Reflections on the teaching of the same angle, inner angle and inner angle of the same side in junior one mathematics (1)
The angle formed by the intersection of straight lines is developed on the basis of studying the positional relationship of straight lines on the plane, which is one of the key chapters of this chapter. The related concepts and conclusions of congruent angle, internal angle and internal angle of the same side mentioned in this section are very important. Their derivation is the beginning of "containing but not revealing" infiltration reasoning in junior middle school, and these concepts and conclusions are also an important basis for further studying the properties and judgments of parallel lines, triangles and quadrangles. In a sense, it plays a milestone role and provides good materials for embodying the new curriculum concept and students' mathematical inquiry. Therefore, this part plays a very important role in this chapter and future research.
In the seventh grade, the first geometry class in the eighth grade felt his unprecedented effect. Grade seven students are curious, competitive and highly plastic. A good beginning is half the battle. The teaching quality of the first few classes of geometry has a vital influence on the future, so the correct guidance of teachers is particularly important. In the classroom, we should stimulate students' thirst for knowledge through various means, enhance students' self-study and self-confidence, adhere to the student-oriented, and implement the new concept of new curriculum reform in classroom teaching.
This lesson first introduces a new lesson naturally and directly through the intersection of two straight lines, and then sets four questions to let students give full play to their enthusiasm, initiative and creativity through their own review. The purpose of designing these questions is to deepen the teaching focus, and then students can better understand the concept and distinguish this kind of angle by studying the concept and structural characteristics of the same angle in detail with teachers and students. Students learn feelings by analogy in the study of internal angle and internal angle on the same side. After that, students can experiment with their hands and brains in activities to deepen their understanding of concepts. The selection of exercises is also an interesting way of knowledge competition, which can stimulate students' thirst for knowledge and consolidate new knowledge. Finally, using tabular summary to improve the knowledge structure, students can clearly understand the knowledge that should be mastered in this class.
The teaching design of this class is based on the teaching materials, but it is not completely constrained by the teaching materials. Exploring? Guess what? Arguing? By analogy, we should constantly set up some targeted problem situations, stimulate students' thinking, guide students to discuss independently, and strive to make students actively learn mathematics knowledge in a lively atmosphere. Students' participation is very high, and the expected teaching effect has been achieved.
In addition, this lesson also permeated with a variety of mathematical thinking methods, for example, the analogy thought from the study of vertex angles and adjacent complementary angles to the study of three angles, the method of simplifying complex graphics into simple words and separating graphics, and the classification thought of diagonal classification, which are all important thinking methods for studying mathematics in the future.
The "question menu" of the whole class is mostly pointed out by the teacher, so students may be a little passive and the way to ask questions is relatively simple. Secondly, there are some shortcomings in the introduction of this course. Only when three lines intersect and there are only two intersections, two lines must be parallel to each other. This is a special case of three-line octagon, which is easy for students to misunderstand that congruent angles or internal angles must be equal. Finally. This class has a large capacity, and it is difficult for some students with difficulties to digest it all. These are all doubts.
Reflections on the teaching of isomorphic angle, internal angle and internal angle of the same side in junior one mathematics (2)
Grade seven students are curious, competitive and highly plastic. A good beginning is half the battle. The teaching quality of the first few classes of geometry has a vital influence on the future, so it is particularly important for teachers to correctly guide the angle formed by the intersection of straight lines. This section is developed on the basis of studying the positional relationship of straight lines on the plane and is one of the key chapters of this chapter. The related concepts and conclusions mentioned in this section, such as congruent angle, internal angle and internal angle of the same side, are very important. Their derivation is the beginning of "containing but not revealing" infiltration reasoning in junior middle school, and these concepts and conclusions are also an important basis for further studying the properties and judgments of parallel lines, triangles and quadrangles.
This lesson first introduces the new lesson naturally and directly by placing three thin sticks, and then sets five questions, so that students can give full play to their enthusiasm, initiative and creativity by trying to learn by themselves. The purpose of designing these questions is to deepen the teaching focus, make students' reading more targeted and avoid blindness. Students' mutual evaluation can increase the depth of discussion, teachers' final evaluation can unify students' views, and students can understand, increase their wisdom and cultivate their ability of induction and summary in the process of discussion and evaluation. Then through the gestures of both hands, let the students use their hands and brains to experiment and experience, and deepen their understanding of the concept in the activities. The choice of exercises is also from shallow to deep, which plays a role in consolidating new knowledge. Finally, a hanging summary is given: "If two straight lines are cut by a third straight line and the same angle is equal, what is the positional relationship between the two cut straight lines?" Encourage students to consciously read and preview books after class to find answers.
The teaching design of this section is based on the textbook, but it is not completely bound by the textbook. Exploring? Guess what? Demonstration "mathematical thinking mode In teaching, we constantly set up some targeted problem situations to stimulate students' thinking, guide students to discuss independently, and try our best to let students actively learn mathematical knowledge in a lively atmosphere. Students' participation is very high, and the expected teaching effect has been achieved.
But the "question menu" of the whole class is mostly pointed out by the teacher, and the students may be a little passive. Secondly, this class has a large capacity, and it is difficult for some students with difficulties to digest it all, which will be improved in the future teaching process.
Reflections on the teaching of isomorphic angle, internal angle and internal angle of the same side in junior one mathematics (3)
In the creation situation, I ask students to answer the quantitative and positional relations of any two of the four angles formed by two intersecting lines, review the known knowledge of vertex and adjacent complementary angles, emphasize that all four angles formed by two intersecting lines are at the same vertex, and then ask a question: What kind of positional relationship will exist if the two angles formed by one intersecting line are added together? Lead out the main content of this section.
In self-study, I ask students to understand the position characteristics of congruent angle, internal angle, ipsilateral internal angle and secant, experience the formation process of the concepts of congruent angle, internal angle and ipsilateral internal angle through analogy transfer, and then summarize the concepts of congruent angle, internal angle and ipsilateral internal angle.
I asked the students to do exercises in the courseware with up-to-standard feedback. I found that it is no problem for students to find congruent angles, internal errors and internal angles of the same side in simple graphs, but it is a big problem to find incomplete congruent angles, internal errors and internal angles of the same side in graphs with four or more complex line segments.
I reflect on the teaching process in time and feel that students don't understand the concepts thoroughly. They simply remembered the structure of the figure: "isosceles angle is shaped like the letter F, inner angle is shaped like the letter Z or N, and the inner angle on the same side is shaped like the letter U". When looking for angles, students only remember to look for figures, but ignore that in the "three-line octagon", the section line must be determined first, and then the congruent angles and internal angles on the same side of the section line and the internal angles on different sides of the section line can be found by combining the graphic features (f, z or n, u). So, how to determine the section line in the drawing? I adjusted the course in time and explained to the students how to find thread cuts.
Combined with the example on page 7 of the textbook, we find that? 1 and? 4 is the same angle, but it is not difficult to see through careful analysis. 1 OB and BC on both sides (I set the intersection of AB and DE as O point)? On both sides of 4 are AO and OE, and OB and AO are just on the same straight line AB. 1 and? 4 is a diagonal line cut by AB line between BC line and DE line, so what is the cut line? 1 and? The straight line where the common side of 4 is located. In this way, to determine the relationship between two angles, we must first find the straight line where the common side of the two angles is located, that is, the secant, and then determine the two secants, that is, the straight lines where the other two sides of the two angles are located, and accurately find out the secant and secant. Then, according to the fact that the "crossing position of the cutting line" is an inner angle and the "ipsilateral position of the cutting line" is an ipsilateral angle or an inner angle,
Through the teaching of this section, I think that isosceles angle, ipsilateral internal angle and ipsilateral internal angle are angles with different positional relationships when two straight lines are cut by the third straight line. So first of all, it depends on whether there are only three straight lines in two corners, one side of the two corners is a cut line, and then the straight line on the other side of the two corners is a cut line. So I take "finding the right cutting line and cutting line" as the difficulty of this section. Distinguishing between line cutting and line cutting, students can separate basic graphics from complex graphics, making the complex simple and the difficult easy.
I have seen the teaching reflection on isosceles angle, internal angle and internal angle of the same side in the first grade of mathematics.
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