Differences between different versions of textbooks:
After the implementation of the new curriculum, primary school textbooks have been implementing the policy of "one syllabus and many books". Each version of the textbook has its own characteristics, personality and advantages and disadvantages. Professor Cha Youliang, an expert in Sichuan education, believes that three different sets of teaching materials should be compared back and forth when preparing lessons, so as to choose the teaching content and methods that are more suitable for students. His views coincide with the author's. In teaching practice, the author often compares the growth point, difficult point handling and exercise setting of the same knowledge point in different versions, so as to choose the teaching and learning methods that are most suitable for the students of this class and conducive to the guidance of teachers, and achieve the purpose of integrating teaching materials resources.
The meaning of "comparison" is an important content in the field of "number and algebra" in the curriculum standard textbook, and it is also an important content in the traditional textbook, which belongs to concept teaching; The key point is to let students understand and construct the meaning of ratio in the actual situation, and to communicate the relationship between ratio, division formula and score, so as to lay the foundation for the teaching of ratio and positive-negative ratio. The content of this course is typical, so take this as an example to discuss with colleagues how to compare, integrate, select and use different versions of teaching materials.
First of all, compare the situation-find the growth point.
Situation is the growing point of students' learning knowledge and a powerful promoter of teaching process, and its choice directly affects the generation of classroom. Therefore, we should carefully design and choose the most growing teaching situation. The situation in each edition of the textbook is an important reference for our choice. Under the new curriculum reform, all versions of textbooks follow the writing style of "situation-problem", but the situation of different versions is quite different. In the section "The Significance of Comparison", three thematic maps are presented in the textbook of Beijing Normal University Press (hereinafter referred to as "Beijing Normal University Edition"). The first one is "Look at the following pictures, which are more like picture A". Through the comparison between images, this paper discusses the multiple relationship between length and width in images, which paves the way for the multiple relationship expressed by ratio. The second and third thematic pictures are: comparing who runs fast and which booth is cheaper, which lays the foundation for teaching the ratio of two different quantities to represent a new quantity. After that, the meaning of ratio is introduced.
In the case of PEP, the big brother in the field of textbook compilation, China's first manned spacecraft was launched in Shenzhou 5, and Yang Liwei displayed the national flag in space. By guiding students to compare the multiple relationship between the length and width of the national flag, the ratio is introduced. Then, a situation string is constructed on the topic of "Shenzhou 5", introducing the distance and time of "Shenzhou 5" to guide students to find its speed, and then introducing another usage of ratio: representing the third quantity. On the basis of the two, the textbook introduces the meaning of comparison.
Different from People's Education Edition and Beijing Normal University Edition, the textbook compiled by Southwest Normal University Press (hereinafter referred to as "West Normal University Edition") takes the time and distance of two students from home to school as an example, and at the same time leads to the ratio of time to time, that is, the ratio of equal amount, the ratio of distance to speed, that is, the ratio of different amounts, and finally puts forward the significance of comparison.
The situation of Beijing Normal University Edition is more interesting, but it is difficult for students to grasp it. People's Education Edition is based on what China people are proud of. It has a strong sense of the times, clear teaching clues and is easy for teachers to control, but it hinders students' initiative and is far from the actual life of students in mountain villages. Although the situation provided by the Western Teacher Edition is not so "interesting", it is closer to the students' life experience and more natural than introducing two purposes (expressing several times or scores and the third quantity). It is easy for students to ask and solve problems directly related to the subject, and it is easy for teachers to master them.
Second, leave blank-break through the difficulties.
Blank space is a common skill in painting and calligraphy, and the quality of blank space is directly related to the amount of imagination space given to the viewer. The problem is that the textbook is blank, and the design of the problem reflects the editor's estimation of the students' existing knowledge and experience. Therefore, good questions can not only correctly estimate the learning situation, but also provide guidance for students' thinking direction and serve the development of students' thinking. We can compare the "blanks" of different textbooks, choose the good ones and follow them.
In the teaching of comparative meaning, how to guide students to compare the relationship between two quantities directly affects students' way of thinking and the generalization of comparative meaning. Let's take a look at the blank space and effect of different teaching materials.
After stating the situation, Beijing Normal University Edition directly said, "Let's study the length-width relationship of the rectangle above." Students' vision focuses directly on the relationship between the length and width of a rectangle, but the discussion of the relationship and the application of exploration methods still need students' own choice, which is very open.
The treatment of People's Education Edition is "how to express their length-width relationship with formulas", which directly guides students' thinking to express the relationship between two quantities with formulas. Students will naturally think of using familiar addition, subtraction, multiplication and division and Divison to list formulas, but it is difficult to actively think about the meaning of these formulas and why they should use this formula. However, this processing method paves the way for summarizing the meaning of ratio, "the division of two numbers is also called the ratio of two numbers" and the relationship between ratio, division and fraction.
The Western Education Edition bluntly puts forward that "Zhang Li's time is several times that of Li Lan", which limits students' thinking to the relationship between times and ratios.
Obviously, from the perspective of whether it is conducive to the subsequent development of students' thinking, the blank space of Beijing Normal University Edition is better. Judging from the summary of the significance of whether it is conducive to comparison, the processing method of PEP is more appropriate.
Third, comparative exercises-find a correct foothold.
Exercises help students to deepen their understanding and master new knowledge, which is an important means for students to master knowledge, form skills and develop intelligence. Different versions of textbooks are equipped with different numbers of exercises, which are carefully selected and compiled by experts and scholars. Different exercises represent different values and reflect the different understanding of students' mathematics learning process by educational experts. Interpreting different versions of exercises will help us find the foothold of new knowledge, so as to highlight key points and break through difficulties more efficiently.
After completing the teaching of comparative meaning, Beijing Normal University Edition has set up three types of exercises: the first (and the first) is to talk about the comparative meaning in specific situations; The second category is the ratio meaning combined with the specific situation; The third category is to express the relationship between two quantities in a case by ratio. What is striking is the setting of the first category. In teaching, we mainly talk about how to express the relationship between two quantities by ratio, which belongs to advanced thinking. Exercise involves explaining the specific meaning of proportion, which belongs to reverse thinking. Through the reverse interpretation of the meaning of comparison, students will not only have a deeper understanding of comparison, but also lay the foundation for the teaching of "the application of comparison". It can be seen that the editor has good intentions.
There are two kinds of exercises after class in Jiangsu Education Press (the national standard textbook published by Jiangsu Education Press). The first (the first question) is to express the relationship between two quantities by ratio. It is worth mentioning that the presentation form of this question, combined with specific graphics, uses ratio to express the relationship between two quantities, which embodies the idea of combining numbers with shapes and is conducive to students to establish the relationship between scores and ratios. Secondly, the second type of questions is to fill in the blanks by using the relationship between ratio, division and score, and to consolidate their relationship.
Almost all other versions use ratio to express the relationship between two quantities, which is more conventional.
It is a good choice to compare and draw lessons from the exercises of Beijing Normal University Edition and Soviet Education Edition and combine them. For example, first show the first question in Jiangsu edition, and let students understand the meaning of ratio and its relationship with scores by combining graphics, and then show the first question in Beijing Normal University edition, so that students can understand the meaning of ratio in specific situations. After students finish the exercises, they must deeply understand the significance of comparison.
Fourth, compare "Do You Know"-Infiltrating humanistic points.
The new curriculum standard requires that mathematics curriculum should show the charm, long history and aesthetic value of mathematics culture. In fact, it is to show students the humanistic side of mathematics. The setting of "Do you know" column is the most direct embodiment of the echo of each version of teaching materials and curriculum standards. So as a front-line teacher, how to grasp the quality and degree and avoid putting the cart before the horse in mathematics knowledge and humanistic quality?
Or take the meaning of comparison as an example, what comparative humanistic characteristics should be infiltrated after teaching the meaning of comparison or in the process of teaching comparison? How much should it penetrate? Let's take a look at the arrangement of each version. The Beijing Normal University Edition introduces the anatomical map of the Parthenon in the ancient Greek city of Athens, and introduces the "golden section" to broaden students' horizons and stimulate students' interest in learning. The People's Education Edition shows the floor plans of the five-pointed star, the brokeback Venus and the Parthenon, as the annotation of the "golden ratio". Xi Shi Edition introduces the "golden ratio" from Fibonacci series through mathematical reading, and further introduces the application of the golden ratio in art, architecture and other fields. Su Jiaoban directly introduced the "golden ratio" and listed two examples of using the golden ratio in art.
It is not difficult to see that all the editions put the humanistic emphasis of "Bi" on "Jin Bi", which provides the most direct reference for our teaching.
Compared with the compilation of primary school mathematics textbooks, it focuses on mathematical subject knowledge and mathematical thinking methods, the former is explicit and clear at a glance; The latter is hidden, "still hiding half of her face in front of us behind her guitar." To interpret the textbook, we should not only decompress the subject knowledge, but also understand the thinking method behind it. This highlights the necessity of a comparative interpretation of all versions of textbooks. The smooth and developed network information makes it possible for us to compare different versions of teaching materials. Compare different versions of textbooks horizontally. It belongs to microscopic observation to compare the situation, problem guidance and exercise setting of each edition of teaching materials horizontally and summarize the merits of each edition of teaching materials. It is also necessary to look down vertically, grasp the setting of each textbook system, and summarize the different influences of different expansion methods on learners. It's just a macro grasp, and you can hardly see the trees in the forest, and you can't achieve the purpose of integrating teaching materials; Just from the microscopic comparison, it is similar to seeing the trees but not the forest, which will be taken out of context.
Contrast is for integration and utilization. The teaching materials are carefully compiled by educational experts, with the synthesis of predecessors' rich experience and the summary of their own practice. Interpreting a textbook is equivalent to talking to a group of education experts. However, due to the influence of personnel, region, environment and other conditions, it is not a "universal foundation" and needs to be continuously improved and built. Through "dialogue", we can be familiar with its characteristics, measure its advantages and disadvantages, learn from each other's strengths, use it flexibly, and use the teaching materials creatively and purposefully. Only in this way can it glow with new vitality and interpret efficient classroom.