Thread

1. ForgotMyUUID · 1789802300 · focus · HN ↗

   I’m reminded of that famous debate between Poincaré and Hilbert at the International Congress of Mathematicians in Paris in 1900. It was then that everyone decided to follow Hilbert’s path, and proof came to be valued more than intuition. I think modern math at school and at applied university kind of lost this intuitive part.

   I try to teach my students that mathematics is, first and foremost, a very precise language of communication. It’s sometimes amusing to ask those who don’t like math to do without it entirely, just to see how much harder it becomes to describe the things around them.

   Second thing I tell them, formulas are the essence of mechanisms in their purest form. And in this form, they’re much easier to grasp and mentally manipulate. It always amused me, after taking a mechanics course, to imagine that for any formula, you could visualize a mechanism or process that implements it.

   And third thing, I suppose, the ability to verify one’s own statements as proof. Although, of course, mathematicians would probably tear me apart here for my heresy:sorry, I’m not a mathematician, but an engineer. You can make mistakes by using incorrect assumptions, but at some point, analysis itself will show you that you were mistaken. There’s a wonderful book, How to Prove It by Daniel Velleman, which provides an introduction to proof for the uninitiated like me. I really enjoyed it.

   1. Geof25 · 1789804528 · focus · HN ↗

      People often hate math because it was not explained to them correctly, usually by people who are good mathematicians but know close to nothing about teaching.

      It was so infuriating to see everyone in the class absolutely fail on a specific subject and the "teacher" assumed that everyone must be stupid then. No self reflection, no questioning himself why he is not getting gaussian distribution in marks, just straight Fs.

      1. partyficial · 1789805145 · focus · HN ↗

         a good teacher remembers the journey, not just the destination.

         socratic method exists. almost none follows it.

         1. awesome_dude · 1789806590 · focus · HN ↗

            >socratic method exists. almost none follows it.

            I have a hatred for people who think they can use this method.

            If used incorrectly which it is a great percentage of the time it confuses the student. The person employing the socratic method must actually know the answer and where the student is in their mind. Failure on either account makes it pointless.

            Ask anyone unfortunate enough to ask for help on IRC

            1. Kim_Bruning · 1789810899 · focus · HN ↗

               I sometimes ask more questions than utter new things when trying to explain something.

               But that's because I'm trying to focus down and determine exactly where they're at before I just randomly make things worse by accident :-P.

               I'm not sure if that's the actual socratic method. But people accuse me of using it. Either way, it does seem to work for me.

            2. bananaflag · 1789819038 · focus · HN ↗

               > The person employing the socratic method must actually know the answer and where the student is in their mind.

               The socratic method also has a much higher chance of revealing where the student is in their mind.

         2. moffkalast · 1789815116 · focus · HN ↗

            That only works if the one you're trying to guide can figure it out mostly on their own and is interested in cooperating. Aka does not work for anything below university level.

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