Effectively cultivate students' mathematical language expression ability and promote the development of rational reasoning ability

Second, the topic is put forward

On the basis of re-examining the traditional teaching objectives of geometry, the new curriculum standard puts forward clear requirements for proof: "You can get mathematical conjecture through observation, experiment, induction and analogy, and further verify, give proof or cite counterexamples", "From several basic facts, prove some properties of triangles and quadrangles, understand the necessity of proof, understand the basic process of proof, master the format of comprehensive method proof, and initially feel the axiomatic thought.

Students should "experience observation, experiment, guess, proof and other mathematical activities to develop reasonable reasoning ability and preliminary deductive reasoning ability" through mathematics learning in compulsory education stage. The cultivation of students' logical thinking ability is inseparable from the training of students' mathematical language. Language is a tool of thinking, and the process of thinking depends on language expression. The development of language can promote the development of students' thinking. Therefore, in mathematics teaching, teachers should create conditions for students to reason more. Such as: definition, theorem, rule, formula, process, arithmetic, method, rule, meaning of problem, train of thought, quantitative relationship, formal meaning, etc. So as to train and cultivate students' language expression ability and achieve the purpose of developing students' mathematical thinking.

In daily teaching, we often encounter such a problem: students can think of the conclusion of the problem, but they can't explain the process of thinking and the way of thinking to solve the problem. In particular, many students only pay attention to the result of the problem and ignore the process of solving the problem. Some students will say that they can't write, write or speak, and gradually they will go into the misunderstanding that they dare not say, don't want to say, don't say, and don't say. In view of the above problems, I have determined the subject of "effectively cultivating students' mathematical language expression ability and promoting the cultivation of reasonable reasoning ability"

Third, the purpose and significance of the study.

The purpose of this study is to gradually explore effective junior high school mathematics teaching methods, cultivate students' oral and written expression ability, promote students' rational reasoning ability, make students develop the habit of orderly thinking, standardize answering questions, strive to make students dare to speak, want to speak and know how to speak, cultivate students' ability of autonomous learning, cooperative learning and inquiry learning, and continuously improve classroom teaching efficiency to meet the needs of senior high school entrance examination reform.

Fourthly, the research method of the subject.

Taking experimental operation activities as the main form, students can establish various positional and quantitative relationships between space and plane through analogy and induction, so as to develop students' spatial concepts and geometric intuition in experimental geometry, and gradually get rid of the interlocking logical connection and strict abstract deductive reasoning form of Euclidean geometry.

The research process of verb (the abbreviation of verb)

Research steps

1, preparation stage:

(1) Learn and master the requirements of junior high school mathematics curriculum standards for the cultivation of language expression ability.

(2) To study the present situation of students' language expression ability and the reasons for their poor language expression ability.

(3) make a research plan

2. Experimental stage:

(1) Seeking effective strategies to improve students' language expression ability in mathematics teaching.

(2) Implement specific plans.

(3) reflect on experience and shortcomings.

3. Summary stage:

(1) Observe the changes of students' language expression according to the research.

(2) Summarize the topic and form a research report.

(ii) Implementation process

Mathematician Paulia said: "Mathematics can be regarded as the science of proof, but this is only one aspect. The mathematical theory has been completed and expressed in the final form. It seems that only proof can be purely provable. Strict mathematical reasoning is based on deductive reasoning, and the process of drawing mathematical conclusions and proving them is discovered by perceptual reasoning. " The result of reasonable reasoning is accidental, but it is not completely fictional. It is an exploratory judgment based on certain knowledge and methods. Therefore, how to teach students reasonable reasoning in normal classroom teaching and how to express it in appropriate mathematical language is a topic worthy of discussion.

First of all, through interviews and questionnaires, I investigated the reasons for students' poor language expression ability. Through the investigation, four main reasons are summarized: First, poor psychological quality, strong vanity, fear of wrong or bad answers, and fear of being laughed at by classmates or teachers. Second, I am introverted, I don't want to express myself, or I don't have the opportunity to speak, and I gradually close myself. Third, there is a lack of systematic understanding of knowledge, and it is impossible to analyze and answer questions systematically. Fourth, without a rigorous learning attitude, I want to jump when I can't walk ... I can't use mathematical language to standardize my answers.

It can be seen that language expression ability will directly affect students' mathematics learning ability, and indirectly affect the development of students' personal communication ability and comprehensive quality. The content of experimental geometry is added to the new curriculum. Because it is closer to students' daily life experience; At the same time, it reduces the requirement for the rigor of geometric logic, so that students with different intelligence levels can benefit from mathematical activities; Moreover, mastering the essence of space through activities makes it easier to cultivate students' observation ability, experimental ability, inductive analogy ability and creativity. People pay more and more attention to these obvious advantages. Next, I will talk about my own practice in combination with the new curriculum concept, the reasons for students' poor Chinese ability and classroom teaching:

1. Correct yourself first and standardize your teaching behavior. Prepare lessons carefully, and strive for correct, scientific, concise, standardized, organized, logical and coherent classroom language. Adhere to the use of mathematical language in teaching, not colloquial. The demonstration of blackboard writing is targeted, which gives students a good guide and makes them gradually realize the importance of answering questions from the simple imitation. At the same time, the design of blackboard writing should be beautiful, elegant, concise and standardized, so that blackboard writing can give students beautiful enjoyment ... and thus imitate involuntarily. For example, when teaching practical problems and binary linear equations, I lead students to sum up the five-character policy while writing on the blackboard: setting, listing, solving, checking and answering. Students can complete similar math problems in a standardized way by following these five-word guidelines.

2. Create time and space for students' language expression. In mathematics teaching activities, if teachers only use the contents of textbooks as materials to cultivate students' rational reasoning ability, then there is no doubt that such teaching activities can promote the development of students' rational reasoning ability. However, in addition to school education and teaching activities (subject to the content of textbooks), there are many activities that can effectively develop students' rational reasoning ability. For example, people often need to make judgments and reasoning in their daily lives, and many games also imply the requirement of reasoning. Therefore, it is necessary to further broaden the channels for developing students' rational reasoning ability, so that students can feel that there are "mathematics" and "rational reasoning" in their lives and activities, and form a good habit of being good at observation, speculation, analysis and inductive reasoning.

3. Pay attention to students' experience of new knowledge. Teachers should actively create a relaxed and democratic classroom atmosphere, give full play to students' main role, and show students the rights and opportunities to express mathematics. For example, when learning the parallel axiom that there is a point outside a straight line, only one straight line is parallel to a known straight line, teachers and students can draw pictures and do experiments together, so that students can sum up this axiom. At this time, teachers should encourage students to express themselves boldly. After the teacher's supplementary induction, it is difficult for students to master the technical terms of "a little outside the straight line" and "only one" in this axiom, so that students can read and feel it, understand its meaning, or have a dialogue with their deskmates. While giving students the opportunity to "speak", teachers gradually ask students to answer questions correctly, use accurate words and complete sentences, and pay attention to guiding students to express their language accurately, concisely, methodically, logically and persistently, so that students can learn mathematical terms well, use mathematical terms well and speak standardized mathematical language well. With personal experience and understanding, students will feel and speak.

4, the role model is endless, using students to influence students. In mathematics teaching, we often encounter problems that are difficult to express in words. I let those students who have exemplary roles speak first, so that other students can feel how to express their problems and how to express them in an orderly way. In addition, it is far more obvious for those students who write norms to perform in the front panel than the teacher emphasizes over and over again. For the questions I just came into contact with, I asked my deskmate and the students in the group to check each other after answering the questions and point out each other's shortcomings. Students who have outstanding language expression in their homework or test paper answers, I ask them to show their works to their classmates and influence other students with their standardized answers. This stimulates students' interest and strengthens the importance of language expression.

Sixth, the reflection of research.

In traditional mathematics teaching, geometry teaching is the main way to cultivate students' logical reasoning ability and learn mathematical proof methods. For a long time, mathematics teaching has focused on formally developing students' deductive reasoning ability, ignoring the cultivation of reasonable reasoning ability. It should be pointed out that mathematics needs deductive reasoning and more reasonable reasoning. The discovery of scientific conclusions (including mathematical theorems, laws, formulas, etc. ) It often begins with observation, comparison, induction and analogy of things ... that is, a guess is put forward through reasonable reasoning, and then the guess is proved correct or wrong through deductive reasoning. Deductive reasoning and rational reasoning are two different but complementary forms of reasoning. Great changes have taken place in the handling of geometry teaching in the new curriculum, and the requirements for students' reasonable reasoning and proof ability are different from those in the past. In teaching, we should observe, guess, experiment, discuss and explore, and finally gradually lead to proof, which is a complete process of gradual development of reasoning.

Through the research of this topic, most students have reached the level of dare to speak, want to speak, speak and speak. Students can actively restrain their language expression habits and strive to standardize them. However, there are still some puzzles in the research process, such as: how to make a good transition from oral expression to written expression, how to integrate language expression in mathematics with other disciplines, and how to better take care of those ultra-vulnerable groups; As teachers, everyone wants to constantly cultivate students' expressive ability, but where does the time come from? What if the teaching content can't be completed? What if the students just refuse to talk?

VII. Research results

1, project research plan and report.

2. Case analysis and thesis.

Eight. Research experience of this subject.

I have a brand-new understanding of cultivating students' language expression ability in junior high school mathematics teaching. In junior high school mathematics teaching, mastering mathematics language and mathematics knowledge complement each other. Language, as a "coat of thinking", can help students master knowledge, and knowledge, as the connotation of language, can also help students understand language. Therefore, junior high school mathematics teaching should attach importance to the teaching of mathematical language.