Mathematical language expression ability is an important mathematical ability. From the process of mathematics learning, students can understand the spiritual essence of knowledge and improve their mathematical thinking level through their own personal practice and active construction. The following is a 3000-word reading note on mathematics educational psychology that I have carefully arranged for you. Welcome to read and learn!
Mathematics teachers' work mainly focuses on classroom teaching practice, and mathematics educational psychology can help teachers to continuously improve the level of classroom teaching research.
Firstly, it provides theoretical guidance for classroom teaching. Mathematics educational psychology provides general principles, processes and methods for mathematics teaching. Teachers can combine these principles with specific teaching contents and turn them into certain teaching procedures. For example, concept teaching generally includes the following links: concept background, attribute analysis of specific examples, definition, concept discrimination, simple application of concepts, and concept refining. Teachers can arrange teaching activities according to these links and design appropriate materials to realize each link.
Thinking: Concept teaching is the basis of mathematics teaching and learning. Only when students really understand the concept can they pave the way for future study. But the actual teaching situation is: the teacher leads out the concept quickly and simply, and the students read it aloud several times. The teacher began to say a few points for attention, which discrimination questions will appear in the exam (mostly multiple-choice questions). And then everyone started to be cheerful? Brush the questions? . Students think that the content of concept class is simple and can be done in class. But there are big problems hidden under the surface of the classroom. Do the students really understand this concept? Where did this concept come from? Is it artificial? Or is it because of some need? I don't think many students have thought about such a problem. Of course, I also despised these aspects in my previous teaching. In the future teaching, I will work hard in this respect.
Secondly, help teachers analyze, predict and interfere with students' mathematics learning. Using the principle of mathematics educational psychology, teachers can correctly analyze the reasons of students' learning performance and take certain intervention measures to achieve the expected results. For example, students make repetitive mistakes in solving problems. What should teachers do? What many teachers do is to emphasize repeatedly? Remember? But the actual effect is not ideal. (I usually do the same in teaching. I have doubts for a long time, but I can't find a better method and theoretical guidance. After reading this book, I still have a lot to gain. _? ) o) research shows that the reason for repeated mistakes is firstly that there are defects in concept learning. At the same time, students often start to work when they don't have good habit of solving problems. What's more, the eyes scanned a few data and began to calculate. For example,? Is the symmetry point of point A about the Y axis in the second quadrant? What do many students see? Point a is in the second quadrant? . After discovering problems, teachers can ask some suggestive questions in teaching, such as? What concepts are involved in the question? What does this condition mean? What is the connection between conditions and conclusions? Can you think of any knowledge points or concepts related to this conclusion?
Thinking: In the usual teaching, we often encounter repeated problems. Students make mistakes repeatedly, but they still can't start with the problems just mentioned. It shows that there are still some problems in our usual teaching. For example, when talking about the existence of parallelogram, students are often presented with their own problem-solving steps (according to the midpoint coordinates). It doesn't explain why it should be done, and what is the principle? In fact, in the final analysis, it is because the basic properties of parallelogram itself are bisected by diagonal lines. A simple problem of moving points caused by nature, but if you only talk about moving points, students will find it too difficult. Some students will not listen carefully, and some students don't know the principle, so they can only rely on rote memorization of the steps given by the teacher. You can't cope with a slight change in the topic. Therefore, the usual teaching should be traced back to the source, so that students can understand how this topic is carried out step by step from a basic nature. Grow up? Become a moving point problem. I hope I can do it without telling students too much? Routine? As far as possible? Distracted? Mathematics teaching based on.
Third, provide teachers with methods to study students' situation. The situation of students is very different, and the reasons for learning difficulties are also different. Mathematics educational psychology can help teachers understand the specific reasons in various ways and provide basis for teachers to take targeted measures. For example, many junior high school students have difficulty in algebraic operation, and we can find the reasons from the students' homework and the results of various tests. This difficulty. This difficulty may be related to the development level of intelligence, poor understanding of arithmetic, poor operation ability of numbers and bad operation habits. If teachers master the theory and research methods of mathematics educational psychology, they can trace back to the source, find the root of students' learning difficulties, prescribe the right medicine and promote students to improve their learning effectively.
Thinking: When it comes to computing power, I have been deeply touched recently. This time, many students in my class have problems in the operation of the third question of 23 questions in the third grade model test. I focused on similar problems of parabola in class and practiced it many times. This kind of question gives us a feeling of being relaxed at ordinary times. After finding a fixed angle (or equal angle), it can be calculated according to two similar situations. Because the thinking is very clear, and the data of the topics we usually do are very simple, I neglected the training of computing ability. Lead to student exams? It's easier to start than to go deep? In some cases, some students can't figure out the answer, some students can't figure out the abscissa but the ordinate, and some students can't believe their own answers, thinking that they have miscalculated, so they forcibly change them. After the exam, I am also thinking about what kind of problems are hidden behind this phenomenon. First of all, I usually pay more attention to the training of methods and less attention to the training of computing ability. Secondly, I seldom give them time-limited training, so what they usually do when they have enough time is very different from what they do when they take the exam. Time is limited during the exam, students are nervous and the effect is not good. Finally, I feel that students are not very flexible and cannot make good use of the idea of combining numbers with shapes. Those students who worked out the abscissa basically didn't work out the ordinate, because they brought the abscissa into the parabolic analytical formula to calculate the ordinate (so all previous efforts were in vain). This problem can be solved if students can look at the formula with the help of the geometric properties of figures or the method of operational holism. In addition, there are too few methods to master. Students basically set the coordinates of a point (the point is on a parabola), so it is difficult to work out the final answer directly (if you don't carefully observe the essence of the figure). But if we change the method, we can set the side length of the triangle as m, then use m to represent the coordinates of the points, and then bring the coordinates into the parabolic analytical formula, and we can solve it quickly. The key point is that this method represents coordinates and is linear about m, so the ordinate is not difficult to calculate. In short, there are still many problems in the usual teaching, which leads to the unsatisfactory scoring rate of this question. So thank the author (director Lin). If I hadn't encountered such a problem, I might never have found such a problem and made some thoughts. Although I didn't think deeply enough, I think I got something worth it. The next step is to make some improvement measures in teaching to make up for it.
Just mentioned the computing ability, in fact, computing ability is a very important mathematical quality (mathematical literacy). "Psychology of Mathematics Education" mentioned that calculation includes accurate calculation, mental calculation and estimation according to laws. According to the algorithm, students' reasoning ability can be trained, the skills of operating according to procedures can be formed, and the literacy and habit of doing things according to rules can be cultivated. Is this also training students? Contract spirit? . Just like Director Lin mentioned in qq space and WeChat official account before? g？ problem China people are relatively scarce now? Contract spirit? It leads to only obeying the rules that are beneficial to you and not obeying the rules that are unfavorable to you. Such compliance? Rules? A little mercenary. Another example is the housing price problem that we have been paying more attention to in recent years. When housing prices skyrocket, no one will go to the developer to make trouble, but if the price of the second phase of the property is lower than that of the first phase, then those owners who bought the first phase will inevitably make trouble. Because they feel that their interests have been violated. But if you simply follow the contract, as long as the developer sells your house at the contract price, it is normal to perform the contract. The rise and fall of the second-phase property price has nothing to do with the owner of the first-phase property, and there is no default by the developer. But China people are like this, which is beneficial to them (the second-phase price increase, the first-phase owners feel that they have made money), and they will accept it, and the unfavorable ones will make trouble. I think this is the lack? Contract spirit? Incarnation I remember reading a book in which a history teacher asked the students: Should we abide by unequal treaties? The key is whether you really. Contract spirit? . I think this society will become more and more fair only if all of us can abide by the rules. More rules, less human feelings!
Back to calculation, mental arithmetic and estimation can cultivate students' ability to fully grasp the problem situation and insight into the essence of things, as well as the ability to accurately understand the characteristics of data, reasonably choose algorithms and correctly judge the rationality of results. Estimation is the overall grasp of the situation, which is realized by analogy with the existing teaching mode in the mind, and it is an intuitive judgment of the essence of things, so it is a qualitative thinking form with greater flexibility. Prediction reflects a person's gentle and reasonable judgment and choice when facing problems, and the basis for forming this quality is accurate calculation. On the basis of accurate calculation, students are required to constantly estimate the calculation results, so that students can form intuition suitable for estimation, and then cultivate their ability to judge the development prospects and results of things. When dealing with problems, people can rely on this intuition to judge what method to use, the feasibility and possible results of the method. In fact, in the real world, accuracy is relative and fuzziness is absolute.
Let's talk about the intuitive ability of geometry. Geometry is a mathematical object, which abandons the material properties of an object and only considers it from the perspective of its spatial form. Geometry is a more general concept, even abandoning the extension of space. For example, triangles, parallelograms and circles are two-dimensional, straight lines are one-dimensional, and points have no dimensions. The point is probably the top of the line, and the abstract concept that is extremely accurate can no longer be divided into several parts. So, what is the basis of geometry? Pure form? Take the spatial form and relationship of abstract objects as their own research object. For what? Pure form? We can't draw conclusions by doing experiments, we can only draw some new conclusions from some conclusions through intuitive thinking and logical reasoning, and finally we can draw geometric theorems through logical reasoning and proof. The cultivation of geometric intuitive ability runs through mathematics teaching in primary and secondary schools. Specifically, when learning qualitative plane geometry, we can get that the sum of axioms and triangles is equal to 180 through SAS. Based on this, what is the basis of studying the characteristic properties of isosceles triangle and parallelogram, and gradually use these two basic tools to demonstrate and solve all other theorems and exercises in plane geometry.
Feeling: Geometric intuition is very important for students to solve geometric problems. Students who are sensitive to geometric intuition can see the key points of the problem at a glance and understand it from complex conditions. Clear thinking, find the basic geometry and get the basic conclusion, so as to solve the problem quickly and efficiently. As for how to cultivate students' geometric intuitive ability, I think it is still necessary for students to establish model ideas. What do you see? Type? The corresponding mathematical geometric model, and then draw the basic conclusion. When encountering problems, students must be allowed to observe for themselves to see if they can find the basic graphics by themselves. If they can't, teachers should give timely guidance, and students must find it themselves. It is better for students to find it once by themselves than for teachers to speak 10 times, so the guidance of teachers is very important.
Mathematical language expression ability is an important mathematical ability. From the process of mathematics learning, students can understand the spiritual essence of knowledge and improve their mathematical thinking level through their own personal practice and active construction. Through math communication between classes, groups or friends, I gradually learn to express my ideas clearly, accurately and logically, and I am good at listening to and understanding others' ideas, so as to realize mutual learning and improvement among my classmates.
Feeling: Teachers should give students more time and space to express their ideas and exercise their mathematical language expression ability. Can't it just be like this? A word? Do not organize students to discuss and communicate. But spend a lot of time on repeated problem-solving training. This kind of teaching will make students fear mathematics and make them feel that mathematics is just brushing questions and doing exercises. In this way, students will lose interest in mathematics, and it is difficult to learn mathematics well. Let students boldly share their ideas with teachers and classmates in class. Even if his idea is wrong and his direction is deviated, it is also an opportunity to exercise his expression. When teachers understand students' thoughts, they can prescribe the right medicine and help students solve problems quickly and accurately. Therefore, teachers should listen more in class and try to leave time for students. I'd rather say it myself than be afraid of lack of time.