A few points of cognition and thinking after the teaching of the human-taught version of "Mathematics Wide Angle Collection"

Some cognition and thinking after the teaching of the human-taught version of the third-grade mathematics volume "Mathematics Wide Angle One-by-One Collection"

Liu Heng, the sixth primary school of Ankang High-tech Zone

"Repetitive Problems" and "Set Thinking" are the teaching contents of the textbook "Mathematics Wide Angle - Collection" in the ninth unit of the third grade book, which is the starting lesson of logical thinking training and the basic teaching of collective thinking. Set thinking is not unfamiliar to the third grade, but the set ideas learned before are basically the "one-to-one correspondence" ideas in the process of counting and calculation, as well as the practical activities of "categorizing and classifying" things. On the basis of what has been learned before, this textbook adds the mathematical practice exploration of overlapping and repetitive phenomena, and uses the exploration method of set graph to understand the mathematical practice problems of "correspondence, classification and classification, overlapping and repetition", which is a new knowledge point. Example 1 in the textbook lists the students who participated in the kicking shuttlecock competition and the jump rope competition through a statistical table, and the total number of participants is not the sum of the number of participants, which triggers the cognitive conflict of the students. Through cooperation and communication, exploration and comparison, the collection chart is discovered, and the set chart (Wayne diagram) is used to visually represent the relationship between the number of people in the two competitions, so as to help students find a solution to the problem. The teaching materials require students to initially experience the collective thought by discovering and solving problems in life, and to be able to solve problems in their own methods, which lays the necessary foundation for subsequent learning. After experiencing the formation process of the collection chart, students perceive the intuitiveness of the collection chart and the shortcut of neither repetition nor omission, fully understand the meaning of each part of the collection chart, and feel the collection beauty in life. Students have some direct experience with the "correspondence and repetition problems" in life, but further learning is needed to use the "set thinking" viewpoint method to cognitively solve such mathematical problems. In the following, I will talk about my post-teaching cognition and thinking from the aspects of unit teaching knowledge points and unit teaching objectives, teaching methods and teaching strategies in combination with the classroom teaching practice of this semester, so as to facilitate future learning and teaching activities.

A graph that visually represents a set and its relational plots with a closed curve is called a Wayne diagram (also known as a Venn diagram). John Venn Wayne) was a nineteenth-century British philosopher and mathematician who invented the Wen's diagram in 1881.

First, the unit teaching knowledge points and unit objectives are achieved

(1) Unit teaching knowledge points:

1. Use "one-to-one correspondence" and "enumeration" to find "duplicate" things and quantities;

2. Understand the "Wayne diagram", that is, the "set diagram" and use it to solve practical mathematical problems;

3. Use the method of "classification induction" to fill in the set chart in combination with the actual mathematical problems;

4. Use simple permutation combination skills, think comprehensively through the combination of classification and number form, and use "set diagram" to solve mathematical practice problems;

5. Give the thinking questions arranged in the combined textbook, review and review the "collocation" problem, and cultivate students' simple permutation and combination thinking, orderly thinking and logical reasoning ability, so as to lay the foundation for the "mathematical wide-angle" learning in the next volume;

6. The meaning of the set circle (figure): the internal range of a closed curve represents the set, and the illustration of a certain type of quantity or thing and its number or relationship with several or more sets is called the set circle (figure), also called the Wayne diagram, also known as the Wen's diagram.

7. The names of the components of the set diagram are: full set, empty set, intersection, union, subset, complement set, empty set, element, set, etc., this part of the knowledge to high school to specific learning, everyone can understand it;

8. The calculation formula of the simple set problem: the number of parts + the number of other parts - the number of repetitions = the actual total

Actual total + number of repetitions - number of parts = number of parts

Actual total + number of repetitions - number of other parts = number of parts.

(2) Achievement of unit teaching objectives:

1. Let students experience the process of generating the set chart, understand the meaning of the set chart, experience the benefits of the set chart, and learn to use the set of thinking methods to think about the problem.

2. Enable students to use intuitive diagrams to solve simple practical problems with the help of collective thinking methods, and cultivate students' awareness of solving problems with different methods.

3. Use life examples to let students feel the close connection between mathematics and life, and further establish the awareness of learning mathematics with mathematics.

II. Teaching Methods and Teaching Strategies:

1.Through group cooperation and communication, guessing and other activities, students can initially perceive the formation process of the collection map, and can clearly understand the meaning of each part, so as to solve the simple repetitive problems in life. And feel and discover the ubiquity of mathematics in life.

2.Use cooperative learning, inquiry learning and comparative learning to discover the advantages and characteristics of intuitive diagrams and lay a theoretical foundation for solving repetitive problems.

3.Experience the process of cooperative learning and independent learning, develop the habit of diligent thinking and good learning, and cultivate the awareness of cooperative learning and improve the interest in learning mathematics.

4. Take the sports meeting as the main line, feel the mathematics in life, so as to lead the progress of the classroom, and through learning to collect ideas, experience the basic way of thinking and basic logical ideas of mathematics.

5.Enable students to understand the meaning of the parts of the set chart with the help of the set chart, and be able to express it in mathematical language. Through the set graph, discovery explores different column calculations to solve the problem of repetition.

6. The way of group cooperation, personally experience the formation process of the collection map. Develop the habit of being diligent and studious, while cultivating a sense of cooperative learning and interest in learning mathematics. 7.Organically combine independent inquiry with meaningful receptive learning.

Students are experienced in "subtracting the number of repetitions", so on the basis of fully respecting students' experience and cognition, let students explore independently, complete independently, and then report and communicate. Cooperate with the student report, use the multimedia courseware to show the Venn diagram, use the teaching method to guide students to recognize and understand the Venn diagram, and through the visual demonstration of the process of merging the two collection circles, guide the students to discuss and find that "the elements in the collection cannot be repeated", experience the heterogeneity of the collection elements; "the order of the collection elements can be different", and experience the disorder of the collection elements. And ask the students to think about the meaning of each part of the picture, especially "those who participate in both and participate in these two competitions", and experience the meaning of intersection and union.

8.Let go of students and let students experience the calculations related to handover and intercourse.

Students will list a variety of methods based on the wiring or Venn diagram when answering columnar questions. Let go and let students try to solve and fully demonstrate the student's approach while giving full recognition. Let students combine the Venn diagram to understand the meaning of each equation, and realize that to find "the number of elements of the union of two sets" is to add the number of elements of the two sets and subtract the number of elements of their intersection. Highlight the basic methods to deepen students' experience of intersection and computing and their understanding of collective knowledge.

9.Focus on "conflict" and stimulate students' desire and interest in inquiry.

Ask the question "How many people are participating in these two competitions?" After that, the student's different answers have the potential to trigger "conflict." Grasping at this "conflict" and asking ," can you be sure there are 17 people?" "Can you prove why not 17 people?" In this way, it stimulates students' desire to explore, allows students to actively participate in problem-solving activities, solve problems in a personalized way of thinking and handling problems, and provide guarantees for them to independently construct the meaning of knowledge.

10.Cultivate students' awareness and ability to collect and organize information.

In line with the principle of coming from practice to practice, the classroom introduces the method of representing the set and its intersection and merger with the Venn diagram through the actual life of the students, so that the students can personally perceive the thought of the collection, experience the process of knowledge generation, experience the thought of the collection in the process, feel the repetition in the process, and have an epiphany of the solution to the problem of repetition. Let students experience the mathematical process of problem solving and get a mathematical learning experience.

11.Cultivate the rigor and rigor of students' thinking.

The most important thing in the teaching of mathematics is not the teaching of mathematical knowledge, but the teaching of mathematical thinking and mathematical thinking methods. Mathematical ideas run through the entire mathematical system. Therefore, it is very necessary and very important to infiltrate some mathematical ideas into students from an early age. An important part of this is the cultivation of students' mathematical thinking rigor. Rigor is one of the basic characteristics of the mathematical discipline. In the teaching process, I focus on cultivating the rigor of students' thinking, such as the process of interpreting the Wayne diagram, asking students to express the meaning of each part. The big circle means "the number of people participating in the jump rope" and "the number of people participating in the kicking shuttlecock", and after removing the part that all participate, it is "only the number of people who participate in the jump rope" and "only the number of people participating in the kicking shuttlecock", and the word "only" is added, although there is only a word difference, but the meaning is completely different. There is also "participating in both jump rope and kicking" to make students understand that this is a participation in both activities.

12. Exercise the ability to solve problems according to the actual situation.

Specific situation, specific analysis. The after-class thinking questions designed at the end of the class are both exercised and improved for the students' ability to flexibly apply the knowledge they have learned.

Third, mathematical wide-angle post-teaching thinking:

1. About the use of courseware:

The courseware shows the small animals home and introduces them into the classroom, making the classroom teaching more efficient, vivid and lively. Transform the teaching process with a certain degree of compulsion into efficient self-study for students, so that children can combine experience and emotion in group cooperation, and students' interest in learning is high, their attention is more concentrated, and their thinking is more active, so as to better grasp knowledge and develop skills.

2. About the collection and collation of mathematical data:

Cultivate students' awareness and ability to collect and organize information. The abstraction of the set is only possessed when it finally forms the conclusion, and in the process of conclusion formation, it must be based on a large number of concrete contents. In line with the principle of coming from practice to practice, in the classroom we let students personally perceive the ideas of the collection from the reality of life, and let them personally experience the process of generating the collection map, so that students can experience the thought of the collection in the process, feel the overlap in the process, and understand the solution to the overlapping problem. Let students experience the mathematical process of problem solving and get a mathematical learning experience.

3. On the scientific nature of mathematical thinking:

Cultivating the rigor of students' thinking is one of the basic characteristics of the mathematical discipline. The most important thing in the teaching of mathematics is not the teaching of mathematical knowledge, but the teaching of mathematical thinking, the method of mathematical thinking. Mathematical ideas run through the entire mathematical system. Therefore, it is very necessary and very important to infiltrate some mathematical ideas into students from an early age. An important part of this is the cultivation of students' mathematical thinking rigor. Rigor is one of the basic characteristics of the mathematical discipline. For example, the courseware shows the Wayne diagram, guides the students to fill in and understand the process, and lets the students express the meaning of each part. In the classroom, students always pay attention to rigorous thinking.

4. About the transformation of fixed thinking:

In teaching, we must pay attention to overcoming students' mindset. It can prompt students to discover problems, cultivate students' spirit of questioning, and in the long run, from questioning to seeking differences, breaking through traditional concepts, and boldly creating new theories. Ability to solve problems according to the actual situation. Thank you!

Attached: "Mathematics Wide Angle - Collection" Home-School Co-education Exercise 1, the school organizes to watch theatrical performances, the seats in the East East are 7 from the left and the 10th from the right, how many seats are there in this row?

There are 50 people in the third (1) class, of which 25 like to eat apples, 22 like to eat oranges, and 13 like to eat both apples and oranges. How many people don't like to eat both fruits?

3. In the mid-term examination of the third (4th) class this semester, 36 students have obtained excellence in mathematics, 29 people have obtained excellence in Chinese, 28 students have obtained excellence in chinese and mathematics, and 9 students have not obtained excellence in chinese mathematics.

There are 55 students in the third (6th) class, 20 students in basketball competitions, 12 people who participate in both basketball competitions and table tennis competitions, and 14 people who do not participate in both events. How many people participate in table tennis?

5. 37 people in class three (4) who have completed chinese homework, 43 people who have completed math homework, 31 people who have completed both roles, each person has completed at least one kind of homework, how many students are there in class three (4)?

6. Overlap and paste 2 pieces of colored paper with a length of 10 cm, how many centimeters is the length of the overlapping part? If 3 pieces of colored paper also overlap, how many centimeters of colored paper will grow in total after the overlap?

7. In the third grade, there are 107 children who go on a spring trip, 78 people bring mineral water, 77 people bring fruits, and each person brings at least the same. How many people in the third grade bring both mineral water and fruit?

8. 35 people in our class have subscribed to "Mathematical Kingdom", 18 people have subscribed to "Language World", of which 9 people have subscribed to both magazines, how many people in our class?

9. Each person in the three (2) class chess interest groups will play at least one chess game, 21 students who can play chess, 17 students who can play Go, and 10 people who can play both kinds of chess. How many students are in this group?

10. A math quiz. Among the 36 people in the class, 21 people did the first smart problem, and 18 people did the second smart problem, and each of them did at least one problem correctly. How many people are doing both right?