The accumulation of inquiry experience can not be completed by simple activities and thinking, but emphasizes a real situation, the learning and experience of mathematical thinking methods. Therefore, teachers should carefully create problem situations, organize moderately open inquiry activities, inspire students to broaden their thinking, obtain diversified information from multiple directions and angles, and accumulate rich inquiry experience.
Teaching "Calculation of Triangle Area", students at each table prepare two envelopes, one containing four different triangles (isosceles and isosceles acute triangle, right triangle and obtuse triangle) and the other containing two identical triangles (acute triangle, right triangle or obtuse triangle). Then, around the requirement of "using these materials in the envelope to cut out the graphics we have learned", openurl won rich classroom rewards for his free operation and independent exploration-some students cut out triangles along the midpoint of both sides and then put them together into parallelograms; Some people first find the midpoints on both sides of the triangle, then make the vertical line of the bottom along the two midpoints, then cut out two small right-angled triangles along the vertical line, and then make up the triangles above to form a rectangle; Some people confuse the two.
The acute angle, right angle or obtuse angle of a triangle are spliced into a parallelogram.
Judging from the textbook arrangement system of this unit, this lesson has the function of connecting the preceding with the following. "Continuation" is the method of consolidating one figure into another, and "enlightenment" is the method of combining two figures into one learned figure in the next class. From the perspective of students' thinking, these are two completely different ways of thinking, which can guide students to think from different angles. Rich materials make students' inquiry more valuable. Students have experienced the activity experience of how to cut, paste, spell and change graphics, and accumulated the exploration experience of drawing general conclusions from special situations.
The acquisition of inquiry experience is a process of continuous guessing, verification and speculation. Create diversified and open inquiry situations for students and lead them to gallop freely in a broad mathematical background. Students' accumulated exploration experience will be more scientific and rich.
Second, guide students to experience the process of mathematics docking life and transform life experience into mathematics experience.
Students have accumulated some primitive and preliminary mathematical experience in their lives. For the knowledge and understanding of mathematics, it is sometimes necessary to have a rich background of life experience, so that life experience and mathematics experience can be "effectively docked" and daily life experience can be "mathematized". Therefore, we should be good at capturing the mathematical phenomena in life, excavating the life connotation of teaching knowledge, and closely linking mathematics with life, so that students can personally experience the process of transforming life experience into mathematics activity experience and fully accumulate "mathematics" activity experience.
When students study the year, month and day, they can't experience the duration of the year, month and day like "minutes and seconds". Teachers pay attention to extracting students' life experience in teaching, and ask students to describe how long a month is a year with some things they have experienced in life. The students raised their hands to speak one after another, and some said, "The Spring Festival this year to the Spring Festival next year is a year." "May 7 this year is my birthday, and then on May 7 next year, I will grow up by another year, that is, another year." "My father will be paid this month until next month." "From this time today to this time tomorrow is a day." ..... Students' experience of contacting years, months and days in daily life constitutes the mathematical reality for them to further learn new knowledge.
Mathematics teaching should be based on students' real life, "mathematize" these life experiences, promote students' mathematical thinking, and generate new mathematical activity experiences. Using life experience to help experience and understand the formation process of new knowledge is not only simple and clear, but also vivid, which is conducive to students' experience rising from one level to a higher level and realizing the transformation or reorganization of experience.
Third, guide students to experience the process of operation and thinking, and accumulate experience of effective operation.
"Intelligent automatic start" and hands-on operation are important ways and methods for students to learn mathematics. Hands-on operation can turn abstract knowledge into a visible and clear phenomenon. Students participate in the whole process of acquiring knowledge through hands, brain and mouth, so that operation, thinking and language can be organically combined, and the experience gained will be profound and firm, thus accumulating effective operational experience.
Teaching "Calculation of Rectangular Area", the teacher prepared some squares of 1 square decimeter for each group before class, and then guided the students to carry out the following research activities-
Teacher: There is a rectangular cardboard on your desk. Do you know its area? How can we know?
Health: You can put a square with an area of 1 square decimeter.
Teacher: Watch carefully during the swing and see what you can find.
(student operation. )
Health: Our arrangement is four in each row, which can be arranged in three rows. Four times three is 12. Then the length of this rectangle is 4 decimeters, the width is 3 decimeters, and the area is 12 square decimeter.
Teacher: How do you know that the length is 4 decimeters and the width is 3 decimeters?
Health: The side length of each square is 1 decimeter, and there are four squares in the horizontal direction, so the length is 4 decimeters. ...
Then, the teacher gave each group four rectangles of different sizes, put a square to calculate the area of the rectangle, and asked the students to record the data in the table to see what they found.
Length (decimeter)
Width (decimeter)
Area (square decimeter)
(student operation. )
1: I put five squares along the length and three squares along the width, so the length is 5 decimeters, the width is 3 decimeters, and the area is 15 square decimeter.
Health 2: I swing very fast. I only used seven diamonds. I just put five squares along the length and two squares along the width. I can also see a * * * pendulum where 5 times 3 equals 15. The area is 15 square decimeter. (Teacher-student evaluation)
Health 3: My rectangle is 3 centimetres long, 2 centimetres wide and 6 square centimetres in area.
Health 4: I found that the area of a rectangle may be multiplied by its length, but I'm not sure.
Teacher: We calculated the length, width and area of these rectangles with pendulum, and some students guessed the calculation method of area.
The process of students "swinging" a rectangular area not only enriches the experience of feeling and perception, but also provides rich resources for their thinking collision. Hands-on operation is not only an intuitive and vivid "finger movement", but also a rich and vivid thinking activity. In this process, it realizes the organic integration of operation experience, thinking experience and strategy experience, and accumulates rich experience in mathematical activities.
Fourthly, guide students to experience the process of abstract generalization and accumulate the experience of abstract generalization.
Abstract generalization is the key means to form concepts and draw laws, and it is also the most important thinking method to establish mathematical models. When learning mathematics, students need to go through the process of observation, thinking and comparison to gain rich perceptual experience, and then discard individual and non-essential attributes from numerous mathematical facts or phenomena and abstract the essential attributes of * * *.
Teaching "additive commutative law", teachers and students get the following formula through a series of teaching links: 28+ 17= 17+28, 4+3=3+4, 20+40 = 40+20, 82+0 = 0+82 ...
Health: After the two added numbers are exchanged, the result is equal.
Teacher: What did you change? The result of addition can be said to be-and. Who said that again?
Health: exchange the positions of addends, and their sum remains the same.
Teacher: That's good. When two numbers are added and the positions of addends are exchanged, their sum remains the same. Can you still write such a regular equation? How much can you write?
Student: I can write, I can write countless times.
Teacher: It seems that we will never finish it in this life. What should we do? Is there a better way? You can also discuss it when you think about it.
Students discuss after thinking.
Health: I use a+b = b+a, A stands for addend, and B stands for addend, and the results are still equal after swapping places.
Teacher: such a good way is really not simple! Clap for you.
……
Many mathematical problems often have the same thinking mode behind seemingly different mathematical scenes. Therefore, abstract generalization can deepen students' grasp of the essence of things, form a general understanding, and accumulate abstract and formal experience of specific problems.
Fifth, guide students to experience the process of reflection and promotion, and accumulate emotional and ideological experience.
The experience of mathematical activities belongs to the students themselves and has obvious personality characteristics. As far as learning groups are concerned, the experience of mathematical activities is diverse. Therefore, the accumulation of experience in mathematical activities requires students' self-reflection and active communication with their peers.
The teaching of "calculation of parallelogram area" is guided by the teacher in the summary session: in this lesson, we learned the calculation of parallelogram area. Let's recall how we studied it, whether we encountered any difficulties and how we overcame them. The students spoke one after another: at first, I used the method of square to calculate the area, but it was too complicated. Later, I thought I should study a simpler method; I can see at a glance that cutting a triangle from a parallelogram and translating it to the other side will transform it into a rectangle, so it is much more convenient to get the parallelogram area from the rectangular area. As long as it is cut along the height, it can be transformed into a rectangle, and it is not necessary to cut a triangle, but also a trapezoid; After I transformed the parallelogram into a square clamp, I mistakenly thought that the length and width of the rectangle were equivalent to the two sides of the parallelogram respectively. Later, with the help of my deskmate, I found it wrong. It seems that I should observe carefully in my future study. Then, the teacher demonstrated the process of transforming parallelogram into rectangle with courseware, and raised the question: We will learn the area calculation of triangle in the next class. How are you going to study it?
Our teaching goal can't be limited to one class. We should have a long-term vision and let students benefit for life. In the usual process of mathematics learning, we should guide students to check their thinking activities, reflect on how they found and solved problems, what basic thinking methods and skills they used, and what good experiences they had ... so that students can realize a leap from quantitative accumulation to qualitative understanding of mathematics. The ideological experience produced by this experience is the most valuable. At the same time, the more complicated mathematical activities are, the more positive emotional will is needed. This experiential component is also indispensable for students to experience basic mathematics activities.
Mathematics teaching needs to let students experience the learning process personally, so as to obtain the most essential and valuable experience of mathematics activities. Tao Xingzhi, a famous educator, made such a metaphor: We should take our own experience as the "root" and the knowledge generated by this experience as the "branch", and then we can connect other people's knowledge, and other people's knowledge can become a part of our knowledge organism. Therefore, let students experience in the experience, accumulate in the experience, and let the "root" of the experience grow deeper.