It is not a bad thing to be controversial, and the common purpose is to strive for excellence and improve the quality of education.
Another mathematical problem spread across the web. Recently, Mr. Liu, who lives in the Jiang'an District of Wuhan City, Hubei Province, encountered trouble when tutoring his granddaughter in the second grade of primary school: the cat mother caught some fish, and gave an average of 7 kittens, and each kitten got just as many fish as the remaining fish. How many fish did the mother cat catch?
Mr. Liu said that the standard answer to the question in the textbook is 48, but he feels that there are no restrictions mentioned in the question, and any multiple of 8 can be used as an answer. For example, each kitten is divided into 8 fish, and the remaining fish are also 8, and the total number of fish is 64. In response to Mr. Liu's doubts, the Wuhan Municipal Education Bureau replied that this question mainly examines the students' understanding of the average score and the division with the remainder, and gives a detailed analysis.
Objectively speaking, there is actually nothing wrong with this question. Because such mathematical problems actually imply common sense of life and language logic. Since it is said that it is necessary to "divide the 7 kittens equally", it is to divide as much as possible until it can no longer be evenly distributed, and there is also the "premise that the remainder is not greater than the divisor".
This question, obviously, teaches the child the concept of multiplication and division and the remainder, but it also transmits life situations and logical thinking to the child.
In fact, to put it bluntly, this question is to test the concept of "the remainder is smaller than the divisor", if you say it directly, the "core" of the topic is equivalent to being removed, and it loses the significance of the investigation.
And if according to the standard of "not rigorous enough", as some netizens joked, "whose cat can fish", "whose cat can count", "why is it about a pound" and so on. In this way, many mathematical problems have problems, and there are too many restrictive factors that the proposition person needs to consider when making a mathematical problem, which is not conducive to the teaching of knowledge.
Of course, although the views are different, this grandfather's truth-seeking and rigorous appearance is still quite cute and worthy of praise. The Education Bureau's patient explanation and response also showed a rigorous and serious attitude towards each exercise in the textbook. This is the practice of the concept of "education is no small matter", and it is also the responsibility of educators.
In 2019, there was also a math problem that became popular, and the focus of the debate was "expanded by 2 times, is it 2 times or 3 times the original?" The book answer is 2 times, but many students understand it as 3 times. In this regard, the Ningbo Municipal Education Bureau of Zhejiang Province admitted that the main reason for the different understanding of this problem is that the teacher's language expression in the proposition is not accurate enough, and said that it will pay more attention in the future, and also encourages children to continue to study and think.
Looking back at these controversial mathematical problems, the problem is not precisely in mathematical science, but has become a language problem. This also reflects the essential differences between mathematics and language, as well as the closeness of the two disciplines.
As the saying goes, reason is not clear, controversy is not a bad thing, the common purpose is to strive for excellence, to improve the quality of education. Whether it is for the author of the question, or the compilation and review of the textbook, the energy and testing ability are certainly limited, so it is necessary to introduce "public supervision", nothing more than to do a good job of "if there is a change, if there is no encouragement". Similar interesting and beneficial interactions can often be had.
Red Star News special commentator Fan Cheng
Edited by Yin Shuguang
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