My two cents on mathematical proof

I don't think proof is necessary for math in primary or middle school (may be high school should have a few) for the following reasons:

1. In real life, at work, there is very little use of mathematical proofs.  Even in scientific research, the so called proofs are defined as preponderance evidence and elimination of false arguments. 

2. Finding answers is a more important skill than rigorous proofs.  Estimation, inventing ways to calculate are more important skills than proving in practice.

3. For improving thinking skills, proving mathematical thereoms requires demonstrating an answer given by others.  It encourages rationalization rather than finding out truth.  It encourages being passively pushed by others than active pursuit.

4. For education in mathematics, finding an answer and later justify and make sure the answer is right itself involves proof.  I'd say finding and justifying answers requires more complete skills than proving.

5. Again, for education in mathematics itself, understanding the importance of mathematical problems, keeping the curiosity of exploring mathematics as a subject is more important than proving.  Even Euler sometimes was not that rigorous in proofs.

6. I am not saying rigorous proof is not important.  But it mainly belongs to a chosen few, who really requires such skills.

所有跟帖： 

• 全盘接受。 -soundofsilence- ♀ (0 bytes) () 01/15/2015 postreply 13:00:53

• 你说了 -时间呢- ♀ (21 bytes) () 01/15/2015 postreply 13:13:02

• 这个是 -soundofsilence- ♀ (9 bytes) () 01/15/2015 postreply 13:45:45

• 好像是这意思 -自由落体- ♀ (0 bytes) () 01/15/2015 postreply 13:02:56

• 就是思维训练了。其实学数学也是思维训练。除了四则运算，其他以后基本都用不着 -monochrome- ♀ (0 bytes) () 01/15/2015 postreply 13:05:05

• 就是，从来没用过微积分，但现在中学都学。如果从将来用的角度讲，80%的人高中科学全都可以不学的：） --百科-- ♀ (0 bytes) () 01/15/2015 postreply 13:12:58

• As stated in OP, problem solving requires more complete skills -SwiperTheFox- ♂ (0 bytes) () 01/15/2015 postreply 13:16:11

• Complicated skills contain many small steps of proofs. -trivial- ♀ (316 bytes) () 01/15/2015 postreply 13:25:16

• My answers: -SwiperTheFox- ♂ (1173 bytes) () 01/15/2015 postreply 13:32:53

• It seems that we have totally different understanding of what is -trivial- ♀ (100 bytes) () 01/15/2015 postreply 13:40:18

• 不明点赞又是俺哈 ：））） -msrbcm- ♀ (0 bytes) () 01/15/2015 postreply 13:18:33

• 点赞 to you too:) -SwiperTheFox- ♂ (0 bytes) () 01/15/2015 postreply 13:23:30

• Even though you don't think proofs are necessary, -trivial- ♀ (160 bytes) () 01/15/2015 postreply 13:19:52

• I wouldn't consider it (mathematical) proof :) -SwiperTheFox- ♂ (306 bytes) () 01/15/2015 postreply 13:22:45

• It is an analog. -trivial- ♀ (191 bytes) () 01/15/2015 postreply 13:28:11

• BTW, provided that you can find out the answer without any proof -trivial- ♀ (0 bytes) () 01/15/2015 postreply 13:29:34

• Re :) -SwiperTheFox- ♂ (380 bytes) () 01/15/2015 postreply 13:37:02

• What is OP? -trivial- ♀ (0 bytes) () 01/15/2015 postreply 13:41:15

• Original Post -SwiperTheFox- ♂ (0 bytes) () 01/15/2015 postreply 13:42:55

• 说得好。定理证明是很枯燥的事，更多是属于哲学的范畴。远不如应用数学有趣。太早搞证明提题弄不好会把数学兴趣灭掉。 -飞*星- ♂ (0 bytes) () 01/15/2015 postreply 13:24:50

• 同意，应用题更能加深理解和提高解决问题的能力 -jujubug- ♀ (0 bytes) () 01/15/2015 postreply 13:28:54

• 过早做应用题有自己的问题，其实也很大，另外再说。 --百科-- ♀ (0 bytes) () 01/15/2015 postreply 13:44:36

• 好，且听下回 -jujubug- ♀ (89 bytes) () 01/15/2015 postreply 14:09:24

• agree! -jujubug- ♀ (0 bytes) () 01/15/2015 postreply 13:27:56