First, careful preparation before class is the premise of a good paper lecture.
Ausubel pointed out: "The only important factor that affects students is what learners already know. To understand this, we must teach it accordingly. " Therefore, teachers should carefully prepare papers before evaluating classes, so as to be aware of them.
First of all, we should do a good job in the statistics of relevant data, including the statistics of test results and the scoring rate of each question. Count the highest score and average score, so that students can know their approximate position in the class in this exam; Count which are "frequently-occurring diseases", which excellent students lose more points in which middle and high grade questions, which students have made remarkable progress, which basic questions are infallible and which questions belong to "group problems". Only by fully mastering the data can we make targeted comments on the overall situation of students' test papers.
Secondly, we should analyze the root causes of students' mistakes. After mastering the scoring rate of each question, choose the questions with low scoring rate, analyze the root causes of students' mistakes, and find out which ones are "carelessness" and "misunderstanding". If it is a "careless" mistake, the teacher does not need to explain it on the knowledge level, but mainly analyzes it from the psychological level of students' problem solving; If students make the mistake of "misunderstanding", they should be allowed to discuss more with since the enlightenment. Teachers should not only talk about reasoning, but also tell students how to think about it. It is necessary to overcome the situation that "it sounds easy, but it is not right to do it", so that students can really understand and master it.
Second, grasping the key points in class is the key to a good lecture on examination papers.
No matter from the consideration of time or the analysis of teaching effect, it is impossible to evaluate the test paper comprehensively. The teacher should grasp the key points, so what should the test paper say at the end? I think we should pay attention to the following points when marking papers.
(A) about typical mistakes
According to the preparation before class, the content of the evaluation should be determined according to the students' answers, and the wrong questions of individual students should be prompted in the form of marking papers, which can no longer occupy classroom time. For typical mistakes, because they are representative, they are the key to improve students' mathematical ability, so we should focus on comments. When looking for the cause of the error, we should not only stay on the knowledge points, but also trace back to the source, find out the thinking method of mathematics and expand it, so that we can argue on the topic and explain one topic to drive another.
(2) Talking about a topic is changeable.
Educator Paulia believes that "if we don't use' topic change', we can hardly make any progress." In other words, when commenting on test questions, you can't just pay attention to the topic. For questions involving a wide range of knowledge and skills, we should strive to achieve "more changes in one question" and "more practice in one question", such as strengthening or weakening the conclusion of the question, increasing or decreasing the conditions of the question, changing the situation of the question, and guiding students to expand their thinking and get through it vertically and horizontally.
(C) the way of thinking
Mathematical thinking method is an essential understanding of mathematical content and methods used, and it is a universal "universal method". Flexible use of various mathematical thinking methods is the fundamental to improve the ability to solve problems. Therefore, when marking test papers, we should pay attention to guiding students to sum up and understand the ideas and methods in various mathematics test questions, and cultivate students' ability to solve problems with mathematical thinking methods.
For example, when explaining the right-angled triangle test paper, there is a topic: in the "old city reconstruction", a city plans to plant some kind of turf in a triangular open space in the city (as shown in figure 1) to beautify the environment. It is known that the price of this turf is one yuan per square meter, so how much does it cost to buy this turf at least? The topic is not very difficult. In class, I asked students at the middle and lower levels to introduce their own solutions, and asked other students to comment on the rationality of the problem-solving process and the mathematical ideas contained in it. Because of the infiltration in normal teaching, students can point out the idea of transformation, that is, using it as an auxiliary line, transforming an obtuse triangle into a right triangle to solve it. Then I guide the students to find out the rest of the problems solved by transforming thinking method in the test paper, and point out that transforming thinking method is an effective thinking method to study and solve mathematical problems. It turns the unknown into the known and the complex into the simple, and has a wide range of applications in mathematics. Through such comments, students can understand the spiritual essence of mathematical thinking methods, and form habits and concepts in the process of application, so as to master them systematically.
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Figure 1
(4) Talking about a kind of problems
In the unit examination, the examination of the same knowledge, skills and methods will appear repeatedly in different ways, and these are often the focus of this unit. In the simulation questions of the senior high school entrance examination, we can condense the similar questions in the previous papers into one type of questions, make appropriate supplements and extensions, summarize and generalize these questions, and form rules and methods.
For example, in the unit test of quadratic function, the following two problems appear: Question 1: In the rectangular coordinate plane, the vertex of the image of quadratic function is A( 1, -4), and after passing through point B (3,0), find the analytical formula of this quadratic function. Question 2: In the plane rectangular coordinate system, the position of △AOB is as shown in Figure 2: ∠AOB=90, AO=BO, and the coordinate of point A is (-3, 1).
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Figure 2
(1) Find the coordinates of point B;
(2) Find the analytical formula of parabola passing through three points A, O and B. ..
Both of these problems are to find the quadratic resolution function. When commenting, I put them together and added another question.
Question 3: Given that the intersection of a parabola and the X-axis is A (-2,0), B (1 0) and passes through point C (2 2,8), find the analytical expression of the parabola. Through the comments on these three topics, three cases of solving quadratic resolution function by undetermined coefficient method are revealed: vertex, general and intersection. This kind of evaluation can enable students to extract strategies to solve a class of problems from the process of solving problems, thus improving the mathematical value of test paper evaluation.
The above points do not require every class to be comprehensive, and teachers can seize one of them for special comments every time they evaluate the class.
After discussing and dealing with the related problems in the examination paper evaluation class, the teacher should carefully select one or several groups of intensive variant exercises from multiple angles and in all directions according to the basic knowledge, methods and ideas involved in this examination paper after class, so as to give students the opportunity to practice, summarize and reflect further. This is an extension of the evaluation of test papers and a necessary link to ensure the teaching effect of the evaluation of test papers.
"Students are the masters of mathematics learning", and the evaluation of test papers should also insist on providing students with sufficient opportunities to participate, guiding students to actively participate in evaluation activities, so that students can truly become the masters of the evaluation classroom.
(Editor: Zhang Huawei)