High school inquiry learning report
Throughout the "Mathematics Curriculum Standards", the outstanding requirement is that under the guidance of teachers, students conduct independent inquiry activities from reality.
Exploratory learning is a kind of learning activity driven by curiosity, problem-oriented, students with high intellectual input, and rich content and form. It is a learning method based on the physical and mental characteristics of young people; it is the need to cultivate modern citizens and innovative talents; it is an important subject for the reform and research of mathematics teaching; it is the integration of exploratory learning and research learning. Let's talk about my own views on high school mathematics inquiry learning.
1. The condition for conducting exploratory learning is "level thinking."
“Level thinking” refers to thinking across multiple disciplines or fields. Students often associate some seemingly unrelated things, which is a manifestation of "level thinking" and a basic feature of creative thinking. When many teachers are in class, students often ask questions about the teacher's questions, and even "the bulls are not right." If the teacher simply denies, or falls apart, it will damage the classmate and even affect the enthusiasm of other students.
Example 1: "If a is a natural number, say 7 consecutive natural numbers after a."
A girl who likes English raises her hand: "b, c, d, e, f, g, h";
A boy gets up and corrects: "a+1, a+2, a+3, a+4, a+5, a+6, a+7."
This is the result of “level thinking”, and it is this kind of thinking that is the condition for teachers to guide students to inquiry learning. According to the hierarchical and divergent characteristics of "level thinking", many strange thinking sparks will appear in teaching questions, which is a good material for inquiry learning. The teacher's strategy is to encourage him to explain the basis of the answer and try to derive the rationality of the conclusion. If there is "a little truth", we should promote democracy, derive more reasonable answers, and clarify the ambiguous sense of plausibility. Even if the answer is “absurd”, “absurd” is the best friend of “creativity”. No matter what kind of answer, the students are obtained through their own "level thinking", which deserves to be valued and praised, and cannot be imposed on the will of the students with the teacher's understanding and will.
Second, the premise of inquiry learning is "autonomous activities"
Constructivism points out that mathematics learning is not a passive acceptance process, but an active construction process. That is to say, mathematics knowledge must be based on the individual's operation and communication of experience, and actively construct through reflection. This effectively enables students to comprehend mathematical ideas and mathematical methods, inspire students to think positively, and guide students to explore and discover new knowledge points. Such as,
Example 2: The teaching of the ellipse concept can be carried out in several steps:
Experiment - Students are required to use two small pushpins prepared in advance and a thin line of fixed length to fix the two ends of the thin line, and use a pencil to tighten the thin line, so that the nib moves slowly on the paper, and the resulting figure is an ellipse.
Ask questions and think about discussion.
What are the characteristics of the points on the ellipse?
2 When the length of the thin line is equal to the distance between the two fixed points, what is its trajectory?
3 When the length of the thin line is less than the distance between two fixed points, what is its trajectory?
4 Can you give the ellipse a definition?
Reveal the essence and give a definition.
Through the above-mentioned autonomous inquiry activities, students can experience the methods of abstracting mathematical concepts from life examples, further explore the intrinsic connections and their respective characteristics, and complete the active construction process of new knowledge.
How to induce students to participate and experience the construction of new knowledge? The human body will first establish a teaching situation in which the knowledge point exists in the human body, so that each student can find his or her position in the situation. When teachers create teaching situations, they should fully understand the existing cognitive structure of all students, provide students with a large amount of objective information, and guide students to discover the contradiction between existing cognitive structure and a large amount of objective information. Then, students are induced to use the correct "research method" to study this contradiction. The contradiction is solved. The students have learned the research methods, gained knowledge, overcome the difficulties, and cultivated morality, forming a higher and stronger. Ability.
Third, the effective way of inquiry learning is "mathematical experiment"
Even abstract mathematics is closely related to the examples in life, close to life, return to life, and study the problems that arise in social life and other disciplines from a mathematical perspective. Let students experience and experiment with them to understand the history of “need to produce mathematics”, thus experiencing the value of mathematics, experiencing the value of life created by predecessors, inspiring interest in learning, and thus consciously paying attention to and exploring the formation of mathematical knowledge. And the process of applying.
Study summary report, study work report, company study report, exchange study report, travel study report
For example, after the “example of application of the function”, there is an internship assignment after the textbook. Due to the limited time in the class, I ask the students to rewrite the eighth question on the 142th page of the textbook of “High School Mathematics” into an internship report. At about half of the class time, the student's internship report is basically in its infancy. List one of them here:
Internship report December 8, 2002 Topic The construction and demolition of a residential area in a city The total area of existing residential housing in a city is a m2, of which half of the old housing needs to be demolished. The local authorities decided to build a new house with a 10% housing growth rate when a certain number of x old houses were demolished each year.
Write a functional relationship between year after year and the total area of the housing an.
If the total housing area of the area is exactly doubled now in 10 years, what is the total area of the old houses that should be dismantled each year? .
What is the percentage of the total area of the old housing that has not been demolished in 10 years? . .
Responsible person and participant Huang Zexin Zhang Changan Chen Jiangbin Huang Yifeng This is the result of the students themselves. At that time, I asked a question: If you are the leader of the construction and demolition of a residential housing in an urban area, I would like to ask: "The demolition and construction is involved in the title." We will first dismantle and build it, or will it be built first and then demolished? From a mathematical perspective, is there a difference between the two? The classmates talked in an instant, and the class was full of excitement, but soon there was a conclusion: first build and then demolish. I asked a classmate who was a bit mischievous. Why should I build it first? He said that if I am a leader, I have to think about my people, first dismantle and build, then where do they live? Then, from the mathematical point of view, it analyzes the essential difference between “first build and then split” and “first remove and then build”. I think that as a teacher, we can accurately find out the entry point of the problem, and you can immediately comment.
In teaching activities, teachers should use creative materials creatively, actively develop and utilize various resources, provide students with rich and varied learning materials, become organizers, guides and collaborators of students' mathematical activities, and encourage students to boldly innovate and practice, so that each Students are fully developed.
Fourth, the motivation for inquiry learning is “encouragement-based” and “multiple answers”.
“Encouragement-based” is the external motivation of students' inquiry learning. The teaching strategies and teaching language of teachers are all “external motivation” for students. The pursuit of "multiple answers" is the driving force of students' inquiry learning, and teachers should carefully design some mathematical problems. Such as,
Example 4: In the teaching of the parabola and its standard equations, after the parabola definition "the trajectory of a point on the plane equal to the distance between a fixed point F and a fixed line L is called a parabola", the problem situation is set: The image of the unary quadratic function that has been learned is a parabola. The parabola defined today is literally inconsistent with the parabola that has been learned in the country. There must be some intrinsic connection between them. You can find out the inner connection. ?
This question is novel, the conclusion of the question should be affirmative, and there is no explanation in the textbook, which naturally causes students to explore the mystery. At this point, the teacher pays attention: we should start from y= to derive the moving point on the curve to a certain point and the distance to the fixed line is equal, then we can derive: the distance from the moving point P to the fixed point F is equal to the moving point P to the straight line The distance of L. Let's give it a try! The students have changed their pens and pieces together. After the teacher inspects, they can arrange a student to carry out the blackboard and tell:
∵
∴ + =y+
∴ + - = +
∴ + =
∴
It means that the distance from the moving point P to the fixed point F on the plane is exactly equal to its distance from the straight line y=-, which is completely in line with the current definition. In this way, the enthusiasm of students to explore inquiry learning is mobilized, and the students' self-exploration ability is trained to meet the needs of diverse learning.
For example, the answer in the previous example 1 is as follows: as long as 7 English letters are assigned to the mathematical meaning of the meaning, ie: a is a natural number, let b = a + 1, c = a + 2, d = a + 3, e = a + 4, f = a + 5 , g=a+6, h=a+7, then “b, c, d, e, f, g, h” is another correct answer. In this way, you have found a different answer. Only one difference in thought was originally thought to be the only solution, and now it is infinite. "There is no single answer here," it becomes the truth, and the inquiry of "multiple answers" becomes an eternal possibility. That is to use the divergence and flexibility of creative thinking, to examine each math problem, and actively explore new content, new methods, new reasoning and new expressions that may be contained.
5. The strategy of loving students' enthusiasm for inquiry learning is the “multiple evaluation method”.
The main channel of teaching evaluation is still in the process of self-directed learning and classroom teaching. The evaluation should adopt diversity. In the evaluation of our past examinations, the “step-by-step method” and “the solution” have been embodied. "As appropriate, give the division method", fill in the "reciprocal giving method" of multiple answers in the question. In addition,. All learning activities can be used as the basis for evaluation; the means of evaluation can be more flexible, such as: encouraging "comment evaluation", after the application of "delayed evaluation" and so on. With a handful of rulers, there will be a lot of good students. This is a successful example of some places, schools and teachers in the practice of vegetarian education.
In short, the principles that must be followed in developing students' inquiry learning are:
Give students a space to let them go forward;
Give students a condition to let them exercise themselves;
Give students a time to let them arrange for themselves;
Give students a question and ask them to find the answer themselves;
Give students an opportunity to let them catch themselves;
Give students a conflict and let them discuss it themselves;
Give students a right to let them choose;
Give students a topic and let them create it themselves.
Exploratory learning is a kind of learning activity driven by curiosity, problem-oriented, students with high intellectual input, and rich content and form. It is a learning method based on the physical and mental characteristics of young people; it is the need to cultivate modern citizens and innovative talents; it is an important subject for the reform and research of mathematics teaching; it is the integration of exploratory learning and research learning. Let's talk about my own views on high school mathematics inquiry learning.
1. The condition for conducting exploratory learning is "level thinking."
“Level thinking” refers to thinking across multiple disciplines or fields. Students often associate some seemingly unrelated things, which is a manifestation of "level thinking" and a basic feature of creative thinking. When many teachers are in class, students often ask questions about the teacher's questions, and even "the bulls are not right." If the teacher simply denies, or falls apart, it will damage the classmate and even affect the enthusiasm of other students.
Example 1: "If a is a natural number, say 7 consecutive natural numbers after a."
A girl who likes English raises her hand: "b, c, d, e, f, g, h";
A boy gets up and corrects: "a+1, a+2, a+3, a+4, a+5, a+6, a+7."
This is the result of “level thinking”, and it is this kind of thinking that is the condition for teachers to guide students to inquiry learning. According to the hierarchical and divergent characteristics of "level thinking", many strange thinking sparks will appear in teaching questions, which is a good material for inquiry learning. The teacher's strategy is to encourage him to explain the basis of the answer and try to derive the rationality of the conclusion. If there is "a little truth", we should promote democracy, derive more reasonable answers, and clarify the ambiguous sense of plausibility. Even if the answer is “absurd”, “absurd” is the best friend of “creativity”. No matter what kind of answer, the students are obtained through their own "level thinking", which deserves to be valued and praised, and cannot be imposed on the will of the students with the teacher's understanding and will.
Second, the premise of inquiry learning is "autonomous activities"
Constructivism points out that mathematics learning is not a passive acceptance process, but an active construction process. That is to say, mathematics knowledge must be based on the individual's operation and communication of experience, and actively construct through reflection. This effectively enables students to comprehend mathematical ideas and mathematical methods, inspire students to think positively, and guide students to explore and discover new knowledge points. Such as,
Example 2: The teaching of the ellipse concept can be carried out in several steps:
Experiment - Students are required to use two small pushpins prepared in advance and a thin line of fixed length to fix the two ends of the thin line, and use a pencil to tighten the thin line, so that the nib moves slowly on the paper, and the resulting figure is an ellipse.
Ask questions and think about discussion.
What are the characteristics of the points on the ellipse?
2 When the length of the thin line is equal to the distance between the two fixed points, what is its trajectory?
3 When the length of the thin line is less than the distance between two fixed points, what is its trajectory?
4 Can you give the ellipse a definition?
Reveal the essence and give a definition.
Through the above-mentioned autonomous inquiry activities, students can experience the methods of abstracting mathematical concepts from life examples, further explore the intrinsic connections and their respective characteristics, and complete the active construction process of new knowledge.
How to induce students to participate and experience the construction of new knowledge? The human body will first establish a teaching situation in which the knowledge point exists in the human body, so that each student can find his or her position in the situation. When teachers create teaching situations, they should fully understand the existing cognitive structure of all students, provide students with a large amount of objective information, and guide students to discover the contradiction between existing cognitive structure and a large amount of objective information. Then, students are induced to use the correct "research method" to study this contradiction. The contradiction is solved. The students have learned the research methods, gained knowledge, overcome the difficulties, and cultivated morality, forming a higher and stronger. Ability.
Third, the effective way of inquiry learning is "mathematical experiment"
Even abstract mathematics is closely related to the examples in life, close to life, return to life, and study the problems that arise in social life and other disciplines from a mathematical perspective. Let students experience and experiment with them to understand the history of “need to produce mathematics”, thus experiencing the value of mathematics, experiencing the value of life created by predecessors, inspiring interest in learning, and thus consciously paying attention to and exploring the formation of mathematical knowledge. And the process of applying.
Study summary report, study work report, company study report, exchange study report, travel study report
For example, after the “example of application of the function”, there is an internship assignment after the textbook. Due to the limited time in the class, I ask the students to rewrite the eighth question on the 142th page of the textbook of “High School Mathematics” into an internship report. At about half of the class time, the student's internship report is basically in its infancy. List one of them here:
Internship report December 8, 2002 Topic The construction and demolition of a residential area in a city The total area of existing residential housing in a city is a m2, of which half of the old housing needs to be demolished. The local authorities decided to build a new house with a 10% housing growth rate when a certain number of x old houses were demolished each year.
Write a functional relationship between year after year and the total area of the housing an.
If the total housing area of the area is exactly doubled now in 10 years, what is the total area of the old houses that should be dismantled each year? .
What is the percentage of the total area of the old housing that has not been demolished in 10 years? . .
Responsible person and participant Huang Zexin Zhang Changan Chen Jiangbin Huang Yifeng This is the result of the students themselves. At that time, I asked a question: If you are the leader of the construction and demolition of a residential housing in an urban area, I would like to ask: "The demolition and construction is involved in the title." We will first dismantle and build it, or will it be built first and then demolished? From a mathematical perspective, is there a difference between the two? The classmates talked in an instant, and the class was full of excitement, but soon there was a conclusion: first build and then demolish. I asked a classmate who was a bit mischievous. Why should I build it first? He said that if I am a leader, I have to think about my people, first dismantle and build, then where do they live? Then, from the mathematical point of view, it analyzes the essential difference between “first build and then split” and “first remove and then build”. I think that as a teacher, we can accurately find out the entry point of the problem, and you can immediately comment.
In teaching activities, teachers should use creative materials creatively, actively develop and utilize various resources, provide students with rich and varied learning materials, become organizers, guides and collaborators of students' mathematical activities, and encourage students to boldly innovate and practice, so that each Students are fully developed.
Fourth, the motivation for inquiry learning is “encouragement-based” and “multiple answers”.
“Encouragement-based” is the external motivation of students' inquiry learning. The teaching strategies and teaching language of teachers are all “external motivation” for students. The pursuit of "multiple answers" is the driving force of students' inquiry learning, and teachers should carefully design some mathematical problems. Such as,
Example 4: In the teaching of the parabola and its standard equations, after the parabola definition "the trajectory of a point on the plane equal to the distance between a fixed point F and a fixed line L is called a parabola", the problem situation is set: The image of the unary quadratic function that has been learned is a parabola. The parabola defined today is literally inconsistent with the parabola that has been learned in the country. There must be some intrinsic connection between them. You can find out the inner connection. ?
This question is novel, the conclusion of the question should be affirmative, and there is no explanation in the textbook, which naturally causes students to explore the mystery. At this point, the teacher pays attention: we should start from y= to derive the moving point on the curve to a certain point and the distance to the fixed line is equal, then we can derive: the distance from the moving point P to the fixed point F is equal to the moving point P to the straight line The distance of L. Let's give it a try! The students have changed their pens and pieces together. After the teacher inspects, they can arrange a student to carry out the blackboard and tell:
∵
∴ + =y+
∴ + - = +
∴ + =
∴
It means that the distance from the moving point P to the fixed point F on the plane is exactly equal to its distance from the straight line y=-, which is completely in line with the current definition. In this way, the enthusiasm of students to explore inquiry learning is mobilized, and the students' self-exploration ability is trained to meet the needs of diverse learning.
For example, the answer in the previous example 1 is as follows: as long as 7 English letters are assigned to the mathematical meaning of the meaning, ie: a is a natural number, let b = a + 1, c = a + 2, d = a + 3, e = a + 4, f = a + 5 , g=a+6, h=a+7, then “b, c, d, e, f, g, h” is another correct answer. In this way, you have found a different answer. Only one difference in thought was originally thought to be the only solution, and now it is infinite. "There is no single answer here," it becomes the truth, and the inquiry of "multiple answers" becomes an eternal possibility. That is to use the divergence and flexibility of creative thinking, to examine each math problem, and actively explore new content, new methods, new reasoning and new expressions that may be contained.
5. The strategy of loving students' enthusiasm for inquiry learning is the “multiple evaluation method”.
The main channel of teaching evaluation is still in the process of self-directed learning and classroom teaching. The evaluation should adopt diversity. In the evaluation of our past examinations, the “step-by-step method” and “the solution” have been embodied. "As appropriate, give the division method", fill in the "reciprocal giving method" of multiple answers in the question. In addition,. All learning activities can be used as the basis for evaluation; the means of evaluation can be more flexible, such as: encouraging "comment evaluation", after the application of "delayed evaluation" and so on. With a handful of rulers, there will be a lot of good students. This is a successful example of some places, schools and teachers in the practice of vegetarian education.
In short, the principles that must be followed in developing students' inquiry learning are:
Give students a space to let them go forward;
Give students a condition to let them exercise themselves;
Give students a time to let them arrange for themselves;
Give students a question and ask them to find the answer themselves;
Give students an opportunity to let them catch themselves;
Give students a conflict and let them discuss it themselves;
Give students a right to let them choose;
Give students a topic and let them create it themselves.
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