-Reading Notes on How to Teach Math Well in Primary Schools 1

I believe that teachers who have taught first-grade mathematics must have encountered the following situations.

There are some swans on the lake. Five of them flew away, and there were eight left. How many swans are there on the lake?

The formula for children is: 13-5=8 (only)

There used to be 13 swans on the lake.

Is it right or wrong for children to do this? The front-line teachers are controversial about this solution. It can be said that most teachers' solutions to children are wrong. The reason is that to write the unknown number on the right side of the equal sign, the formula must be 5+8= 13 (only) to be correct. However, for a while, many children just liked to use 13-5=8. Teachers keep correcting mistakes, and sometimes they even get particularly angry. The child finally corrected under the teacher's anger.

Why is this happening? Professor Gao Shuzhu became interested in this phenomenon. He thought, "What caused this phenomenon? Is there a certain cognitive law of children behind this phenomenon? "

Children's cognitive law has three stages: the first is information perception, the second is information processing, and the third is the output of perception and processing results. The third stage is the result of perception and processing. If there is an error in the final output result of the child in the above problems, then the problem must be in the two stages of perception and processing.

There are some swans on the lake. Five of them have flown away, and there are eight left. Children naturally form a problem structure of □-5=8 in the order of things. Because the number is relatively small and the calculation is not complicated, children can easily work out that the number in □ is 13. Therefore, there will be no other processing activities in their minds, and the formulas will be listed directly in the order of things. There have also been articles that show that the human brain has a kind of inertia, and when it thinks it meets the needs of solving problems, it will avoid further thinking. )

This "□-5=8" perceived in natural order is the natural structure of the problem, which is most suitable for children's realistic thinking. Gu, children like it very much. The first priority of teaching is to conform to children's thinking. The teacher's expectation of 5+8=□ is called the processing structure of the problem. To achieve this structure, some processing and transformation are needed. Therefore, teachers should not only understand the processing structure of the problem, but also understand the natural structure that children may be more adapted to. When teachers have this understanding, they can better guide children to change from natural structure to processing structure. ...

So, is the child's formula right or wrong? Right or wrong, can you make it clear?

In this book, Professor Gao Shuzhu mentioned that it is logical for children to put the previously unknown 13 swan directly on the left, and draw an equivalence relationship by using the development order of things (original initial swan number-swan number flying away = remaining swan number). But the relationship between the number of swans flying away and the number of swans left behind = the original swan and the number of children required by the teacher is consistent. These two quantitative relations can be transformed into each other. In a broader sense, the focus of studying a problem should be the quantitative relationship, which has different expressions. No matter what expression is used, the position of "unknown number" and "known number" is the same. Putting it in an unknown location is not the most important thing. As long as the number of children is appropriate, we should think that the children are doing the right thing. As for the unknown number, the statement that the calculated number must be placed on the right side of the equal sign can only be regarded as a customary habit at most, and it cannot be a criterion for judging right or wrong.