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在数学教学中常常听到学生这样的反映:“课堂上都能听懂,就是不会做题。”造成这种状况的一个重要原因是在课堂教学中,教师往往只讲怎样做,不讲为什么这样做,更不讲为什么会想到这样做。因此要求教师不仅要赐人以鱼”,更要“诲人以渔”,使学生不只是停留在解题过程和方法上的模仿,还要进而过渡到对思维的模仿,最后达到能进行创造性的思维活动。这就需要我们平时讲课中竭力避免直接灌入,尽量提出问题,启发学生积极思维,使学生自己独立思考问题,对学生进行分析问题、解决问题的能力的培养。例如球的体积公式,现行六年制重点中学高中数学课本《立体几何》P119上是这样写的:“和柱体、维体一样,也可以应用祖日恒原理推出球体的体积公式”,我们取一个底面半径和高都等于R的圆柱,从圆柱中挖去一个以圆柱的上底面为底面,下底面圆心为顶点的圆锥……”(在五年制的统编教材中,则更是直接地把结果和证法端出来)。相应的教学参考书上介绍了
In mathematics teaching, students often hear this kind of reflection: “Classrooms can understand and do not do questions.” An important reason for this situation is that in classroom teaching, teachers often only talk about what to do, do not speak Why not do it, and why not think about it? Therefore, teachers are required not only to give people fish, but also to “get people to fish”, so that students do not only stay in the process of imitating the problem-solving process and methods, but also then transit to imitating the thinking, and finally achieve creativity. This requires us to try to avoid direct infusion, try to ask questions, inspire students to think positively, make students think independently of issues, and develop students’ ability to analyze problems and solve problems, such as the volume of the ball. The formula, the current six-year key middle school high school mathematics textbook “Three-Dimensional Geometry” P119 is written as follows: “And the cylinder, the same body, you can also apply the Zu Riheng principle to launch the volume formula of the sphere”, we take a radius of the bottom Both the height and the height are equal to R’s cylinder. From the cylinder, a circular one with the bottom of the cylinder as the bottom and the bottom with the center as the apex of the cone..." (In the five-year textbook, it is more direct result And proofs come out). The corresponding teaching reference book introduced