Why Do We Have To Learn This?

No one is sitting in 9th grade English class asking their teacher, “why do we have to learn how to read and write?” (or maybe someone is…I actually wouldn’t be that surprised) But anyway math teachers have to field this question on almost a daily basis. And nothing gets questioned more than the dreaded Geometry Proof. why do we have to learn proofs? Waaaaaahhhhhh
I’m thinking I don’t really want to be teaching proofs any more than you want to be learning them. But what comes out of my mouth is usually something along these lines:

{1} the idea of learning and using a whole new system of rules can be applied to any number of situations
{2} completing something like a mathematical proof shows that you can pay attention to detail and proceed in a logical step by step manner which is totally necessary in the fields of computer programming, engineering, architecture
{3} proofs are included in the set of learning standards in this course as set forth by NYS & there’s gonna be a proof on the regents exam so write your congressman if you’d like to complain about it

{others???} I know there are many more good answers to this question and this question’s evil twin, “when are we ever going to use this?”
Thoughts?

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4 responses to “Why Do We Have To Learn This?”

  1. Scott Keltner says :

    If students have a curious question about how (true examples they’ve thrown at me, mid-lecture) 1080p television resolution compares with 720p resolution to the trained eye, what reaction time difference resulted when aluminum bats in baseball were required to be BB-COR certified, how does a GPS signal actually find me, and many others. I have them written on a certain area of my dry-erase board to remind me to find answers, because students are curious about it and I try as hard as possible not to dismiss their curiosity, because some days that’s all they bring.

    I like to think geometric proofs allow students to fit some organized structure to creating a compelling argument, or conclusion. They wouldn’t just show up in court to dispute a speeding ticket with the defense of “I wasn’t going that fast, really” or “The cop should have pulled over the guy who passed me a mile earlier” as their crutch. I would hope they would more carefully plan the steps necessary to having the ticket dropped. I apologize for the sketchy analogy, but I think a court case offers up so many tie-ins to making a defense for an argument, which is one of the critical components I see in geometric proofs–defending each step of the process and justifying those steps based on previous, similar circumstances.

    Maybe try my idea for a week: if a student has a genuinely perplexing question, write it on the board and seek out a resolution to it. I just did a blog post on UPC/barcodes based on my own curiosity of how they worked, but it armed me with a wealth of knowledge when a student happened to ask about it last spring. That post is available here:

    http://scottkeltner.weebly.com/1/post/2012/09/remainders-not-just-the-rest-of-the-story.html

    Pardon the “Top Gun” references. It sets the scene well when talking about remainders to refer to military time, though.

    • kjgolick says :

      Hi Scott. I LOVE that idea! A lot of times, when students ask questions that may be off topic, if it’s simple enough to answer by doing a Google search, I’ll stop class right there & we’ll investigate it together. But the more complex questions like television resolution and UPC codes…those would definitely take a little research. Sounds like your students ask some really awesome questions!

  2. Adam Chawansky says :

    Hi there. If you hadn’t heard about Harold Fawcett, he led an extraordinary geometry course more than half a century ago. What did he do exactly? Check out this link for some information:

    http://www.cut-the-knot.org/ctk/NatureOfProof.shtml

    The most important point in the description, for me, was the idea of transfer. Students weren’t just memorizing definitions and proofs created by Greeks over two millennia ago. They were utilizing the IDEA of precise definitions as axiomatic constructions to reach logically sound deductions. And they were doing it without any formal geometry at all!

    The real point to mathematics (aside from the fact that it’s absolutely critical for anyone in a scientific or technical job), is that it helps us make sense of the world around us using the power of abstraction and generalization.

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