunch", etc.
Path 2: Students extract it from life.
The premise extracted by students must be carried out only after the students have gradually developed the thinking habit of "learning mathematics to see life, and thinking about mathematics in life" after conducting research on a small topic. Students observe life from a different perspective than adults, and the inspiration from them is more vivid. The thinking they trigger in life may become the target of their small project research. For example, large shopping malls often carry out promotional activities. Students and their parents will encounter such questions when shopping: Can we really take advantage of the promotional activities in the shopping mall? When the students raised this question, the teacher immediately realized that this was a good question worth studying. After deliberation with the students, they formed a special topic: "Buy 100 Get 100 Free - The Secret of the Merchant", and carried out a small group with this theme. Topic research. Students are very interested and practical.
Some students discovered that some large supermarkets provide free buses to pick up and drop off customers. Can the supermarkets still make profits in this way? The students brought this question and after everyone's summary, the research topic was formed: "Small Survey of Supermarket Products." Under the keen observation of students, the scope of small topic research has broadened, such as: "Exercise and Height", "Mathematical Problems in the Botanical Garden", "Consumption Ratio of Non-staple Food Types", "The Knowledge of Riding in Cars" and other small topics with remarkable results have emerged. .
Path 3: Frequent problems that trouble students
The closer you are to students, the problems that often trouble students will inevitably find ways to solve them. Such questions have naturally become the content of students' small project research. Schools often hold sports competitions, and children especially want to win in the activities. Faced with failure, they eagerly hope to find the reason and turn defeat into victory, so the topic "The Must-Win Tug of War" came into being. How can homework be completed quickly and with quality? "Efficient Homework Completion Method" has become a difficult problem they want to track. There are also studies on small topics such as "Time and Quality of Calligraphy Practice" and "Knowledge in Aerobics", which not only allow students to experience the joy of scientific research, but also relieve them of lingering worries.
2 The generation process of the problem
No matter which way the problem is generated, the process from the problem to the establishment of the topic can basically be represented by the following flow chart:
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Inoperable deletion
Multiple problems can be easily solved immediately
Subordinate related merger projects
Valuable retention
In other words, these problems that have been sorted out and merged are often the most valuable for research. Its feasibility lies in the ability of students to participate in the research of the topic, but it will have some difficulties. This is most suitable for cultivating students’ research ability and thinking quality.
(2) Formation of research groups
When students conduct research on small topics, many contents need to be completed collaboratively. The members of the research team usually have a close relationship, and everyone has a tacit understanding when doing things, which is very beneficial to speeding up the research and promoting the progress of the research work. Of course, students should learn to communicate with others during the research process and cultivate their spirit of cooperation with anyone. Therefore, this principle of forming a research group can vary from person to person and the policy can be relaxed appropriately.
(3) Formulate an activity plan
The formulation of the activity plan includes the name of the topic, research purpose, list of research team members and division of labor, research methods and methods, relevant instructors, implementation steps, and display Reporting methods and other parts. Its development provides planning guidance for the next phase of implementation.
The following is still taking "Buy 100 Get 100 Free - Secrets of Merchants" as an example to focus on the "research purpose", "research methods and methods" and "implementation steps".
1. Research purpose:
In order to carry out practical activities in a more targeted manner, it is particularly critical to determine the purpose of the activity. Focusing on this topic, after repeated thinking, we are This is determined as follows:
(1) Use the mathematical knowledge of percentages to analyze and study mathematical problems in life.
(2). Cultivate students’ practical ability and communication ability through investigation and practice. 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 and methods: Based on the characteristics of this activity, we adopt a method of combining social surveys and interviews to collect data in the form of group cooperation, and analyze the data within the group to form research results.
3. Specific implementation steps:
(1) Social survey (actual survey data in shopping malls), collection of promotional posters (compared with actual survey),
(2). Interviews (visiting customers and parents to understand consumer psychology)
(3) Summarizing the situation and analyzing the data (organizing and analyzing the situation within the group)
(4) Research report format (novel and persuasive)
(5) Results promotion (use groups as a unit to present research results to the whole class, and also learn from the experience of other groups, Improve the research results of this group)
The group divides labor according to the method, and the tasks are assigned to everyone.
(4) Implementing the activity plan
With clear action guidelines, there will be laws to follow during the implementation phase of the problem. During the implementation of the activity plan, the principles we follow are:
1 The principle of constant monitoring
After the plan is formulated, it is likely not only not to be perfect, but also major problems may occur. direction deviation. The teacher's guidance must be followed up. For problematic plans, teachers and students work together to find the crux of the problem and seek appropriate solutions, conduct repeated discussions, foresee gains and losses, and make repairs.
For example, when conducting the small topic "Into the Internet", the students collected relevant information through a series of research activities such as determining several aspects of research, dividing the work, and then going online to search for information in groups. Some data on our country’s economy, education, military, agriculture, etc. However, in the process of progress of this subject, its "mathematical characteristics" have been ignored. Students only rewrote larger data, but the listing of data did not bring about 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 into "Going Online to See Changes". Use the relevant mathematical knowledge learned (number operations, statistics) and mathematical thinking methods (analogy, synthesis, analysis) to present the recent tremendous changes in the motherland in various ways such as tables and comparative data. Some students used different statistical forms in their reports, some used before-and-after comparison of data, and some used lists to present to everyone the problems they discovered using mathematical vision and mathematical thinking. With this change, students must organize and analyze the collected data and explore deeper issues using mathematical knowledge and mathematical methods.
2 Principles of Cooperation and Consciousness
When formulating the activity plan, we divided the research group members into arrangements. For example, in the "Beautifying Campus" activity, they were responsible for researching the site. This does not mean that as long as he finds a research site, he will not have to do anything else. But be responsible to the end. In addition, everyone has put forward their own opinions during the research. Do you agree or not? Why? What is your own point of view? Everyone needs to be involved. In other words, division of labor is only the tasks that you are mainly responsible for and completed by individuals, while cooperation should be throughout the research process.
Our research on small topics cannot be just for the sake of research, our research should have its high research value. Under the principles of "always monitoring" and "cooperation awareness", our practice should allow students to achieve the following goals:
1. Understand the purpose of society
Each of us They are all realizing our personal life goals and ideals in the context of social life. Therefore, understanding society bit by bit through every little thing and every activity is a cumulative process that makes students gradually mature and truly grow up. For example, during the study of "Little Housekeeper", students learned about the necessary conditions for "family", the smallest unit of society, to gain a foothold in society and survive, which initially left a mark on students' minds with a sense of survival.
2 Understanding the purpose of mathematics
What is the importance of learning mathematics? Students will naturally realize how important mathematics is in the process of conducting small project research. In the research of any small mathematical topic or some small non-mathematical topics, the research methods and conclusions need to be supported by mathematical knowledge.
Therefore, students who have participated in small-project research in mathematics not only have a strong ability to apply mathematical knowledge, but are also more proactive in learning mathematics than students who have not participated in small-project research.
3 The purpose of understanding oneself
In a questionnaire survey, there was a question "What is the purpose of your study?" The answer was to get praise from the teacher and to make the parents happy. There were 65 of them, 22 for those who thought they would be scientists when they grew up, and 13 for others. This finding shows that students are not clear about their growth goals. Why does this happen? It's because students don't understand themselves at all. Just in a passive state. After conducting small-scale research, we found that this situation has greatly improved. During the research process, the students learned what I was good at and what aspects of knowledge I urgently needed to master, and they began to ask themselves to take the initiative to learn. In this process of change, the purpose of self-understanding is achieved.
(5) Reporting and communication
In the communication and reporting stage, the first thing to do is to report selectively. Because during the project research stage, the amount of information students obtain through various channels such as surveys, interviews, and the Internet must be considerable. When reporting, the research results should be communicated to the whole class in a group format, and the presentation should be focused and should not cover everything. Second, attention should be paid to the process of communication and reporting of experimental research. First of all, the content of students' small-topic research may have been studied by previous people, or it may have considerable scientific and technological content that students cannot yet reach this level. If this is the case, then shouldn’t we stop studying such topics? No. Because students' small project research is carried out for the purpose of experiencing the scientific research process, understanding scientific research methods, and learning to research and solve problems. Even if the student's research results are not typical, or even unsuccessful at all, it is not important. Therefore, the focus of the communication is the methods used by students to carry out research, what they have learned during the research, or the confusion they encountered, and the problems that cannot be solved at present.
It should also be noted that not all small project research can be completed after communication in class. Some topics may have other undiscovered research value, and students can continue research after class. For example, when students were conducting research on "Going to the Internet to See Changes," one of the information they reviewed included: my country's cashmere production ranks first in the world. However, after the students investigated this data, they triggered new thinking: What is the relationship between cashmere production and environmental protection? What other topics are worthy of study from this data? This has raised new valuable questions for further research. In this way, the behavior of research will always run through every period of time in and out of class, so that small-topic research can penetrate into every corner of students' learning and life, and the research atmosphere will permeate among students.
3. New questions and thinking
During the process of small project research, we felt the changes in students. First of all, students' ability to observe life has been enhanced, especially their ability to view life from a mathematical perspective. From the students' mathematics diaries and the mathematics tabloids after the students' practical activities, we are pleased to see that students are consciously using mathematics knowledge. What is even more valuable is that students can consciously record and reflect on it. Secondly, students' mathematical thinking methods have been improved.
But behind the joy, we also saw new problems, which had to make us calm down, stop, and think seriously.
(1) Limitations of the questions
Among the topics we studied, most of them are extensions of textbook knowledge and common problems in students’ lives. , and there is less research on individual issues that are valuable in life (such as applied mathematics in various industries).
(2) Superficial research
In small project research, due to the limitations of students’ existing knowledge and experience, the instructor’s professional skills are shallow, and the research method is single, resulting in The research on some topics was not continued in depth.
(3) Untimely evaluation
The implementation stage of students' small project research is mostly carried out after class, and sometimes the instructor can accompany the entire research process.
However, there may also be conflicts between students' research time and teachers' working hours, resulting in untimely guidance and evaluation, and secondary rework often occurs.
In the process of conducting small project research, we deeply realized that students are the discoverers of problems and practitioners of in-depth research during practical activities. They are not only the main body of the implementation of small project research, It is also the main body of thinking. Therefore, the process of small project research is the process of generating infinite energy. The research brings us surprising changes, which makes us have to continue sincerely.