"The review class is the most difficult." This is a sigh that many math teachers often give out. Review class is neither as "fresh" as the new class nor as "successful" as the practical class. The most important thing is that, up to now, the review class does not have a basically recognized classroom teaching structure (model) like the new teaching. Because this kind of classroom teaching structure means that there are operable teaching procedures. As we all know, the quality of structure determines the size of function. An orderly classroom teaching structure is like a ladder, which enables teachers to lead students to climb stairs with confidence, and then master knowledge better and faster. After experimental research, we currently adopt the following review class structure.

First, show the review objectives (hereinafter referred to as bright label) (about 2 points)

At the beginning of the class, the teacher puts forward the review topic directly, and then hangs the review goal written in advance on the blackboard. The proposed evaluation objectives should pay attention to the following three points:

1. The goal should be comprehensive. The so-called "comprehensive" means that according to the requirements of mathematics syllabus, review requirements are put forward from three aspects: knowledge, ability and ideological morality. You can't favor one over the other, or even just ask for knowledge review, and put aside your ability and ideology and morality. For example, when reviewing statistical tables and charts, we should not only master the knowledge, but also cultivate students' observation ability and adaptability, and at the same time pay attention to cultivating students' meticulous and serious attitude and pursuing beautiful and neat sentiments and habits.

2. aim accurately. That is, targeted. First, the requirements of knowledge, ability, ideology and morality in the goal should be accurate, and second, they should not be confused. For example, the purpose of reviewing statistical tables and charts is to strengthen and distinguish the statistical tables and charts learned, and to prevent cross-talk of related or similar knowledge. The question that puzzles students is: how to determine the unit length? (* * *) Why should the interval of horizontal items in the broken-line statistical chart be left blank according to the actual year? (Personality) What students forget most are: forgetting to write data after drawing, or separating the title from the chart, and so on. When formulating the review objectives of the review class, we should pay attention to combining them with the problems found after these new classes to help solve students' practical problems.

3. The goal should be specific. Don't mention some abstract or vague slogans, such as "cultivating students' good study habits through review". At first glance, it was very specific, but on second thought, it was too vague. It is not clear which habits to cultivate students. In fact, a class can only cultivate students' quality in one aspect according to the actual teaching content, and too much will be counterproductive.

The teaching goal is not only for students, but also for teachers. In the review class, teachers should organize teaching closely around the goal, just like writing a chapter, so the review class should not be "off topic" and should be targeted.

Second, memories (about 8 points)

Memory is a process that requires students to extract and reproduce the old knowledge they have learned, and it is a favorable opportunity for students to associate independently, which should be done as independently as possible. If it is a junior, let them read the book before recalling it; Middle and senior students can also preview one day in advance, which will save some class time. Of course, the memory process can not be separated from the teacher's inspiration and assistance. We often adopt the following strategies:

1. Write independently.

2. Talk to each other at the same table.

3. Enlightened results.

For example, let students remember what numbers they have learned by "composing words" or "making sentences". What "shape"? What "style"? What "quantity"? This is also a good way to "associate" memory.

In the process of memorizing, students are generally only required to write or say "what" without asking "why" or "how", so that all the old knowledge can be "pulled out" in one go and the efficiency of memorizing can be improved. Therefore, when students recall, teachers should not "interfere" or "interrupt" too much, but let students talk and write noisily while flying like dragonflies. At this time, there is only one purpose: to recall old knowledge. For example, ask students to recall: What "horns" have we learned? As long as students name all angles such as acute angle, right angle and straight angle, they don't have to ask their meanings and differences, and they don't have to worry about the order of these angles.

Memory is not only a process of extracting old knowledge, but also a process of further strengthening memory, or a process of inspiring each other to obtain associative results.

If a student's memory is incomplete, it can be supplemented by other students or teachers at this time, or it can be put aside for a while and then perfected in "combing".

Third, carding (about 10)

Sorting is to classify old knowledge points according to certain standards. So combing is the focus of review. Combing should accomplish two tasks: one is to connect knowledge points (seeking common ground), and the other is to divide knowledge points (seeking differences). These in-service teachers should be fully prepared when preparing lessons, otherwise it will cause classroom chaos. Combing is often associated with writing on the blackboard, which makes audio-visual integration and enhances the review effect. According to the similarities and differences of the review content, it is usually adopted:

1. Write on the blackboard while combing. That is to say, combing and writing on the blackboard are synchronous.

2. comb first, then write on the blackboard. That is, teachers and students output the similarities and differences of old knowledge together, and then show the blackboard.

3. Write it on the blackboard before combing. This is more applicable in the lower grades. When using, you can also hang up the blackboard and comb it while watching.

The carding process is essentially a systematic thinking process of organizing knowledge, in which the thinking method is mainly "classification", that is, dividing knowledge according to certain standards. For example, quadrangles can be divided into two categories according to the relationship between opposite sides: two groups of quadrangles with parallel opposite sides (parallelogram) and only one group of quadrangles with parallel opposite sides (trapezoid). In the primary school stage, teaching should generally be based on students' actual learning content and the degree of thinking they have achieved, and it is not necessary to stick to the principle of complete science, so that primary school mathematics knowledge is too macro. This is one of the differences between "subject mathematics" and "scientific mathematics". Just like quadrangles, strictly speaking, two groups of irregular quadrangles whose opposite sides are not parallel should be regarded as one class. There is no need for students to "reinvent the wheel" if they don't learn mathematics in primary schools. It must be noted that our classification is to classify what we have learned, not what students have not learned. In fact, the classification standard is artificial, not to mention that some experts are arguing endlessly at present. For example, there are two cases in which triangles are classified by edges: one is to divide triangles into two categories-equilateral triangles and isosceles triangles, and take equilateral triangles as special cases of isosceles triangles; The second type is divided into three categories-equilateral triangle, isosceles triangle and equilateral triangle. It depends on how to define an isosceles triangle. In the end, it is better to divide it into smaller parts or thicker parts, depending on the amount of review content. Review content should be divided into larger parts, and vice versa.

Four, communication (about 10)

Communication is a prominent feature of review class. Because the main purpose of new teaching is to divide knowledge points and grasp the essential attribute of single knowledge, it is rarely and impossible to be related to subsequent knowledge. In the review class, we just connect and exchange what we have learned, which is the so-called knowledge point summary.

Communication is different from the simple connection between knowledge, but the essential integration of knowledge. Therefore, communication should not only seek common ground in differences, but also seek differences in similarities, which is an important link in the transformation of knowledge structure into cognitive structure. This is what we talked about before. In the memory stage, we only seek "what", but here we also pursue "why" when "communicating". For example, about score and general score have different meanings, but their essence and operation are based on the same theory, that is, the concretization of the basic nature of scores. There are also differences in operational procedures. Dividers always use "reducing the same multiple at the same time", while general fractions generally use "expanding the same multiple at the same time".

In communication, students can ask questions, teachers can show questions for students to think and answer, and blackboard writing can be used to fill in the blanks, depending on the specific operation.

The purpose of communication is not only to seek common ground while reserving differences, but more importantly, to use knowledge flexibly to solve mathematical problems, thus expanding students' thinking.

V. Practice (about 10)

The practice in review class is obviously different from the practice in new teaching or practice class. The exercise in the new teaching is mainly to consolidate the new knowledge just learned, so its exercise composition is that the basic exercise accounts for about 70%, focusing on knowledge; The practice of practical class is to transform skills into abilities, focusing on the formation of mathematical abilities; The practice of review class focuses on the transformation from knowledge structure to cognitive structure, so students should present comprehensive exercises to practice.

It is worth mentioning that the exercises in the review class should be concentrated (designated for a period of time), not scattered. This can not only concentrate students' attention, but also save review time.

Attached are two review course designs. (See two articles in this issue, the review course design of the circumference and area of a circle and the review course design of simple statistics and graphs. )