“ maths ” the content is a new experimental mathematics teaching material for primary school teaching of the plate, “ mathematics teaching is the key to wide ” some important mathematical ideas and methods to penetrate through the simple case, the goal is to cultivate students' thinking and ability to solve practical problems. The new content of many teachers feel confused, confused at the editor's intention, confusion in the grasp of teaching objectives, the confusion in the choice of teaching methods, teaching contents in the treatment of confusion, confusion in the teaching process, the teachers feel difficult to teach. On the other hand, because of the limited students' cognitive ability and life experience, and the abstractness of the contents, the students have many difficulties in learning.

The author in the long-term teaching practice to realize breakthrough: “ maths ” the key is to accurately grasp the teaching goal; establish a life teaching environment; through hands-on research, combination of number and shape, model construction; in the formation of knowledge of mathematics thought method in the process of.

First, accurate positioning of the teaching goal of

The "curriculum standards" clearly put forward in compiling suggestions: “ according to the existing experience of students, psychological development rule and teaching contents, some important mathematical concepts and mathematical thinking should be adopted gradually, deepen and spiral arrangement of ”. This guide is based on the textbook on “ maths ” layout unit, mainly some important mathematics thinking method permeates through some relatively simple examples, let the students try to find strategies to solve the problems from the angle of mathematics in the process of solving the problem of conjecture, experiment, experience the mathematical reasoning of exploration activities, increase the students to solve the practical problems of experience and ability of some important mathematical ideas and methods.

For example: &ldquo 2 in the fifth grade primary school mathematics; find the question, for the implementation of its ” “ basic math knowledge and skills, the basic mathematical thought and basic mathematical activities ” this dimension provides a good carrier, in the process of solving this problem, students can what is the further understanding of random events, to understand and grasp the way of thinking, logical reasoning and the basic process at the same time, how to clear the surface of mathematical thinking; how to understand and solve a variety of optimization problems such as how to use the strategy; — — &mdash — speculation; verification strategy how to find mathematical conclusions; a complex problem into a simple problem; how to put the specific issues for the promotion of the general problem, are to be considered in the process of solving this problem. These hidden teaching goals in the process of solving problems may be easily ignored in the past.

Two, the creation of the teaching situation of life:

We don't find it hard to find out, &ldquo, and ” the contents are from the familiar life examples of the students. In “ &rdquo, “ clothing collocation; table tennis match arrangement ” in the context of penetration of permutation and combination of thought; in the &ldquo Flapjack; ” &ldquo and ” boil tea, penetration or situation; thought; “ post encoding and ID encoding ” feel encoding thought. This arrangement makes the mathematical thought and method had relatively abstract with the realistic background of the rich, in the context of elements, after-school exercises, students are familiar with in the life, vivid and interesting material, so as to stimulate their interest in mathematics curiosity and desire for knowledge, but also let them feel the life in Mathematics is everywhere.

The third grade primary school mathematics volume “ set ”

Teacher: six · before the first festival, our class in the grade discipline competition in the Chinese 7 people won the prize, mathematics has 9 people won the prize, now we give the 16 people to award the good?

Student 1: teacher, isn't it? There are no 16 people!

Teacher: 9+7=16 people, why not 16 people?

Student 2: because some of the 16 people are repeated prizes.

Teacher: repeat? How to understand?

Student 3: because some of the students won the prize, and the mathematics also won the prize.

Teacher: so it was, I got it. Next, we will play a game. The teacher here prepares a red circle and a green circle. Now, please win the Chinese language prize. 7 people stand in the red circle. The 9 winners won the math prize.

Teacher: how do you run into this circle, aren't you supposed to stand in the red circle?

4: teacher, we are both Chinese and math award, award winning, we repeat the

Teacher: Oh, that's the way it is! Students, these two students do you think is the best place to stand?

Student 5: they should stand both in the red circle and in the green circle.

Teacher: it makes sense. Can you use drawing on paper to show the scene?

The student explained the problems with the most concise way, this picture is a collection map, teachers with this picture “ set ” knowledge related to teaching, students learn of intense interest, deeply felt the thick life taste in mathematics.

Three, through

&ldquo 2 in the fourth grade primary school mathematics; planting problems teaching fragments

Teacher: in order to beautify the environment, the gardeners grow a small tree on one side of a 20 meter long road, one every 5 meters.What should I do? Can you help design a tree planting scheme?

Student: independent thinking and the paper draw the schematic diagram of

Teacher: what are the similarities and differences in comparison of these tree planting schemes?

Teacher: if you want to plant trees, the distance between every two trees is equal, and a few meters can be planted every few meters. (1 meters, 2 meters, 4 meters, 10 meters …

Students: group activities, each group selected one of the tree planting situation, and used their favorite way to explore the relationship between the number of tree planting and the interval.

You can draw a picture or set a pendulum with a learning tool.

Teacher: look at the table carefully. What did you find? Communicate in groups.

Feedback and writing:

Length of ÷ =

; spacing interval

A number of interval number = +1

(both species)

A number of interval number = (only one):

A number of interval number = -1 (both for

)

Question: why do we only have one species at one end? The number of trees will be the same as the number of intervals. When two ends are planted, there will be no difference between the number of trees and the number of intervals.

Students discuss and communicate after independent thinking, and teachers cooperate with the corresponding relationship between the interval of the demonstration of the courseware and the number of the trees.

Calculation: a total length of 100 meters, every 2 meters by the path of a tree seedlings, how many trees will be needed?

Different answers show students:

1.100÷ 2+1=51 ( tree);

(both species)

2.100÷ 2=50 ( tree); (only one):

3.100÷ 2— (1=49 tree);

…

Choose one choice: which of the following is the equivalent of a tree planting problem?

1. square bell (

)

2. clothes button (

)

3. saw the wood (

)

4. street lamps (

)

Both ends of A. are , ; and they are only one species; one is only one species; the other is the species; the second is the species; the second is the species; the second is the species; the second is the species; the second is the species; the second is the species; the second is the species; the second is the species; the other is only one species; the second is the species; the other is only one species; the other is only one species; the second is the species; the other is only one species; the second is the species; the second is the species; the second is the species; the other is only one species; the other is only one species; the other is only one species; theBoth ends of

.

The "curriculum standards" pointed out that meaningful learning is the students in the specific situation through effective activities and experience of self construction, teachers create a &ldquo in the classroom; the design scheme of &rdquo for roadside trees; the situation, let students experience two times the effective exploration experience, the first preliminary exploration of how to “? ” the students, starting from the existing knowledge and experience, designed the tree planting scheme through drawing, and perceived the similarities and differences of the three species of tree planting in the comparison. The second group explores “ the length of spacing is ” the two inquiry provides students with multiple experiences of “ and the opportunity to plant &rdquo, and such a full activity experience lays a solid foundation for building models of tree planting. Then the teacher asked the students to use graphics to help students understand the knowledge in the teaching of the teacher students focus on painting line drawing, sketch ability, with the combination of number and shape, establish the corresponding relationship between the interval number and number, number of segments and the number of trees, with the combination of number and shape, the students have the knowledge and experience into the growth point of thinking the development of the development of students' thinking is virtue. At the same time, we start from the actual problems in teaching, and guide students to find out the rules in different situations (bells on the square, buttons on clothes, sawing wood and roadside lights) in analyzing and thinking problems, and experience the process of extracting mathematical models. It is not difficult to see that students have experienced the hands-on operation, cooperation and communication, the combination of number type, and the mathematical process of establishing the model in the learning activities.

Four, mathematics thought method

The mathematical thought method is abstracted abstractly from the mathematical content, which is the essence of the mathematical knowledge and the bridge of knowledge transformation into ability. “ infiltrate mathematical thinking and methods systematically and step by step, and try to show the important mathematical thinking and methods through vivid and interesting examples that can be understood by students, &rdquo. It is one of the general ideas of the experimental teaching material for the new curriculum of the human education edition. Therefore, in &ldquo, mathematics wide angle &rdquo, solving problems in teaching is not the main purpose of teaching. The main task is to infiltrate an idea to students, a very important thought in teaching and research. Like “ &rdquo, “ planting problems; Flapjack ” &ldquo, &rdquo, “ drawer problem;; find the lemon problem ” “ digital encoding and &rdquo and so on; just as a carrier of methods of mathematical thoughts.

Such as: the third grade 2 “ &rdquo in maths; “ overlapping ” that is to allow students to solve problems in the process of feeling with “ Wayne ” to solve the problem of overlapping value, penetrating thought methods solve the problem of overlapping with the set map.

Another example: the fourth grade I “ maths ” in cases of 1:“ how to operate the Flapjack time? ”; example 2:“ the analyst has the guests to build tea, and how to arrange all kinds of things for the guests to drink tea as soon as possible? ”; “ do a do ” in the “ how can the restaurant arrange the order of stir fry to let the guests eat food as soon as possible? ” and so on. By solving these simple examples, let the students from the experience of beauty, or thought in solving problems in “ Tian Ji horse ” let the students experience the story of &rdquo “ game theory; application of the method in practice.

Another example: &ldquo 2 in the fifth grade maths problem; find defective

1 arrange from 5 items to find defective, defective say methods can only ask of diversification, 2 cases has arranged 9 objects to be measured, and ask the students to summarize the optimal strategy to solve this kind of problems, so as to let the students experience the transition to diversified thinking process optimization, effective use of experience Optimization strategies to solve the problem. In addition, it is necessary to infiltrate &ldquo in the study method, and the mathematical ” from the specific to the abstract, from the special to the general mathematical analysis model. Let students discuss how to find the object to be measured is 5 and 9 when the number of defective products, and lists a variety of solutions; and then find out the rules from these programs, and summarize the general methods and optimization strategy; finally, using inductive method to solve a number of items to be measured more for a long time, at the same time it can be concluded whether the correct verification.

To sum up, accurately grasp the teaching objectives; the creation of mathematics scene has the life of the process; experience hands-on exploration, combination of several types and model construction; penetration of mathematical thought and method in the forming of knowledge is to be able to &ldquo ” maths teaching and learning; the awesome.

The author in the long-term teaching practice to realize breakthrough: “ maths ” the key is to accurately grasp the teaching goal; establish a life teaching environment; through hands-on research, combination of number and shape, model construction; in the formation of knowledge of mathematics thought method in the process of.

First, accurate positioning of the teaching goal of

The "curriculum standards" clearly put forward in compiling suggestions: “ according to the existing experience of students, psychological development rule and teaching contents, some important mathematical concepts and mathematical thinking should be adopted gradually, deepen and spiral arrangement of ”. This guide is based on the textbook on “ maths ” layout unit, mainly some important mathematics thinking method permeates through some relatively simple examples, let the students try to find strategies to solve the problems from the angle of mathematics in the process of solving the problem of conjecture, experiment, experience the mathematical reasoning of exploration activities, increase the students to solve the practical problems of experience and ability of some important mathematical ideas and methods.

For example: &ldquo 2 in the fifth grade primary school mathematics; find the question, for the implementation of its ” “ basic math knowledge and skills, the basic mathematical thought and basic mathematical activities ” this dimension provides a good carrier, in the process of solving this problem, students can what is the further understanding of random events, to understand and grasp the way of thinking, logical reasoning and the basic process at the same time, how to clear the surface of mathematical thinking; how to understand and solve a variety of optimization problems such as how to use the strategy; — — &mdash — speculation; verification strategy how to find mathematical conclusions; a complex problem into a simple problem; how to put the specific issues for the promotion of the general problem, are to be considered in the process of solving this problem. These hidden teaching goals in the process of solving problems may be easily ignored in the past.

Two, the creation of the teaching situation of life:

We don't find it hard to find out, &ldquo, and ” the contents are from the familiar life examples of the students. In “ &rdquo, “ clothing collocation; table tennis match arrangement ” in the context of penetration of permutation and combination of thought; in the &ldquo Flapjack; ” &ldquo and ” boil tea, penetration or situation; thought; “ post encoding and ID encoding ” feel encoding thought. This arrangement makes the mathematical thought and method had relatively abstract with the realistic background of the rich, in the context of elements, after-school exercises, students are familiar with in the life, vivid and interesting material, so as to stimulate their interest in mathematics curiosity and desire for knowledge, but also let them feel the life in Mathematics is everywhere.

The third grade primary school mathematics volume “ set ”

Teacher: six · before the first festival, our class in the grade discipline competition in the Chinese 7 people won the prize, mathematics has 9 people won the prize, now we give the 16 people to award the good?

Student 1: teacher, isn't it? There are no 16 people!

Teacher: 9+7=16 people, why not 16 people?

Student 2: because some of the 16 people are repeated prizes.

Teacher: repeat? How to understand?

Student 3: because some of the students won the prize, and the mathematics also won the prize.

Teacher: so it was, I got it. Next, we will play a game. The teacher here prepares a red circle and a green circle. Now, please win the Chinese language prize. 7 people stand in the red circle. The 9 winners won the math prize.

Teacher: how do you run into this circle, aren't you supposed to stand in the red circle?

4: teacher, we are both Chinese and math award, award winning, we repeat the

Teacher: Oh, that's the way it is! Students, these two students do you think is the best place to stand?

Student 5: they should stand both in the red circle and in the green circle.

Teacher: it makes sense. Can you use drawing on paper to show the scene?

The student explained the problems with the most concise way, this picture is a collection map, teachers with this picture “ set ” knowledge related to teaching, students learn of intense interest, deeply felt the thick life taste in mathematics.

Three, through

&ldquo 2 in the fourth grade primary school mathematics; planting problems teaching fragments

Teacher: in order to beautify the environment, the gardeners grow a small tree on one side of a 20 meter long road, one every 5 meters.What should I do? Can you help design a tree planting scheme?

Student: independent thinking and the paper draw the schematic diagram of

Teacher: what are the similarities and differences in comparison of these tree planting schemes?

Teacher: if you want to plant trees, the distance between every two trees is equal, and a few meters can be planted every few meters. (1 meters, 2 meters, 4 meters, 10 meters …

Students: group activities, each group selected one of the tree planting situation, and used their favorite way to explore the relationship between the number of tree planting and the interval.

You can draw a picture or set a pendulum with a learning tool.

Teacher: look at the table carefully. What did you find? Communicate in groups.

Feedback and writing:

Length of ÷ =

; spacing interval

A number of interval number = +1

(both species)

A number of interval number = (only one):

A number of interval number = -1 (both for

)

Question: why do we only have one species at one end? The number of trees will be the same as the number of intervals. When two ends are planted, there will be no difference between the number of trees and the number of intervals.

Students discuss and communicate after independent thinking, and teachers cooperate with the corresponding relationship between the interval of the demonstration of the courseware and the number of the trees.

Calculation: a total length of 100 meters, every 2 meters by the path of a tree seedlings, how many trees will be needed?

Different answers show students:

1.100÷ 2+1=51 ( tree);

(both species)

2.100÷ 2=50 ( tree); (only one):

3.100÷ 2— (1=49 tree);

…

Choose one choice: which of the following is the equivalent of a tree planting problem?

1. square bell (

)

2. clothes button (

)

3. saw the wood (

)

4. street lamps (

)

Both ends of A. are , ; and they are only one species; one is only one species; the other is the species; the second is the species; the second is the species; the second is the species; the second is the species; the second is the species; the second is the species; the second is the species; the second is the species; the other is only one species; the second is the species; the other is only one species; the other is only one species; the second is the species; the other is only one species; the second is the species; the second is the species; the second is the species; the other is only one species; the other is only one species; the other is only one species; theBoth ends of

.

The "curriculum standards" pointed out that meaningful learning is the students in the specific situation through effective activities and experience of self construction, teachers create a &ldquo in the classroom; the design scheme of &rdquo for roadside trees; the situation, let students experience two times the effective exploration experience, the first preliminary exploration of how to “? ” the students, starting from the existing knowledge and experience, designed the tree planting scheme through drawing, and perceived the similarities and differences of the three species of tree planting in the comparison. The second group explores “ the length of spacing is ” the two inquiry provides students with multiple experiences of “ and the opportunity to plant &rdquo, and such a full activity experience lays a solid foundation for building models of tree planting. Then the teacher asked the students to use graphics to help students understand the knowledge in the teaching of the teacher students focus on painting line drawing, sketch ability, with the combination of number and shape, establish the corresponding relationship between the interval number and number, number of segments and the number of trees, with the combination of number and shape, the students have the knowledge and experience into the growth point of thinking the development of the development of students' thinking is virtue. At the same time, we start from the actual problems in teaching, and guide students to find out the rules in different situations (bells on the square, buttons on clothes, sawing wood and roadside lights) in analyzing and thinking problems, and experience the process of extracting mathematical models. It is not difficult to see that students have experienced the hands-on operation, cooperation and communication, the combination of number type, and the mathematical process of establishing the model in the learning activities.

Four, mathematics thought method

The mathematical thought method is abstracted abstractly from the mathematical content, which is the essence of the mathematical knowledge and the bridge of knowledge transformation into ability. “ infiltrate mathematical thinking and methods systematically and step by step, and try to show the important mathematical thinking and methods through vivid and interesting examples that can be understood by students, &rdquo. It is one of the general ideas of the experimental teaching material for the new curriculum of the human education edition. Therefore, in &ldquo, mathematics wide angle &rdquo, solving problems in teaching is not the main purpose of teaching. The main task is to infiltrate an idea to students, a very important thought in teaching and research. Like “ &rdquo, “ planting problems; Flapjack ” &ldquo, &rdquo, “ drawer problem;; find the lemon problem ” “ digital encoding and &rdquo and so on; just as a carrier of methods of mathematical thoughts.

Such as: the third grade 2 “ &rdquo in maths; “ overlapping ” that is to allow students to solve problems in the process of feeling with “ Wayne ” to solve the problem of overlapping value, penetrating thought methods solve the problem of overlapping with the set map.

Another example: the fourth grade I “ maths ” in cases of 1:“ how to operate the Flapjack time? ”; example 2:“ the analyst has the guests to build tea, and how to arrange all kinds of things for the guests to drink tea as soon as possible? ”; “ do a do ” in the “ how can the restaurant arrange the order of stir fry to let the guests eat food as soon as possible? ” and so on. By solving these simple examples, let the students from the experience of beauty, or thought in solving problems in “ Tian Ji horse ” let the students experience the story of &rdquo “ game theory; application of the method in practice.

Another example: &ldquo 2 in the fifth grade maths problem; find defective

1 arrange from 5 items to find defective, defective say methods can only ask of diversification, 2 cases has arranged 9 objects to be measured, and ask the students to summarize the optimal strategy to solve this kind of problems, so as to let the students experience the transition to diversified thinking process optimization, effective use of experience Optimization strategies to solve the problem. In addition, it is necessary to infiltrate &ldquo in the study method, and the mathematical ” from the specific to the abstract, from the special to the general mathematical analysis model. Let students discuss how to find the object to be measured is 5 and 9 when the number of defective products, and lists a variety of solutions; and then find out the rules from these programs, and summarize the general methods and optimization strategy; finally, using inductive method to solve a number of items to be measured more for a long time, at the same time it can be concluded whether the correct verification.

To sum up, accurately grasp the teaching objectives; the creation of mathematics scene has the life of the process; experience hands-on exploration, combination of several types and model construction; penetration of mathematical thought and method in the forming of knowledge is to be able to &ldquo ” maths teaching and learning; the awesome.

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