Stiffness is the basic feature of mathematics class, and rigor of thinking is one of the keys to learning mathematics well. The imprecise thinking of questioners often appears among teachers, which directly affects students' math scores. For example, at the end of the first semester of a school year, there is such a judgment question on the sixth grade math test paper: "A's 1/3 equals B's 1/4, then B is greater than A."

Judging from the reference answer, the questioner thinks it is necessary to tick "√". I think the questioner's original intention is on the premise that "A and B are both positive numbers". At this time, a×1/3 = b×1/4 → a/3 = b/4 → a: b = 3: 4 → b number is greater than a number. However, if there is no premise that "both a number and b number are positive numbers", we should consider:

1. When the number A and the number B are both zero, it should be considered under the knowledge system that primary school students have already learned. At this time, the number a is equal to the number B.

2. If we consider that numbers A and B are both negative, although primary school students haven't learned them yet, they learned them as soon as they entered junior high school. At this time, the number of B should be less than the number of A. For example, if the number of A is -3 and the number of B is -4, there will be (-3) x 1/3 = (-4) x 1/4, but-3 >; -4。

To sum up, as far as the original proposition is concerned, the conclusion should be divided into three situations:

1. When numbers A and B are both positive numbers, number A is less than number B. ..

2. When both numbers A and B are zero, number A equals number B. ..

3. When both numbers A and B are negative, number A is greater than number B. ..

Therefore, I personally think that the original question is a proposition that lacks a major premise. As a judgment question, mark "×".

Some people may think that students who have never studied negative numbers can tick "√". I don't think this is reasonable. First, primary school students have learned zero and know that natural numbers and zero are both parts of integers. For students with rigorous thinking, pay attention to the fact that when the numbers A and B are all zero, the original proposition is false. Secondly, primary school students will encounter this problem when they enter junior high school. At that time, he will find that when the number A and the number B are both negative, the original proposition is also a false proposition, and he will also realize that the original knowledge of primary school and junior high school is not contradictory, and the knowledge system contains richer and more complete content.

There are countless such examples, and you will see more in middle school. As long as we are serious and responsible for students in teaching, we should always pay attention to cultivating students' comprehensive and complete habit of thinking, so that students can gradually develop the characteristics of rigorous thinking.