tag:blogger.com,1999:blog-1075593398139537131.post3347077891835694937..comments2023-09-21T01:38:02.574-07:00Comments on Without Geometry, Life is Pointless: Proof Doesn't Begin with Geometry: The Life Cycle of a Math ProblemAvery Pickfordhttp://www.blogger.com/profile/10433339146333801163noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-1075593398139537131.post-9752779166125387962014-09-01T12:28:50.099-07:002014-09-01T12:28:50.099-07:00Very interesting, I never really considered the ac...Very interesting, I never really considered the actual thought processes that were involved in solving a problem, especially when it comes to proofs and finding to solutions to open problems. I personally have worked on the perfect cuboid problem for some time and I'm still stuck somewhere between wild guess and educated guess lol. I've been a mathematics tutor for about 10 years, maybe this will give me some insight on teaching students new concepts. I've recently branched out into the web, hoping to reach a larger audience.<br /><br /><a href="http://mindonmath.blogspot.com/" rel="nofollow">Mind on Math Blog - Education, Philosophy, and the Joy of Mathematics</a>Richardhttps://www.blogger.com/profile/15696695771238819419noreply@blogger.comtag:blogger.com,1999:blog-1075593398139537131.post-57711927529014721952013-11-12T10:17:56.906-08:002013-11-12T10:17:56.906-08:00This is fantastic stuff. Definitely gets me think...This is fantastic stuff. Definitely gets me thinking. I have a few thoughts and questions for you:<br /><br />Immediately<br />What about situations like my sinkhole problem? (http://robertkaplinsky.com/work/sink-hole/). When I ask them for guess immediately before we have given dimensions or units, the guesses seem all over the place and not very useful. That being said, in other situations where I am asking for a price, it seems much more worthwhile. Am I missing something?<br /><br />Individually<br />This is a great paragraph. I have done class guesses, group guesses, and individual guesses. Anecdotally, it seemed like individual guesses were best but this make a strong case for sticking with it.<br /><br />Bounding<br />Do you do bounding AND estimating? For example, first have them give their best guess, and then do upper and lower bounds? Do you have all of this done individually? Certainly students have more time for this than "immediately", right?<br /><br />Each of these posts is making me wish even more that I could have also been at your session.Robert Kaplinskyhttps://www.blogger.com/profile/12730219834465583755noreply@blogger.com