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在一次课外辅导活动中,我采用自主、合作、探究的方式,讲了一道初中数学竞赛练习题,通过探索、合作研究,把思路开拓出来, 不是把某种方法甚至绝妙的方法简单地告知学生,而是展示求证的过程,收到了良好的效果．现将题目展示如下．题目已知:a、b、c、d、m、n、p、q都是正数,且a+m=b+ n=c+p=d+d=1．求证:aq+bm+cn+dp<2．这是一道证明题,求证的结论非常明确,只要以结论为目标去努力．从求证的结构看,首先要把a与q粘在一起,出现aq项;b与 m粘在一起,出现bm项;c与n粘在一起,出现cn项;d与p粘
In an extracurricular tutoring activity, I used the methods of autonomy, cooperation, and inquiry to talk about a mathematics exercise in junior high school. Through exploration and collaborative research, I developed ideas and did not simply inform students of a method or even a wonderful method. Instead, it demonstrated the process of verification and received good results. The topic is shown below. The topic is known: a, b, c, d, m, n, p, q are all positive numbers, and a+m=b+n=c+p=d+d=1. Proof: aq+bm+cn+dp<2. This is a proving question, and the conclusion of confirmation is very clear, as long as the goal is to work hard. From the structure of verification, we must first stick a and q together, and then we have the aq term; b and m will stick together and the bm term will appear; c and n will stick together and the cn term will appear; d and p will stick together.