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一、重视反例的作用。学生初学平几,在分析论证过程中,常会主观臆断,推理缺乏根据。教师可以抓住时机,诱发一些毛病,引起学生重视。例1、P是△ABC内任意一点。求证(1)∠BPC>∠A; (2)AB+AC>PB+PC。先用三角板上的直角在图上摆弄一下,再用直尺对AB、PB、AC、PC顺次指一下,学生受到“启发”,就会这样回答: ∵∠BPC是钝角,∠A是锐角, ∴∠BPC>∠A。∵AB>PB,AC>PC,∴AB+AC>PB+PC。接着让学生议论、辨析,这样论证有无根据。然后指出造成错误的原因。这样学生就会少犯主观、
First, pay attention to the role of counter-examples. Students beginners a few, in the process of analysis and argument, often subjective assumptions, reasoning lack of basis. Teachers can seize the opportunity to induce some problems, causing students attention. Example 1, P is any point within △ ABC. Prove (1) ∠BPC> ∠A; (2) AB + AC> PB + PC. First with the right angle on the board on the map fiddle with, then ruler on the AB, PB, AC, PC in turn refers to the students are “inspired”, it will answer: ∵∠ BPC is obtuse, ∠A is acute , ∴∠BPC> ∠A. ∵AB> PB, AC> PC, ∴AB + AC> PB + PC. Then let the students talk about, discrimination, so there is no argument. Then pointed out the cause of the error. Such students will make less subjective,