First of all, in the creation of problem situations, there is a hierarchy.
Teaching clip of Discovery Law: The teacher shows a circle. Q: What kind of number is this? Health: Round. The teacher followed with a square. Q: What kind of number is this? Health: Fang. Show me another triangle. Q: What kind of number is this? Health: It's a triangle. On the basis of these three figures, the teacher made another set of figures: circle, square and triangle. Teacher: Students, can you guess what the shape of the next figure is? Health: The next figure is a circle. Because according to the order of appearance just now, the first one appears as a circle, the second one as a square, the third one as a triangle, and then the three figures can be regarded as a group, and two groups have already appeared, so there should be a third group below. The first figure in each group is a circle, so the next figure must be a circle. Teacher: Your reasoning is really well founded. It seems that this arrangement still hides the law. (blackboard writing: regularity) today, let's discuss "finding regularity" together. (Write the word "search" before the rules on the blackboard)
The creation of problem situations should adhere to the principle of simplifying the complex, pay attention to the presentation of problems, and let the problems be presented to students simply and clearly. However, most of our teachers often only pay attention to the childlike, novel and unique situation, and show the complicated and chaotic situation to students, ignoring the guiding role of the situation. In the process of finding laws, teachers create problem situations layer by layer: from a single circle, square and triangle to a whole group of circles, squares and triangles, which is essentially a demonstration of laws and the infiltration of knowledge. It helps students find and solve problems in the process of exploration, and it also plays a potential role in supporting and promoting the structure of mathematical knowledge.
Second, in the process of understanding the concept, it presents hierarchy.
Teacher: Students, Haohe River in Nantong has become a famous tourist attraction in China. The vast and clear Haohe River is surrounded by the earliest museums, libraries and normal schools in China, as well as the textile museums, water supply museums, architecture museums and kite museums built in recent years. In addition, the Wenfeng Tower stands on the ground, which makes modern architecture and historical and cultural architecture set each other off, reflecting the rich cultural atmosphere of Nantong. Do you want to visit? Teacher: There are so many scenic spots. How can you visit them? Health: Visit one by one along the river. Teacher: Along the river, which is the sideline of Haohe River. (blackboard writing: sideline) multimedia demonstration. Teacher: This is the first normal school in China-Nantong Normal School, and it is also the teacher's alma mater. There is a swimming pool in the school. Can you point out the sideline of the swimming pool entrance? Hand painting, multimedia demonstration. Teacher: This is the school football field, and the football field also has sideline. Can you point it out? Is the white line in the middle its sideline? Teacher: honor cards represent the footprints of the apprentice's growth. Does the honor card have a sideline? Can you point out their sideline? Teacher: Students, we already know the sideline just now. It can be said that every surface of an object has its own sideline. Is there a sideline in math books? This is the boundary line of the cover of the math book. Who can point out the edge of a triangular ruler? Teacher: Can you point out the boundary of one side of the objects around us? You can communicate with your classmates and deskmates after you find it. Teacher: We draw the surface of the object and get such a plane figure. Can you draw their sideline with a watercolor pen? Please take out the watercolor pen and finish the second question of P62. After the students had a deep understanding of the edges of objects and plane figures, the teacher concluded: We call the length of the surface of objects or a peripheral line of plane figures their perimeters. (Blackboard: Perimeter) Mathematics Curriculum Standard
The implementation plan points out: "According to the specific situation of students, the teaching materials should be reprocessed and the teaching process should be creatively designed." Teachers do not directly teach students the concept of perimeter from simple plane graphics, but according to students' cognitive development law and existing knowledge and experience. After deeply understanding the editor's intention and the connotation of the text, they opened a teaching overture for students without real and favorite attractions, so that students can deeply understand what a "sideline" is. It seems simple that students browse the familiar route of tourist attractions to the edge of a plane, and then abstract to the edge of a plane figure. The essence of this is to make students successfully realize the double leap of the concept of "space and graphics", with clear teaching level and reasonable classroom structure, which lays a solid foundation for the subsequent easy understanding of the concept of "perimeter".
Third, in the promotion of thinking strategies, there are levels.
Teaching clip of "Looking for the Law": Teacher (showing the situation map): If you put it like this, what color is the 15 potted flower from the left? (pause) Try it yourself and see if you can solve it yourself. Students think independently, and after most students form a preliminary understanding, teachers organize students to communicate. Teacher: Who would like to introduce the opinions of your group to the whole class? Health 1: I draw and draw: ○○○○○○○○○○○○○○○○○○○○○○○○○○ Health 2: I use "+"for blue flowers and "one" for red flowers. Teacher: This is a simple expression. Do other students think so? Health 3: I think so: 1, 3, 5 ... pots are all blue flowers, and pots 2, 4 and 6 are all red flowers, which means that odd numbers are blue flowers, even numbers are red flowers, and 15 pots are singular, so they are blue flowers. Teacher: Your idea is really good. Do other students understand his ideas? This problem is solved by singular and even numbers. Is there any other way? Health 4: You can also use the calculation method: consider one group for every two pots, and the pot of 15 ÷ 2 = 7... 1, 15 is the first in the eighth group, and the first in each group is a blue flower, so the pot of 15 is a blue flower. Teacher: Do you know what the quotient of 15÷2 means? What does the remainder 1 mean? Quotient: 15÷2 indicates that there is such a complete number of groups, and the remainder indicates which pot in the next group. Teacher: You are really something. Your thinking is clear. Can you describe it again? Teacher: Here is another question for the teacher (show me the rules for placing a red flag, a blue flag and two yellow flags). What colors are the flags on the 2nd1and 23rd from the left? What about the face of 2 10? Health: You can find 2 1 face and 23 faces in drawing, but drawing 2 10 face is too troublesome. Teacher: Can it be judged by singular or even numbers? Health: No. Because from the front, odd numbers may be red flags, yellow flags, or even numbers. I think it is more convenient to use the calculation method. ……
Students' thinking is different, which determines that teachers start teaching with basic thinking and gradually improve in the process of teaching design. Using simple symbols to represent objects, that is, drawing strategies and calculation strategies judged by odd and even numbers, expresses the thoughts of most students, which is also the most basic way of thinking. Teachers do not point out the advantages and disadvantages of methods in time, but design and hide another regular arrangement problem, so that students can optimize their thinking strategies in communication, questioning and speculation and gradually improve their thinking level. Therefore, classroom teaching design should pay attention to the differences of students' psychological characteristics, cognitive ability and thinking quality, arrange the design according to the development order from low to high, reflect the hierarchy of teaching objectives and student activities, coordinate different levels of teaching objectives with different types of student activities, promote all students to develop on their own basis, and gain successful experience and development motivation.
Fourth, in the strengthening of knowledge, there are levels.
Teacher: Let's judge which of the following figures are corners and which are not. For graphs that are not angles, talk about the reasons for judgment. Life judgment, collective correction. Teacher: The golden five-pointed star has accompanied us into one era after another. A five-pointed star is a figure composed of angles. Did you find the angle on the five-pointed star? Students count the horns. Teacher: Can you form an angle with two sticks in your hand? All beings have manipulated the sticks in their hands and are full of interest. Health 1: Yes, I put the two ends of two sticks together and separate the other two ends to form an angle. Teacher: Can you form more corners with two sticks? Health 2: You can also put it in a cross. The students talk and demonstrate. One, two, three and four can form four corners. Teacher: The teacher will give you another stick. What number can you work out with three sticks? Count it. How many angles are there? Stick a sticker on the students. Has been shown to the public. Teacher: Can you count how many corners you made? Who placed the most corners in the drawing?
This clip always takes students as the main body, and teachers grasp the age characteristics and cognitive characteristics of lower grade children, from basic to variant ideas: first, deepen students' diagonal understanding from basic exercises; Then let the students count the angles in the five-pointed star alone to further feel the characteristics of the angles and their existence in life; Finally, through hands-on activities, students can set up, explore and communicate, which improves their interest in learning. When practicing, the teacher first puts a two-piece figure and counts the angles. Adding another stick will also increase the thinking coefficient. It is worth mentioning that, because the number and shape of sticks are different, and there are regular and irregular plane figures, the students' operation level has improved, the mathematical thinking level has naturally risen to a new level, and students' interest has increased. The open gradient exercise method designed by the teacher is obviously the intermediate station to revitalize the classroom.
With the deepening of curriculum reform, we should follow students' cognitive curve, pay attention to the differences of students' thinking quality, and deepen the principle of hierarchy to details, so that our classroom is full of the excitement of jointing, the joy of flowering and the joy of harvesting. Order is an objective law, the premise is to follow the order of textbooks and texts, and the key is to follow the order of students' cognition. It is the goal that our teachers strive to pursue, and it is also the basic quality and ability that teachers should have in the new period.
(Editor Zhang Huawei)