Keywords: finding problems, putting forward problems, analyzing problems, solving problems and cultivating abilities
First, the research status and trend analysis of this topic at home and abroad.
(1) Review and reflection on traditional mathematics teaching in China;
The "advantage" of China's traditional teaching lies in that students can acquire knowledge in a short time and in a large dose; Good problem-solving training, students' problem-solving ability (calculation, reasoning, demonstration, etc. ) strong and so on. However, there are also obvious "shortcomings": for example, students are passive in learning and inactive in thinking; Poor problem awareness, will not take the initiative to find questions to ask questions. In recent years, Professor Lu Chuanhan and Professor Wang from the School of Mathematics and Computer Science of Guizhou Normal University and Dr. Cai Jinfa from the University of Delaware jointly conducted a cross-cultural study on "Proposing and Solving Mathematical Problems" for senior primary school students in China and the United States. The results show that China pupils are better at solving mathematical problems than American pupils, especially in calculation and reasoning. However, the problem-solving thinking is not active, limited by formulas and imitation examples, and the intuitive guessing and hands-on ability is weaker than that of American primary school students; The ability of American pupils to ask questions is obviously higher than that of China pupils, and they are active in thinking, intuitive in guessing and reasonable in reasoning. It can be seen that the traditional mathematics teaching model in primary and secondary schools in China only pays attention to training students to answer the questions that have been raised, and requires students to strengthen training repeatedly according to a certain problem-solving model, while ignoring how to guide students to find problems, ask questions and explore and solve unconventional problems, thus seriously affecting the cultivation of students' innovative consciousness and ability. In the process of promoting the new curriculum, how to create high-quality mathematical problem situations, guide students to actively study mathematics, think deeply about mathematics, and promote the improvement of students' mathematical literacy is an unavoidable problem.
(2) The former Soviet psychologist Machuskin and others made a pioneering and systematic study on problem-based teaching. Based on the latest achievements of contemporary thinking science, they made a profound psychological demonstration on the essence of problem teaching and made a concrete and scientific study on the operation mode and principles of problem teaching. It is believed that the problem is the starting point of thinking, and the process of solving the problem is also the process of creative thinking.
(3) Modern constructivist learning view and instructional design theory regard problem solving as the basic strategy of constructive learning. The United States, Australia and other countries have also conducted in-depth research on this issue, believing that the problem is the beginning of thinking, and the process of solving the problem is the process of thinking development. American mathematics curriculum and evaluation standards clearly point out that students should have the ability to find and ask their own questions.
This topic is based on cultivating students' awareness of discovering mathematical problems and their ability to put forward, analyze and solve mathematical problems, and then cultivating students' innovative ability, making up for the shortcomings in traditional teaching, catering to the needs of the development of the times for innovative talents and conforming to the trend of mathematical education reform at home and abroad.
Second, the topic is put forward
Mathematics, as the foundation of modern science and technology, permeates all levels of society and is widely used. Mathematics education should not only enable students to master mathematics knowledge, but also cultivate students' learning ability to acquire knowledge independently and innovative subjective consciousness, thus promoting students' subjective development. On the basis of existing knowledge and experience, the research of this topic is to let students actively discover, ask, analyze and solve problems, and recreate knowledge through their own emotional experience, thus fundamentally changing the disadvantages brought by "exam-oriented education", thus stimulating students' subjective initiative and cognitive drive in learning mathematics, improving the teaching efficiency of primary school mathematics and reducing students' learning burden.
At present, with the deepening of classroom reform, teaching concepts such as "cultivating students' innovative consciousness", "students are the masters of the classroom" and "autonomous learning and inquiry learning" have become the consensus of everyone. The research process between teachers and students and students' independent innovative learning are inseparable from the skeleton of the problem. However, in specific teaching, teachers still pay more attention to how to teach, how to make students learn knowledge and master skills, and rarely involve how students learn, especially how to make students learn with problems. However, if a person has no doubt, where can he get research and innovation?
Under the advocacy of new courses and new ideas, the success of mathematics teaching lies in whether students' mathematical ability is cultivated, and the strength of mathematics teaching ability is largely manifested in whether students can ask mathematical questions and use what they have learned to solve practical problems in life. Therefore, under the guidance of the concept of "mathematics standard curriculum standard", combined with the present situation of educational reform in our city, districts and schools, we have established this topic.
Third, the definition of the topic, the definition of the topic and theoretical assumptions.
1, the definition of the theme
(1) "Mathematical problem"-refers to the situation that can't be solved by existing mathematical experience and methods. If a mathematical problem is regarded as a system, then at least one element in this system is unknown to students. If students know all the elements that make up this system, then this system is not a problem system for students, but a stable system. Therefore, mathematical problems have two remarkable characteristics: one is obstacle; The second is acceptability.
(2) "Asking questions"-refers to creating new questions or re-expounding known mathematical problems in the context of independent mathematical problems. Asking questions is an important course goal, which not only helps to promote students' understanding of mathematics knowledge and improve their interest in learning, but also helps to cultivate students' creative potential of finding problems and lay the foundation for their lifelong learning and development.
(3) "Problem-solving"-refers to the psychological activity that individuals adopt new strategies to find answers to new problems in new situations according to the relevant knowledge obtained, which is not only the purpose of mathematics teaching, but also the methods and means of mathematics teaching.
(4) "ability to ask questions" and "ability to solve problems"-refers to actively trying to ask mathematical questions from the perspective of mathematics, and using the knowledge and methods learned to seek strategies to solve practical problems; In the face of new mathematical knowledge, we can actively find its practical background and explore its application value. "We can find and put forward simple mathematical problems from our daily life." We can have different solutions to the same problem and have experience in solving problems with our peers. Using mathematics to "solve problems" includes not only being able to solve ready-made problems with mathematics, but more importantly, being able to find or put forward problems from the perspective of mathematics, and using the knowledge and methods learned to solve problems. It has the following characteristics: ① Life; ② comprehensiveness; ③ practicality; ④ Procedural; ⑤ Developmental.
2. Theoretical assumptions
The teaching of solving practical problems in primary school mathematics is an organic whole composed of interrelated and interactive elements such as teaching materials, teachers and students. On the premise of not increasing the number of elements and attaching special conditions, by adjusting the internal elements and their relationships, the overall function of solving practical problems in primary school mathematics is formed, the best development of primary school mathematics literacy is promoted, and the basic laws of solving practical problems in primary school mathematics teaching are explored.
Fourthly, the practical significance and theoretical value of the research.
Modern school education shoulders the heavy responsibility of training scientists and high-tech talents. The core quality of talents is innovative consciousness and innovative ability, and all kinds of innovative behaviors and achievements are derived from problems. No problem, no innovation. The results and forms of mathematical creation and innovation are all mathematical problems. To cultivate students' independent innovation ability, it is necessary to strengthen the training of students to ask mathematical questions.
Our teaching activities should guide students to ask questions and understand problems from the perspective of mathematics, gradually cultivate their ability to solve practical problems by comprehensively applying the knowledge and skills they have learned, and improve their application consciousness; Make students feel the close connection between mathematics and real life, enhance their desire to learn mathematics, and improve their ability to choose information, organize information and solve problems with information from the perspective of mathematics; Cultivate students' spirit of independent exploration and consciousness of cooperation and communication, develop students' thinking, make students feel the value of mathematics in the process of solving problems, and enhance their confidence in learning and using mathematics well. .
Fifth, the theoretical basis of the research.
1, activity constructivism
The constructivist learning view of modern psychology holds that learning is a process in which learners actively construct internal psychological representations in their own way, so it emphasizes the initiative, sociality and situational nature of learning; It not only emphasizes finding and putting forward mathematical problems from situations, but also attaches importance to independent exploration, analysis and solution of mathematical problems, and finds new problems in solving problems.
2. Innovative education theory.
According to the theory of innovative education, learning mathematics means learning innovative ideas, cultivating innovative consciousness and ability, and mastering innovative knowledge and skills. From this perspective, learning mathematics means learning how to find, propose, analyze and solve mathematical problems.
3. The philosopher Popper once said: "It is the problem that inspires us to learn, develop knowledge, practice and observe." Popper believes that creative thinking activities start from various problems, and the logical starting point for scientists to explore should be problems. Popper's scientific evolution formula "P 1 (Question) TT (Hypothesis) EE (Negation) P2 (Question)" takes the question as the starting point and end point of scientific activities.
VI. Research objectives
(1) theoretical objective:
1, combined with school-based research, explore teaching strategies, cultivate students' ability to discover, propose, analyze and solve practical problems, optimize teaching process and improve teaching quality.
2. Cultivate students' ability to solve practical problems through independent exploration, cooperation and exchange and diversified evaluation methods.
3. With the help of reflection on mathematics, teachers gradually absorb advanced curriculum ideas and teaching methods in the process of practice, thus realizing self-improvement.
(2) Training objectives:
1. Cultivate students' creative ability to find, put forward, analyze and solve practical problems, their enthusiasm for mathematics and their will to overcome difficulties, and lay a high psychological quality for participating in the fierce competition in the future knowledge economy era.
2. Promote students' all-round and personalized development, so that each student can get different development in mathematics, gradually change the learning style, and cultivate students' innovative consciousness and ability.
3. Through exploration and research, update teachers' views on students, teaching and occupation, and improve the level of teaching and scientific research in our school.
(iii) Outcome targets
Explore an effective teaching method to raise and solve problems, summarize the rules of problem teaching, and form papers, teaching designs, classroom teaching records, teaching cases, etc.
Seven, research methods and steps.
(1) research methods:
1, experimental method.
2. Investigation methods.
3. Case study method.
4. Literature research method.
5. Natural research method.
6. Experience accumulation method.
(2) Experimental steps:
The first stage (June 2007 ~ February 2008): the preparation stage.
1, project application;
2. Write the experimental scheme;
3. Organize theoretical study and training.
The second stage (March 2008 ~ July 2065438+00): the project implementation stage.
1, research and cultivate students' ability to ask questions and solve practical problems;
2. Accumulate data, write experimental papers, educational stories, teaching reflections, etc. (Each experimental teacher is responsible);
3. Discuss, improve and develop.
(July 2009): Mid-term evaluation of the project.
1, experimental data display and evaluation
2. Write the mid-term evaluation report
3, put forward the requirements and objectives of the next phase of the experiment (proposed by the project leader).
The third stage (August 2065438+00 ~ February 2065438 +00 10): summary acceptance stage.
1, sorting out the experimental data;
2. Organize the main members of the research group to give special lectures or reports, and summarize the experimental experience of key teachers;
3. Write experimental work reports, research reports and conclusions.
Eight, experimental content and measures
1. To study the arrangement characteristics of solving practical problems and the psychological characteristics of students' questions in Curriculum Standard Textbook.
2. Design a classroom teaching plan that conforms to the teaching law of solving practical problems, be good at grasping the generated teaching resources in the implementation process, and explore the "situation-problem" teaching mode of mathematics;
Students' learning: questioning, independent cooperation and inquiry; Teacher's guidance: enlightening, inducing, correcting mistakes, solving puzzles, teaching and setting mathematical situations (observation and analysis)-putting forward mathematical problems (exploration and conjecture)-solving mathematical problems (solution and refutation)-paying attention to mathematical application (learning to do and use).
3. Carry out mathematical practice activities with solving practical problems as the main content, and construct the curriculum model of mathematical practice activities.
4. Make a reasonable evaluation of students' learning to solve practical problems and explore the evaluation methods of students' learning to solve practical problems.
9. Conditions for completing the study.
1, strengthen theoretical study. Invite educational experts and scholars to give necessary theoretical guidance to the members of the research group, hold educational salons, educational seminars and other activities on a regular basis, make full use of expert resources, famous teachers' resources and the accumulated experience of education and scientific research in the past, gain information advantages with other research bases, provide theoretical trends to the members of the research group in time, and ensure the rational operation of the research.
2. Improve organizational construction. Set up the project core leading group, define the division of labor, cooperate in research and strengthen project management.
3. Adhere to practical exploration. Make full use of our school's successful experience in long-term mathematical teaching practice and exploration to promote the research of this topic. Encourage teachers to take the road of practical research, strengthen the attempt, reflection, dialogue and cooperation in practical research, and enhance practical wisdom.
4. Establish a safeguard mechanism. The school guarantees the investment of scientific research funds, provides the time and conditions needed to complete this project, and undertakes the management task of this project.
refer to
[1] Mathematics Curriculum Standard for Full-time Compulsory Education (experimental draft), Beijing: Normal University Press.
[2] Interpretation of Mathematics Curriculum Standards for Full-time Compulsory Education (Experimental Draft), Beijing: Normal University Press.
[3] Zheng Yuxin's Problem Solving and Mathematics Education, Nanjing: Jiangsu Education Press.
[4] Zhu Dequan, Representation of Mathematical Problem Solving and Metacognition Development, Beijing: Educational Research.
Achievements:
In 2005, the project "Close the connection between mathematics and life and improve students' practical ability" won the first prize in the province; In 2006, the periodical summary of "Close the connection between mathematics and life and improve students' practical ability" won the second prize of the province. In 2006, the lesson "Solving Practical Problems" taught by experimental teacher Han won the first prize in the national competition; In 2007, the experimental project of "Close the connection between mathematics and life and improve students' practical ability" won the advanced collective of Shanxi Province's "Tenth Five-Year Plan" project.
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