Breaking through the bottleneck of algorithm and simple calculation teaching: genetic bottleneck effect

In the second volume of Mathematics for Grade Four published by People's Education Publishing House, the algorithm and simple operation are presented as an independent chapter. The five algorithms of addition, subtraction, multiplication and division occupy an important position in mathematics and are known as "the cornerstone of the mathematics building". Simple calculation is an important means to train students' thinking and one of the main ways to cultivate students' sense of numbers. The requirement of "Mathematics Curriculum Standard" is to "explore and understand the operation law, and use the operation law to perform simple operations".

In classroom teaching, we often encounter the embarrassing situation that students make many calculation mistakes and teachers are helpless in the face of students' mistakes. Every teacher can clearly realize that there is only one reason for this situation: students' understanding of the operation law is not deep enough. The problem that has been bothering everyone is that we have found the problem, but we can't start. How to help students deeply understand the law of operation has become the bottleneck of teaching. After classroom tracking and reflection, the author thinks that to break through this bottleneck, teachers need to establish a strategic position and grasp the teaching materials from a macro perspective.

First of all, we should establish the concept of big mathematics.

Our teacher must first find out what is the purpose of learning algorithms. Judging from the superficial phenomenon in some parts of the textbook, learning the algorithm seems to be preparing for simple calculation. Therefore, most of our teachers only see the function of the algorithm in simple calculation in isolation, and think that learning the algorithm is for simple calculation, which limits teachers and students to a narrow and closed area and lacks comprehensive and systematic knowledge. In this way, the goal of exploring and understanding the law of operation in teaching often passes by. Make students practice mechanically without knowing the operation rules. In such a classroom, how can students flexibly use the algorithm to perform simple operations?

We need to look at the operation law from a macro perspective. After the definition of operation is given, the most important basic work is to study the properties of operation. Among the various properties of operation, the most basic one is usually called "algorithm". Operation law is a universal law in operation system, which can be used as the basis of reasoning. For example, prove other properties of the operation according to the algorithm, and prove the correctness of the algorithm according to the algorithm and properties.

Second, we should establish the teaching concept of big computing.

In classroom practice, we often meet students who use arithmetic laws to "simply calculate" some difficult problems. The reason is that teachers only organize teaching around simple operations, especially the tips of "calculating the following problems with simple methods" and "calculating as simply as possible" strengthen students' simple mechanical consciousness. When facing a problem, students do not analyze the problem carefully, but try their best to do simple calculations.

In order to solve this problem, teachers must establish the teaching concept of big computing, and can't talk about simple computing without computing teaching. After students master the algorithm and apply it to simple calculation, they should be integrated into the background of operation in time. We can present the complex exercises that can't be simple with the algorithm, and we can also present the simple exercises.

Third, we should have the awareness of communication and knowledge connection.

Arithmetic and simple arithmetic unit only present students with an essential and concise model, and the function of this model is to find a mathematical basis for his previous algorithm.

From the lower grades, I began to learn four operations of addition, subtraction, multiplication and division, and the operation rules can be seen everywhere. For example, ① learning addition: students know where to exchange two addends, and the sum remains the same. -additive commutative law. (2) When learning multiplication, add five twos, which can be listed as 5×2 or 2×5, and the product is unchanged. -Multiplicative commutative law. Another example is the example of buying bread in Unit 1 of the second volume of Grade Two: "I made 54 loaves, we bought 22 loaves, and we bought 8 loaves. How many pieces of bread are left? " Formula: 54-22-8 54-(22+8). -Simple addition and subtraction. (4) Book 2 of Grade 3: Each phalanx has 8 rows, each row has 10 people, and how many people are there in the three phalanxes? -the law of multiplicative association.

It seems that students' learning of algorithms does not start from scratch. Students' brains are rich in perceptual materials. If teachers can help students communicate the connection between old and new knowledge and activate students' existing learning experience and knowledge reserve, then the problem that students can't deeply understand the operation law can be solved. For example, it is easy for students to confuse multiplicative associative law and multiplicative distributive law. Many students will make this mistake: (4×8)×25=4×25+8×25.

Of course, we should predict such mistakes before class. In the new class, teachers can contact the definition of multiplication to help students understand. The definition of (4×8)×25 slave multiplication is 32 25s, which is not equal to 4 25s plus 8 25s. And it can be compared with (4+8)×25, so that students can understand the multiplicative associative law and the multiplicative distributive law in essence and will not be confused by appearances.

Furthermore, once students have established the relationship between the multiplication law and the definition of multiplication in their minds, such a difficult problem can be easily understood and transformed if 38×99+38 is 100 38s and 38×99 is (100- 1) 38s.

Fourth, we should have the consciousness of providing colorful life scenes for abstract and boring operation rules.

Limited by the cognitive characteristics of primary school students, the study of abstract and boring operation rules needs rich visual materials to support it. At the same time, the characteristics of mathematics also need to abstract and summarize the perceived image materials. In the textbook, all the algorithms are placed in the familiar life situations of students. For example, in the study of multiplication and division, you can add such a situation: each piece is matched with 25 yuan, and each piece is matched with 20 yuan. How much are eight suits? In the simple operation of addition and subtraction, we can once again present the example of buying bread in Unit 1 of the second volume of Grade Two: "I made 54 loaves, we bought 22 loaves, we bought 8 loaves, how many are left?" ……

Our teachers should provide students with typical and familiar materials, so that students can explore and understand the laws of operation independently. Then students will not get those cold conclusions and fancy skills, they will get many valuable mathematical thinking methods and learning experiences, they will get the improvement of thinking ability and positive and happy emotional experience.

In short, in the context of the new curriculum, we need to have a broad vision, a sense of changing the teaching mindset, accept dialectical teaching concepts and broaden our thinking space, so that students' dialectical thinking can be effectively activated, students' thinking can be "alive" and classroom teaching can be dynamic and creative.