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记得2009年中考复习时遇到这样一道题目:如图1,在边长为2cm的正方形ABCD中,点Q为BC边的中点,点P为对角线AC上一动点,连接PB、PQ,则△PBQ周长的最小值为_____cm当时全班能做对的不到10个人.面对如此惨的境况,我意识到了在新授课《轴对称的应用——输气管最短问题》教学中的不足:先让学生通过阅读课本并知道“在管道L上找到泵点C,使AC+BC最小”点C的找法,接着在老师的带领下按课本提供的证明方法重新证明了一遍,看学生的表情似乎认同了上述找法的合理性,至此我认为新知学习到此结束,最后就进入第二个活动——新知运用、变式训练.现在想来,这种粗放式的数学学习活动根本就触及不到数学本质的学
I remember in the 2009 exam review encounter such a problem: Figure 1, in the side length of 2cm square ABCD, the point Q is the BC edge of the middle, the point P is the diagonal AC on a moving point, connecting PB, PQ , Then △ PBQ circumference of the smallest _____cm class was able to do when the right to less than 10. Faced with such a tragic situation, I realized that the new teaching “axisymmetric applications - the shortest pipe problems” teaching Insufficient: first let the students read the textbook and know “find the pump C on the pipe L, AC + BC minimum ” point C to find, and then under the guidance of the teacher to prove the method provided by the textbook to prove Again, look at the students’ facial expressions seems to agree with the reasonableness of the above method, so I think the new knowledge to learn this end, and finally entered the second activity - the use of new knowledge, variant training now want to come, this extensive Mathematics learning activities simply can not touch the mathematical nature of science