Primary school mathematics; First grade; Solve problems; Ability training
The ability to solve problems is an important symbol of students' mathematical literacy. Among the eight aspects of mathematical literacy in PISA design, at least three aspects are directly related to solving problems. The famous American mathematician said, "Problem is the heart of mathematics". The four mathematics learning fields (number and algebra, space and graphics, statistics and probability, practice and comprehensive application) stipulated in the mathematics curriculum standard have their own goals and tasks, and also have the same goals. Through learning in various fields, students' awareness and ability to solve problems are cultivated, and their emotions and attitudes are consistent. In other words, problem-solving runs through students' mathematics learning and all fields of study. The cultivation of problem-solving ability is not only an important task in all fields of study, but also affects the learning of all fields.
The standard sets the goal of solving problems in each learning period. The first learning period is the basic stage of students' learning. The goal is: under the guidance of teachers, find and put forward simple math problems from daily life; Understanding the same problem can have different solutions; Experience in solving problems in cooperation with peers; Learn to express the general process and result of solving problems. As the first year of primary school mathematics learning, teachers should pay more attention to the cultivation of students' problem-solving ability. Based on my own practice, study and thinking, this paper talks about some ideas on cultivating the problem-solving ability of first-year students in mathematics.
First of all, several phenomena
1. In the first grade math class, the teacher asked: What do you observe from the picture?
Health: There are beautiful flowers, trees, blue sky, green grass and so on. The students still can't answer, and the teacher feels powerless.
After teaching a few things, the teacher asked: Can you speak with the numbers you have learned?
Health 1: There are five people in my family.
Health 2: My mother bought me three apples to eat.
Health 3: Dad bought me two apples.
Health 4: My grandmother bought me five pears.
……
3. Write two addition and subtraction formulas according to a picture. When students write subtraction, some will subtract the two sides to form the meaning of comparing two data, rather than the relationship between partial numbers and total numbers.
4. Math problems in the first grade are generally presented in the form of pictures or illustrations. Students sometimes have the following situations when answering questions: (1) can't calculate the formula, just count and give the answer; Misreading or not understanding the meaning expressed by the topic; In the problem of finding the partial number of a known total, the answer to the question is given directly in the form of a statement, and the total number is written as the answer after the equal sign.
5. After learning a few words in class and changing the problem of a situation map, some students can't figure out what method to use. In other words, in middle school, in the same situation, the data becomes bigger and the description method changes, and some students may make mistakes.
……
Second, a little thought.
The Montessori education law describes children's mathematical experience in this way: in the living environment of ordinary children, there is nothing related to mathematical accuracy. There are trees, flowers and animals in nature, but nothing related to mathematics (precision). Children's mathematical tendency may lack opportunities to play, which will affect their future development.
As this passage says, in the phenomenon of 1, students naturally deviate from mathematics without explicitly asking them to ask questions related to mathematics. Phenomenon 2: Students' refining of mathematical information in life is relatively narrow, and they don't imagine all aspects. Phenomenon 3, students tend to compare the two groups of data directly and list them as subtraction formulas, but they have not found the quantitative relationship between the total number and the partial number. The topic was originally to let students understand the internal relationship between addition and subtraction. In the following examples, students also tend to observe more intuitive things and data directly. For unfamiliar situations and abstract numbers, students can't understand them as simple, familiar and intuitive, and they can easily solve them. That is to say, due to the limitation of life experience and thinking characteristics, first-year students prefer intuitive, familiar and simple learning content when learning mathematics. Teachers need to put forward clear mathematics learning goals and consciously guide students to establish the connection between life and mathematics. If teachers go against children's cognitive laws and do the opposite, students may have difficulty in understanding problems, fear of solving problems and lose interest in mathematics learning. According to the cognitive rules and thinking characteristics of first-year students, I want to cultivate students' problem-solving ability and develop their mathematical literacy from the aspects of mathematical speaking, mathematical operation and mathematical thinking.
Third, some strategies.
(A) Mathematics to speak
Chinese should cultivate students' language ability, so should mathematics. There are different ways to solve mathematical problems. To understand mathematical problems, students should not only understand the living mathematical language, but also mathematize the living language, explain it with mathematical concepts and laws, and express it with mathematical symbols. Therefore, it is very important to cultivate students' mathematical speaking ability to cultivate students' problem-solving ability.
1. Discover and tell mathematical information and problems in life.
Phenomenon 2, the teacher asked students to find that the setting of mathematics in life is better from the perspective of mathematics. If students learn every mathematics content, they will have such an opportunity to express their connection with life and mathematics, so that students can deeply feel the practicality and interest of mathematics learning and become interested in mathematics learning. At the same time, students pay more attention to mathematics in their lives, build more examples and representations, and be well informed, so as to better understand and solve mathematical problems.
In the understanding of numbers, teachers can let students talk about people, things and things around them with numbers; After learning the meaning of addition, let the students talk about what phenomena in life can be expressed by addition. After learning subtraction, let the students talk about what subtraction can represent in life. It can also help students to have a deeper understanding of the internal relationship between addition and subtraction from two aspects of addition and subtraction.
In their own lives, first-year students generally don't deliberately think about the math information around them, just know that there are several people at home and their mother bought some apples. At this time, teachers should reflect the guiding role and help students establish a broad understanding of mathematics in their lives. Teachers can guide students, besides fruit, what else can be expressed by numbers, or remind students with a specific example to open the door of students' thinking. Teachers can take themselves as an example and often give some examples to participate in students' discussions, guide students to open their minds in time, cultivate students' ability to observe life phenomena from the perspective of mathematics, and stimulate students' interest in learning mathematics.
2. Make up stories to understand the meaning of mathematical problems and formulas.
The arrangement of mathematics textbooks is not only to guide students to discover information in life, but also based on mathematics in life. The math problems of grade one are presented with situation diagrams or physical objects and graphics, and a small amount of words are described. When reading a topic, students often misread the meaning of the topic or pull out the information. Some teachers are afraid that the first-year students are too young to understand the topic, so they will say the meaning of the topic themselves and let the students solve the problem, so as to improve the correct rate of solving the problem. Doing so virtually deprives students of the opportunity to understand the meaning of the problem itself, which is easy for students to develop learning inertia and is not conducive to the cultivation of students' problem-solving ability.
In another case, students will calculate addition and subtraction, but they don't quite understand the practical significance of the operation. This is the case with Phenomenon 3. Students don't understand that subtraction is the inverse operation of addition, so they can't write two subtraction formulas correctly.
In mathematics learning, teachers should try their best to create opportunities for students to speak. The more students don't understand, the more they have to speak. For example, a scene map is a life story with a plot. Children's ability to read pictures is better than that of words. He will be happy to tell the story in the picture. What the teacher should do is to remind him to pay attention to the information of mathematics and learn to observe it carefully. Teachers can also let students join the life situation and make up math stories with physical and geometric figures. Students can use their own stories to tell the mathematical information and problems in the pictures, which shows students' understanding of the topic, which is convenient for students to further abstract the problems into mathematical formulas, and can also lay a good foundation for reading and understanding more complicated mathematical problems in the future. Such as phenomenon 3, such problems, teachers can make up stories for students, give the actual situation of graphics, and list the formulas of addition and subtraction according to the stories, so that students can deeply understand the internal relationship of addition and subtraction.
Formula is a high abstraction and generalization of mathematics in life. It is normal for first-year students to have difficulty in understanding, and understanding the meaning of addition and subtraction is related to students' later mathematics study. After students learn addition and subtraction, they must solve the problem of addition and subtraction. In order to further improve students' problem-solving ability, teachers should pay special attention to strengthening students' understanding of the meaning of formulas. Let the students make the mathematical formula into a mathematical story, and let the students understand the meaning and application of the formula again. Students restore abstract mathematical symbols into interesting life stories, which not only deeply feel the close relationship between life and mathematics, but also stimulate a strong interest in learning, so that students can establish vivid mathematical representations in their minds, understand the connotation of mathematical knowledge and enrich the extension of mathematical knowledge. When making up stories, teachers should guide students to tell the information of mathematics, and the simplicity that has nothing to do with mathematics should stop. For example, with the formula of 3+5, different students can make up math stories in different situations, such as "My mother gave me three sweets, my grandmother gave me five sweets, and now I have several sweets". But try to avoid detailed and specific information unrelated to mathematics, such as describing how sweet and delicious sugar is.
Mathematical activities
Mathematics Curriculum Standard emphasizes that students master basic knowledge and skills through mathematical activities, experience the process of knowledge formation in activities, and cultivate students' mathematical ability. The first-year students' abstract thinking level is low, and they are divorced from specific situations, so it is difficult to learn activity mathematics. Therefore, teachers should design more vivid, interesting and intuitive mathematical activities when learning "addition and subtraction of numbers within 10" and solving problems, so that students can improve their understanding and knowledge of mathematical problems through situational performance, action demonstration, learning tool operation and drawing comprehension, so as to improve their ability to solve problems.
1. Scene performance
Situational performance can reproduce students' life experience, let first-year students correctly understand the meaning of math problems and help them solve them correctly. On a line, Xiao Ming is left four and right five. How many people are there in this line? Students are likely to be regarded as nine people. If the teacher asks the students to actually count, it is easy for the students to understand that Xiao Ming has been counted twice by everyone, and one * * * is 8 people.
2. Action demonstration
Action demonstration is also a good way to enhance students' understanding of the problem. Many people with strong understanding and expression skills like to use gestures to enhance their language effect and make it easier for others to understand. The first-year students' mathematics learning is lively, interesting and lively, and they can express their thinking through gestures for many problems. For example, teachers can guide and encourage students to express life prototypes of addition and subtraction with gestures, such as: division, combination, coming, going and taking. If they can express clearly that students have a clear understanding of the meaning of the question, then it is simple to form formulas with symbols and numbers.
3. Learning tool operation
The operation characteristics of learning tools are intuitive, simple and easy to operate, which can help students establish simple ideas between mathematical information and problem solving. For example, the subtraction problem in textbook writing is basically to let students calculate formulas through graphics. Some students can't feel the changing process of quantity and don't understand the meaning of figures, so it's easy to list them as addition formulas. If the operation of drawing with learning tools shows dynamic changes, students will understand the meaning of subtraction more easily, and then guide students to look at pictures and understand the expression forms of pictures, which can initially help students learn to look at pictures, read questions and solve problems.
4. Drawing comprehension
Drawing simple sketches and line drawings is a good strategy for students to solve problems. But this problem-solving strategy should also be used by students from an early age, which will help to solve complex problems in the future. Teachers can guide students to use simple figures, such as triangles and circles, to replace people and things in the problem, draw the meaning of the topic, simplify the requirements of the topic, and help students learn to solve problems independently. When students' thinking in images gradually surpasses abstract thinking, teachers can also simplify graphics into line segments and teach students to draw and see line segments.
(3) Mathematical thinking
In the process of collecting and analyzing information and problems (including in life and books) and solving problems many times, students have accumulated rich mathematical experience and can talk and think about life and mathematics together. In the process of speaking and doing, students develop the ability to think about problems, and can analyze, summarize, reason and apply them preliminarily.
Every time students analyze information and solve problems, teachers should emphasize that students speak their own ideas, so that students can draw quantitative relations about simple and specific addition and subtraction problems, such as: the number of boys+the number of girls = the total, the number of red flowers+the number of white flowers = the total number of flowers, and so on.
After students have rich feelings about the cases of additive quantitative relations, teachers guide students to think about the similarity of these quantitative relations, so that students can obtain a simpler and more general quantitative relationship model through observation and thinking: "number of parts+number of parts = total".
Finally, aiming at similar problems in life, the quantitative relationship model is used to verify the quantitative relationship and problem-solving methods. Then, through the variant application of this quantitative relationship model, the structural migration of quantitative relationship is realized.
The problem-solving process of students is such a cyclical process. In this process, teachers guide students to think and learn to think, which is the greatest progress of students. Only when students learn to think can they learn to solve problems independently and improve their ability to solve problems.
The primary school stage is the basic stage for students to cultivate their abilities and habits. Mathematics, a coherent and systematic subject, must lay a good foundation from grade one. Problem-solving ability is the basic skill of primary school mathematics learning and future study life. As a math teacher, I will continue to think and practice the cultivation of problem-solving ability in the next grade one teaching.