I. Research topic
The first unit of sixth grade mathematics in Beijing Normal University is the foundation and focus of this book. After learning the understanding of the circle, in order to better understand the students, learn the lesson of the circumference of the circle, so that the teaching activities have a good starting point and the teaching priorities and difficulties have a good breakthrough. Before class, I made a class survey of the sixth grade of my generation. At the same time, 10 students were randomly selected for individual interviews, and a study group in the class was randomly selected for group observation.
Second, the research objectives
1. Understand the knowledge base of students learning "circle".
2. Understand students' life experience and learning experience related to "circumference".
3. Understand the difficulties that students may encounter in learning "circumference".
4. Understand students' interests and favorite learning methods when learning "Circle".
Third, the research object
Because classroom teaching is for the whole class, the research object is all sixth-grade students (26 people).
Fourth, research methods.
Questionnaire survey, student interview and group observation
Verb (abbreviation of verb) The content and purpose of the investigation.
(a) questionnaire survey (all students in the class):
1, find the perimeter of the figure below. (Unit: cm)
2
5 2
Objective: To investigate students' mastery of the existing knowledge base (the understanding of perimeter meaning) and method base.
2. What do you think is the key to the circumference?
Objective: To investigate students' experience of the conditions that affect the circumference.
How do you think the circumference of a circle should be measured?
Objective: To investigate students' experience of what they have learned (measuring experience-turning music into straightness). (2) Interview (randomly selected 10 students)
1, do you know pi? What do you know?
Objective: To investigate students' experience of what they have learned (pi experience).
2. What is your biggest difficulty in learning the perimeter of rectangles and squares? What way are you willing to take to solve the difficulties? How do you want to learn new knowledge? (Read books for self-study, ask others, explore by yourself, discuss in groups, and be explained by the teacher)
Objective: To investigate students' learning styles and interests.
(3) Group observation (randomly select a study group in the class)
Can you get the circumference of this round object?
Objective: To investigate the students' experience of the knowledge (circle) and the difficulties they may encounter, as well as the problems they may encounter in group measurement activities.
Statistics and analysis of the survey results of intransitive verbs
1, find the perimeter of the figure below. (Unit: cm)
The answer is right and wrong.
Finding the perimeter of a rectangle and finding the perimeter of a square are not done.
No.22 1 2 1
four
Percentage 84.6% 3.8% 7.7% 3.8%
15.4%
Through investigation, it is found that most students in our class can accurately grasp the meaning of perimeter and calculate the perimeter of the figure according to the known conditions, but some students can't accurately get the perimeter of the figure.
2. What do you think is the key to the circumference?
The diameter, radius, area, pi, size and center of the circle are all unknown.
No. 108 1 1420
Percentage 38.4% 30.8% 3.8% 3.8%15.3% 7.7% 0
Most students answered correctly (including diameter, radius, area and size), accounting for 88.5%. Without visual support, there are still 1 1.5% students who get completely wrong answers (pi, center).
How do you think the circumference of a circle should be measured?
Answer the question, you can do it, you can't do it.
Both methods can adopt winding method and rolling method.
No. 1 1672
24
Percentage 42.3% 23. 1% 26.9% 7.7%
92.3%
Students seem to have some experience in measuring circumference, but 7.7% students lack common sense, methods and skills in life.
(2) Interview (randomly selected 10 students)
1, do you know pi? What do you know?
Results It is said that π π value is related to Zu Chongzhi.
Number of people 5 1 2 1 1
Children's understanding of π is almost only that it is between 3. 1415926-3.1415927, and the general value is 3.14, but the meaning of π is almost unclear. Only one child has read this book. I don't know π because children can't understand and accept that a number is represented by a symbol. I don't usually read many stories about mathematicians. Teachers should consciously train students to read more books in this field, guide students to understand the meaning and calculation process of π, let children know the wisdom of China people, and enhance their confidence in loving mathematics and learning it well.
2.( 1) What is your biggest difficulty in learning the perimeter of rectangles and squares? What way are you willing to take to solve the difficulties? How do you want to learn new knowledge? (Read books for self-study, ask others, explore by yourself, discuss in groups, and be explained by the teacher)
Difficulties:
The result is not difficult to understand the following formula.
No. 136
Solution:
Results Reading, self-study, asking others, teacher's explanation, group discussion and inquiry.
No.3 1 222
Students' understanding of the figures and perimeters they have learned only stays in the results; Children don't remember the process of exploration in class deeply enough; After the teacher's guidance, I said that I like teamwork. Explain that the previous teaching did not pay enough attention and exploration, and the children's summary and reflection were not enough.
(3) Group observation (one study group is randomly selected in the class: 4 people)
Can you get the circumference of this round object?
Result analysis:
Students have the basis of "knowing the circle" and a clear concept of perimeter. When the students need the circumference of a circle, the four of them discussed and put forward the need for learning tools (rope, scissors, ruler, pen), so they quickly got the circumference of a circular piece of paper by wrapping.
But when I asked, what should I do if I get the circumference of a circle drawn on paper? Students are somewhat helpless. In my step-by-step hint: Do you know who has something to do with the circumference? What does it matter? Combining the relationship between the perimeter and the side length of a square and exploring the relationship between the perimeter and the diameter of a circle, students deduce that the perimeter of a circle is always more than 3 times the diameter. Then, under my guidance, I deduced the formula of the circumference of the circle. Although it took a long time for group cooperation, I am glad that they actively participated in solving a problem in various ways and reasonably cooperated with the team spirit. Let me know more clearly: children gain some mathematical ideas and methods while gaining knowledge.
I firmly believe that with the above analysis, teachers can really grasp the starting point of teaching and be more targeted when designing this course.