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至今,我还记得在初中第一次上代数课时老师讲的第一句话:“代数,代数,就是用字母代表数”。直到大学,老师给我们讲解代数的定义时,才觉得这句话是极不正确的。然而,在怀着极大的好奇心进入初中的学生心里,它却留下了深刻的印象。至少,它说明了代数比算术更为抽象。每个中学生都要经历从算术到代数的飞跃,从正数到负数的扩展,而且总是不那么容易。所以我们常常给初中生提这样的问题:“-a是负数吗?”由于引进负数概念时,课本上是“用以前学过的数”的前面放上“+”“-”号来定义正负数——“带有负号的数叫做负数”,不少学生总是习惯的认为a表示正数,“-a”表示负数。因此,我们要反复强调:“当a<0时,a表示负数”。提醒学生要特别注意这种“看不见负号的负数”。
So far, I still remember the first sentence of the teacher’s first time in junior high school for the first generation of mathematics: “Algebra, algebraic, is to use letters to represent numbers.” Until the university, when the teacher explained the definition of algebra to us, he did not think this sentence was extremely accurate. However, in the hearts of students who entered the junior high school with great curiosity, it left a deep impression. At the very least, it shows that algebra is more abstract than arithmetic. Each middle school student experiences a leap from mathematics to algebra, an expansion from positive to negative, and it is not always easy. Therefore, we often ask the junior high school students the question: “-a is a negative number?” Since the concept of negative numbers was introduced, textbooks were preceded by the “+” and “-” signs to define positive numbers. Negative numbers - “negative numbers are called negative numbers.” Many students are used to thinking that a is a positive number and “-a” is a negative number. Therefore, we must repeatedly emphasize: “When a <0, a represents a negative number.” Remind students to pay special attention to this “negative negative sign.”