Catalogue of research on mathematical micro-topics

First, the content analysis of teaching materials

1. A Comparative Study of Textbook Content Design and Traditional Content

2. The characteristics and analysis of classroom activities and exercises in textbooks.

3. Research on the design and function of the textbook theme map.

4. Research on Mathematical Culture in Primary Mathematics

Second, to adapt to the new mathematics teaching methods and means of reform

1. Research on Teachers' Effective Teaching Strategies

2. Research on the teaching methods of autonomy, cooperation and inquiry in primary school mathematics.

3. Study on students' learning style

4. Improve the research of classroom activities and homework.

5. Research on the design characteristics and teaching methods of number and calculation content.

6. Research on the design characteristics and teaching methods of space and graphic content.

7. Research on the design characteristics and teaching methods of practical activities.

8. Research on the design characteristics and teaching methods of statistics and probability content

9. Research on primary school mathematics teaching AIDS and learning tools.

10. Research on the Courseware of Primary School Mathematics Teaching under the New Textbook

1 1. Research on the Application of Multimedia Technology in Primary School Mathematics Classroom

12, let mathematics move from classroom to life, and cultivate students' application consciousness.

13 and the study of three-step guidance teaching mode

Third, study the evaluation methods suitable for teaching materials.

1. Research on Cultivating Students' Self-evaluation and Self-reflection Ability

2. Research on the evaluation of primary school mathematics students' innovative thinking.

3. Evaluation of interest, methods and habits in mathematics learning.

4. Research on diversification of evaluation methods

5. Experimental study on using "student growth record bag"

6. Research on the content of mathematical evaluation and the method of recording results.

Final report of micro-project:

Report on the Project of "Research on the Effectiveness of Primary School Mathematics Classroom Patrol"

First of all, the questions raised

In today's primary school mathematics classroom, formal, inefficient and even ineffective classroom patrol still exists universally. In this kind of class, when the teacher arranges students to study by themselves or do their homework, they either wander around the students aimlessly, just going through the motions for patrol; Or just understand the learning progress of most students and maintain the learning order without giving any guidance to students; Or just pretend to listen sideways and "enter" instead of "deep"; Or just urge the students: "Please hurry!" Or find students' mistakes very impatient, "why don't you!" " In their view, classroom patrol is to successfully complete their own teaching.

In view of the above phenomenon, I have made some thoughts on how to improve the effectiveness of classroom patrol in primary school mathematics. In the process of research, the following questions need to be analyzed and solved: What is the attitude of students towards classroom patrol? How to make students welcome and actively cooperate with teachers to complete each classroom tour? How to cultivate the excellent and help the weak in the investigation, improve the depth and breadth of excellent students' problem solving, and cultivate the self-confidence of underachievers? How to guide students to develop good classroom study habits during patrol? How to preset different class tours for students of different classes and stages? How to adjust the teaching preset scheme according to the classroom generation during the inspection? How to promote the interactive communication between teachers and students through patrol, better communicate the feelings between teachers and students, and thus build an efficient and colorful mathematics classroom?

Second, the study of the problem.

(1). The student-oriented educational concept leads the research process.

At the beginning of the research, I was reading Professor Guo's Education for Students. I know that student-oriented education is a child-oriented education that "everything is for children, highly respects children and relies on children in an all-round way", and this whole book runs through this brand-new concept; I know that the educational ideal pursued by student-oriented education is: to find an educational method, so that teachers can teach less, students can learn more, and schools can be less noisy, disgusted and useless, with leisure, happiness and solid progress; "Since God has given talents, let them be employed!" This is the highest realm pursued by student-oriented education; Knowing the value orientation of student-oriented education means "resolutely turning from teacher-oriented education to student-oriented education, and taking the initiative of students as the most effective and important strategy to solve educational problems at present." In my opinion, the above-mentioned student-oriented educational thought can guide me to conduct in-depth research on this subject.

(2). Comparison between student-based patrol and teacher-based patrol.

The phenomenon of classroom patrol cited by the author in the question is a typical classroom patrol under teacher-based education. Obviously, the teacher-based lecture tour in primary school mathematics classroom is teacher-centered, textbook-centered, and classroom-centered, which fundamentally violates the student-based educational viewpoint of "all for students, high respect for students, and full dependence on students". Students should be the center of primary school mathematics classroom patrol under student-oriented education. Teachers should go deep into students' learning process, carefully discover students' mistakes, deal with classroom generation, guide students to develop good classroom learning habits, and build efficient and colorful mathematics classrooms through effective classroom inspections to serve students' learning and development.

(3). Psychological investigation and analysis of students in the process of classroom patrol.

In order to understand the students' thoughts on mathematics teachers' patrolling the classroom, grasp the students' psychological state in the process of patrolling the classroom, and better serve the students who patrol the classroom, I conducted a survey of all middle and senior students in our school in the form of anonymous questionnaire, and made a detailed analysis of the relatively rich original data.

1. When answering the questions independently, the teacher came to his side, and 47.5% of the people showed their exercise books on purpose, hoping that the teacher would point out the maze. These students can actively cooperate with the teacher's patrol psychologically; 5% students don't cooperate with the teacher's inspection at all, and they will cover their homework immediately because they are afraid that the teacher will see it; Students who are a little nervous and always feel a little unnatural account for 46.3%; Without feelings, 38.8% students solve problems as usual, holding an indifferent attitude.

Analysis: Whether the students cooperate with the teacher's patrol has a certain relationship with the students' psychological quality and academic performance, and also has a great relationship with the teacher's attitude or, more specifically, the degree of affinity and patience.

2. What will you do when the teacher encounters a problem during the inspection? 63.8% raised their hands to ask the teacher for advice; 12.5% are afraid of being criticized by the teacher for raising their hands; 8.8% are afraid of classmates' jokes and dare not raise their hands; 67.5% of the students are vacant, so do other topics first.

Analysis: When solving problems independently, it is common to encounter problems. Most students can raise their hands and ask the teacher for advice. But more students choose to be empty, and their active attitude is still lacking. Nearly two-tenths of students need psychological counseling and the spirit of asking questions.

3. In group discussion, 365,438+0.3% want teachers to come to their own group and only listen to group discussion; I hope the teacher will guide me and become a member of the group, accounting for 46.3% of the participants in the discussion; 5% require teachers to go to other groups so as not to affect their own groups.

Analysis: Most students want teachers to participate in or guide their own group discussions, which shows that students welcome teachers to patrol in group cooperation, and also shows that students' team cooperation ability needs to be further cultivated.

4.26.3% people want the teacher to come to my side to watch me when doing related operations in class; 77.5% people hope to get guidance from teachers; 15.0% is afraid that the teacher will find mistakes in his homework, so it is best not to go to him.

Analysis: Most students want the teacher's guidance when checking, and a few students don't want the teacher to check for fear of finding their own mistakes. They need teachers to guide them in front.

In the column of advice to teachers in the questionnaire, some students wrote: teachers should patrol while putting it away.

Tell the whole class the problems found in time and give lectures while patrolling, so that the correct rate of the whole class will be improved; When visiting students with poor learning, if you find that they have many problems, please give them some guidance. Don't stay too long, it will waste other people's time. We should guide more students, and don't let some students feel that teachers don't pay enough attention to themselves. Teacher, you sometimes find my novel solution during the inspection, please introduce it to the class; When the teacher is invited to patrol the classroom, he should look around. Don't stand alone behind any student and make him feel uneasy, as if his topic is wrong. Sometimes he doesn't know that the teacher is behind, and he is startled when he turns around. Teachers should not patrol the classroom too many times, if too many will affect us and make us overly nervous; I hope that when the teacher finds our mistakes in the patrol, he will not say it, but just point it with his finger, so that my self-esteem can be greatly satisfied. These are the original words of the students. From the perspective of these confessions, we can easily find out what kind of classroom patrol students need.

(4). Research on Teaching Practice and Classroom Patrol Strategy

In the process of classroom teaching, how to adopt the corresponding classroom patrol strategy according to the specific teaching situation? The author made the following research on its specific teaching examples:

1. Like "a quick tour"

The time of each class is limited, and the tour of each class can only be calculated in seconds. In these few tens of seconds, teachers should capture feedback information, understand and master the learning situation, and make relevant teaching measures quickly, that is, they should have the efficiency similar to "enjoying flowers on horseback". "Looking at flowers" only pays attention to speed, only looks at superficial phenomena, and ignores the essence of the problem. "Looking at flowers" requires teachers' keen observation, effective analysis and judgment, not only to observe all flowers, but also to appreciate a few unique and colorful flowers, and finally to control teaching quickly and reasonably.

After learning the first example of percentage application, the students began to practice the topic in the textbook: there are 48 students in Class One, Grade Six, 30 of whom can swim. What percentage of the class can swim?

When I checked, I found that all the students in my class were right, but when calculating 30÷48, most students in my class listed the vertical 30÷48 in the draft for calculation. Only two students, Xiao Hehua, calculated it this way: 30 ÷ 48 = 5 ÷ 8 = 62.5%, and they didn't use the draft.

I know that although the students have learned the reciprocity of percentages and fractions, they have memorized fractions and decimals and several common values of percentages, such as 1/2 = 0.5 = 50%, 3/4 = 0.75 = 75%, 3/5 = 0.6 = 60%, 1/8. So, I immediately asked these two "flowers" to introduce their algorithms to the whole class, and their introduction was warmly applauded by other students.

2. Be good at "fault tolerance and borrowing mistakes"

A new misconception advocated by student-oriented education is that it doesn't matter if something is worth doing badly. This is not to say that it should not be done perfectly, but to allow a rather clumsy learning process and allow mistakes.

Others say, "mistakes are to learning what sand is to mussels." At first, they couldn't refuse. Later, they changed their strategy and secreted juice to contain sand grains, but cultivated pearls instead. " I think this is a good inspiration for our classroom teaching. In the face of the inevitable mistakes found by students in the classroom patrol, we can only tolerate them at first, and then rely on the students' mistakes to make a little move and push the boat forward. "Fault-tolerant borrowing" may have results.

Case A seminar teaches "Quotient with Formula of 9", and students divide and calculate formulas in groups.

Health1:8 ÷ 2; Health 2: 911; Health 3: 54 ÷ 9; Health 4: 3 ÷ 9

No sooner had student 4 finished than the other three students shouted, "Wrong compilation! Wrong! " Born four sadly bowed his head.

At this time, the attending teacher gently stroked the head of student 4 and said, "Students, in fact, he is great, but this problem will not be done until our sixth grade!" " The students were surprised, and the fourth student slowly raised his head. )

"Who can change 3 in formula 3÷9 into a number and make it the division formula we can solve at present?"

Health 1: change 3 to 27; Health 2: Change 3 to 72.

"If 3 doesn't move, how to add a number to make it a division formula?"

Add 6 before 1:3, which means 63÷9 = 7.

Health 4: (Raise your hand quickly) You can also add 6 after 3, that is, 36÷9 = 4.

……

"Fault tolerance" makes teachers more tolerant and flexible in teaching, which will make students feel less frustrated. "Borrowing mistakes" makes teaching go out of the box of textbooks, and makes the classroom a place where students can speak freely and let go of their thinking. In front of interested children, mistakes will be reduced or overcome. "Fault-tolerant and borrowing mistakes" will definitely make our classroom teaching move towards the realm of "no blame" expressed in the Book of Changes.

3. Advocate "Dayu Water Control"

According to legend, Dayu learned the lesson from the failure of water control by artillery, changed the method of "blocking" and "guiding" floods, and finally succeeded. Students' difficulties are inevitable in the process of learning. In the face of the difficulties students encounter in the process of classroom inspection, we can only make students suddenly enlightened through reasonable guidance and appropriate guidance. As Confucius said, "If you don't get angry, you won't get angry."

Case Teachers and Students * * * After exploring the calculation method of the lateral area of the cylinder, the students began to look for the lateral area in the following picture:

When traveling, I found that Feng Kaili did this: 4x3 =12cm2. How can it be so formulaic? I looked down and quietly started a short conversation with her:

"How to calculate the side area of a cylinder?"

"Multiply this height by the circumference of the bottom of the cylinder."

"What is the figure at the bottom of the cylinder?"

"It's round."

"How to calculate the circumference of a circle?"

"Diameter times pi." a

"Then how did you work it out?"

"I use the circumference of the bottom of the cylinder multiplied by the height to calculate?"

I finally understood that she took the bottom diameter as the bottom circumference. I drew the bottom perspective of this cylinder directly in her supplementary exercise, and made the bottom diameter with dotted lines, as shown below:

"The arrow represents the distance between two points, not the length of all the lines in the middle, so it can only represent the length of the bottom diameter of the cylinder." As I spoke, I drew a line segment between two points with a pen.

"Teacher Wu, I know that the arrow should represent the length of the line segment, not the length of the curve."

4. Firmly believe in "governing by doing nothing"

"Governing by doing nothing" is the essence of Laozi's thought and theory. Its original intention is to conform to nature, public opinion and people's hearts. Not doing nothing, but letting them solve it themselves. This is consistent with the principle of least intervention followed by student-oriented education.

In the primary school mathematics classroom patrol, if students are given as much autonomy as possible without too much intervention, there will be a wonderful realm of "telling more in silence than in voice", their learning nature will break out and we will get unexpected results.

Case students discuss in groups how many symmetry axes a rectangle has.

Student 1: (demonstration) can be folded vertically or horizontally, with one * * * and two pieces.

Health 2: Yes, only two. That's what I thought.

Health 3: No, there should be four, folded in half along two diagonal lines, with the same crease on both sides. So the two diagonal lines are also its symmetry axis.

Health 4: (with a blank face. )

Health 1, 2: this .....

Four people in the group looked up at me from the audience. I know that they have confused "coincidence" and "identity" in the concept of axial symmetry. I just wanted to point it out, but I stopped. If you think about it again, you will surely come to the correct conclusion. I sent an expectant smile to the four of them.

(After more than ten seconds of silence,)

Health 1: (facing 3 excitedly) You are wrong. Both sides of the diagonal are the same, but they do not overlap after folding. All rectangles have only two axes of symmetry.

……

I think, in the classroom inspection, we firmly believe that "governing by doing nothing" will definitely lead our mathematics classroom to the ideal realm of "those who teach well teach little or even don't teach".

Third, research results and reflection

In the course of more than a year's research, I deeply realized that as an important part of mathematics classroom, mathematics classroom patrol must be "all for students, highly respect students and rely on students in an all-round way". I go deep into the students during the class tour to understand their learning process, find out the causes of students' mistakes seriously, deal with classroom generation, guide students to develop good classroom learning habits, and build an efficient and colorful math classroom through effective class tour.

Due to the influence of many factors, there are still many shortcomings in the research of this subject. The research process attaches importance to the generation research in the patrol and reduces the preset research in the patrol. How to make reasonable patrol preset according to different types of teaching content? What is the psychology of the instructor during the inspection? And so on, are worthy of in-depth study.