Tuesday, August 28, 2012

Advice Needed

Ok, I'm in desperate need of some advice.  The last 3 years I have taught Geometry in this order:
1.  Logic
2.  Pts, lines and planes
3.  Angles, parallel lines with transversals
4.  Triangles

While I am happy with the logic materials I have put together, the math blogosphere has shown me that I could do a much better job with it.  I thought that by moving Logic to after Triangles (and before proofs) that I could have more geometric context for logic and utilize sentences that use geometry instead of the nonsense sentences I use now.  Yesterday I rearranged my first month of lessons and was thinking to myself, "self, you're doing a good thing!"  However, one of my colleagues pointed out that in the Triangle unit, we teach the Pythagorean Theorem and its converse and that I need the kids to have logic first.  

My question(s) to you is:  In what order do you teach Geometry?  Is it imperative that the students see logic and its vocabulary before seeing the Converse of the Pythagorean Theorem?  (or will they survive just fine without that context?)

Thank you in advance for your feedback.

2 comments:

  1. Hey, sorry that you haven't received any feedback yet, especially when asking for it so specifically. I'm a new blogger myself, and I've been trying like crazy to at least glance at *every* new blog to see if it might be worth subscribing to. Well, now I've made it to yours. :-)

    I teach the CPM curriculum, and one thing they do which I really like is have the first week be five different "big problems" that introduce the students to some of the Big Ideas they are going to see throughout the course. The fourth lesson in the book is about logical arguments, but it is again just an intro to the idea. It is revisited in little pieces here and there, but the first time they really go into it is in Ch. 3, Justification and Similarity. And guess what topic we just finished, at the end of Ch. 2? The Pythagorean Theorem.

    So. To the extent that I can, I give you permission to teach Logic after Pythagoras.

    That said, I really like some of the "nonsense" things you can do with logic, without any "math". Here's an idea my colleague Ms. W. taught me:

    Write a simple, sequential story about something that might matter to your students, such as the day they went shopping to buy a new phone. Type each sentence on its own line (or lines), cut them out, and have partners or groups try to put them in the correct order. You could have them write something brief to justify the positions they came up with, or have a group present theirs and have the class (respectfully) critique their choices. And if there are parts to the story which didn't have to happen in an exact order, that can be a good source of discussion too. (Just make sure most of it has to be sequential.) This can be a nice introductory lesson to logic, or a stand-alone activity (for a Friday, say) if you want your students to have a little sense of logic without going into it deeply (yet).

    I hope any of that is helpful, food for thought if nothing else.

    I am *only* teaching Geometry this year (the first time that's happened in my 19-year career), so if you want to talk more specifics you can get my contact info at my blog itsallmath.wordpress.com under "About the Author".

    (Wasn't that sly, how I tried to make you check out my blog?)

    Good luck!

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    1. Steve, Thank you so much for your feedback! I did finally decide to teach logic after my triangle unit and will probably still use many of my nonsense sentences, just wanted the option to be able to connect it back to mathematics they have already used.

      It is so tough getting through all the new blogs--thankfully we don't start school until next week, so I have had time to stay on top of the blogs daily and am sifting through the ones that I will stay subscribed to.

      Thank you again!

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