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What is the relationship between mathematics and mathematics education? 100 words or so, highlighting the key points.
Reflections on the New Curriculum Reform of Rural Teachers

Lin Guangyu, a counseling center school in Cangnan County, Zhejiang Province.

Background and thinking:

Recently, I read an article in "Primary School Teaching Reference" magazine-"How rural teachers carry out new curriculum reform-from two teaching clips", and the author was deeply impressed after reading it:

..... At present, the second round of basic education curriculum reform is under way. Many rural teachers think that curriculum reform is computer multimedia, which is a matter for schools in the city. Poor rural conditions and low quality of students. Although the new textbook is used, it is still "wearing new shoes and taking the old road" and it is impossible to implement the new curriculum reform. I don't deny that multimedia has brought many positive factors to teaching, but we can't exaggerate the role of educational means unilaterally. ……

When I appreciate the complete text, what I think is: are rural teachers still "wearing new shoes and taking the old road" when using new textbooks? How do weak schools in rural mountainous areas with relatively backward modern educational technology apply new ideas to implement new curriculum reform? How to carry out the new curriculum reform?

After the impulse, the rest is more thinking. Yes, I quite agree with Mr. Tang. The new round of basic education curriculum reform, for our rural teachers, more changes are: the renewal of ideas, the change of teaching behavior. The "new" rural teachers we expect are "changing the dynasty" of their own ideas, not "changing coaches in the same dynasty". How to infiltrate new ideas into teaching and change teaching behavior, the author has made some attempts. Next, I teach the teaching and research class of mathematics (People's Education Edition), the standard experimental textbook of compulsory education curriculum, and write out the second volume of the lesson "Understanding within 100" and analyze it with you.

Case description:

Part I: Students discover independently and review old knowledge through observation.

Teacher: Slide show: sticks appear one by one, 10 sticks are tied into a bundle with ribbons. )

What do you see?

Health 1: Count one by one, count to ten and tie it up.

Teacher: You observe very carefully. Who else found it? Let's talk about it.

Health 2: Tie them up one by one, 10, then count them one by one, until they reach 100, then tie them up.

Teacher: What is the number of bundles? Did everyone find out? You are so observant! Who can tell us completely what 10 is?

Summary: This is what we have learned, and everyone has mastered it well!

Analysis: Through friendly and natural pre-class communication and slide show, let students discover and review the old knowledge counted within -20: 10, one is ten. Understand the cognitive basis of students' learning this lesson, the method of infiltration counting, and master the starting point of students' learning this lesson.

Fragment 2: The knowledge you have experienced and built is beauty.

Understanding of teaching within 100

1. Count the sticks in this group.

Teacher: Everyone has a stick. Try your eyesight and estimate how many sticks there are in your group.

Health: Our group has about 100.

Health: About 90.

……

Teacher: (Most students estimate that it is around 100. ) blackboard writing: 100

How many? What do we do? (Student: Count) Teamwork. Come and count.

Teacher: How many sticks are there in your group?

Student: There are 92 people in our group.

Health: We have 1 12 in our group.

……

Teacher: Oh, let's count them together. (The projection shows that everyone counts together. ) 10.20.2 1.22 …

How many/much? Can you count?

Teacher: You are not simple. You can count within 100!

……

4. Perception 100

Teacher: How many tens is 100? How about ten tens?

Health: Tie it up!

Teacher: Why?

Sheng Qun: Teacher, you can easily see that it is 100.

Teacher: Just now, we put some tens in the yellow box and some ones in the blue box. (The teacher shows the red box) Where should we put them?

Health: Put it in the front.

Teacher: Which is the front?

Health: Put it on the left of the yellow box!

Teacher: Is that right? (right! )

Teacher: OK, just do as everyone says.

Teacher: This is 100. Draw a picture. How big is a bundle? Show it to other children.

Teacher: How many tens are there in 100? How many tens is one hundred?

Blackboard: 10 Ten is one hundred.

Analysis: In this teaching process, students are provided with opportunities to engage in mathematical activities, so that students can initially feel and understand the meaning of numbers within 100 in the process of estimation and counting, and cultivate their sense of numbers. In the process of counting, by using the method of counting within 20, students can build a knowledge system of ten bundles 10 bundles independently, which embodies that numbers are counted and develops students' sense of numbers. I realized that 10 ten is 100, so I broke through the difficulty of knowledge with great interest: I can accurately count the numbers in the corner close to the whole hundred and the whole thousand hours, and I can understand the meaning of the numbers in multiple digits and the 10 fractional relationship between adjacent numbers.

1. Introduce from real life to stimulate students' interest in learning. Before class, students are required to collect information about percentages and accumulate mathematical information. Students are very interested in this kind of pre-class activities, and have obtained perceptual materials about percentage through practical activities. In class, this kind of life experience reduces their strangeness to new knowledge, thus enabling them to have a preliminary understanding of percentages smoothly. They have brought a lot of items with percentages, and they have been able to read percentages and tell the meaning of percentages. The ability of students has been fully demonstrated, which further shows that underestimating students' ability is more terrible than overestimating students' ability, and students are full of interest and enthusiasm for learning.

2. Examples in life, which students like very much. Hans Friedenthal, a Dutch mathematics educator, believes that "mathematics comes from reality, exists in reality and is applied to reality, and the teaching process should be a process to help students turn reality into mathematical problems". This lesson flexibly deals with the relevant knowledge of percentage and holds a press conference. Adapting the subjects lacking life breath in the teaching materials into vivid topics that students are interested in. Students actively participate in the activities of learning mathematics, and truly feel that mathematics is everywhere in life. Students understand the meaning of percentage more and more in independent discussion, which fully highlights students' dominant position and enables students to discover and master knowledge in exploration.

Fourth, reflection and research.

1. Establish the concept of large class size. Make classroom teaching extend forward, backward and out of class, enrich the connotation of classroom teaching and improve the efficiency of mathematics learning. After class, we will carry out a series of research on small topics, so that students can write math diary and small papers. To improve students' comprehensive ability to use mathematics.

2. From life. Mathematics comes from life, and there is mathematics everywhere in life. In teaching, teachers should handle teaching materials flexibly, connect with real life, absorb and introduce modern and local mathematical information materials closely related to modern production, life and science and technology, and enrich them into the classroom. At the same time, guide students to discover, understand and feel mathematical problems from real life.

3. Go to live. Mathematics knowledge comes from life, and it should also return to life. Extracurricular activities play an important role in mastering, understanding and skillfully using knowledge. Only by experiencing any knowledge can students improve their understanding of mathematical knowledge, cultivate mathematical emotions, promote their innovative consciousness and practical ability to achieve development goals, promote their active development and experience the application value of mathematics.

Facts have proved that mathematical knowledge comes from life. Teachers should actively create conditions, create vivid and interesting life scenes for students in teaching, help students learn, encourage students to be good at discovering mathematical problems in life, develop an attitude of observing and analyzing things around them with mathematics, learn to solve problems in life with what they have learned, and enable students to learn useful mathematics.