Tuesday, March 6, 2012

Common Core Mathematical Practices

I spent two days last week at a conference led by our county ESC entitled Focusing on the Mathematical Practices of the Common Core Grades 9 - 12. Honestly, a lot of the reason I try to go to different seminars is just to get out of the building and shake up my schedule a bit.  It's hard to prepare for 2 days of a substitute, but changing the routine is sometimes worth it.

I was surprised by how much I enjoyed my two days.  Instead of focusing on what's going where in our classes, we talked a lot about how to focus our instruction.  There are 8 standards for Mathematical Practice that I feel like I know inside and out.

1.  Make sense of problems and persevere in solving them.  Perseverance was a big issue that we talked about.  If you have students who will keep trying when they feel like they don't know how to do a problem, then I salute you. Most of mine won't.  I get so tired of seeing blanks after kids have "done" their homework... or big ?s.  (Know what I mean?)

2.  Reason abstractly and quantitatively.  Important here was the ability to decontextualize (make a problem more abstract) and contextualize (apply the numbers at hand).  Tough for a lot of kids.

3.  Construct viable arguments and critique the reasoning of others.  Although it doesn't have to be a formal/written down process, I've started having the kids "check" the work of their classmates (they just accuse me of being lazy and making them do it). It's amazing how much they learn by going through a problem to try and find something wrong.

4.  Model with mathematics.  The kicker to us on this practice was the last line: "They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served it's purpose."  What?!  Check your work?  Make sure it makes sense? And if it doesn't make sense, try to fix it?!  Blasphemy.  And  you'd think I was torturing students in asking them to do that.  Darin Hausberger, (@dhausberger) had a quote that I liked:  "You may have an answer, but is it a solution?"

5.  Use appropriate tools strategically.  Don't automatically reach for the calculator (as we were reminded, paper and pencil are tools too!).  But if there's a calculation that you can't do, go for it. Or if there's something online that you need to use, do that too.

6.  Attend to precision.  I originally saw this as more of a "watch your rounding" type deal. But it turns out that the premise is that students need to make sure to label axes, units, and use the equal sign "consistently and appropriately".

7.  Look for and make use of structure. My big take-away on this one was the use of scaffolding.  In Algebra 1 we do a lot of solving equations in the beginning of the year.  I preach "show your steps" so that they get in the habit of knowing what they're doing to solve.  Now, though, we're solving quadratics by factoring, and showing how to solve 2x - 1 = 0 is something they should be able to do without all of the steps.  Those who are able to do that do.  Those who need a little extra time are still writing it down.

8.  Look for and express regularity in repeated reasoning.  Once you understand something it's ok to use patterns and shortcuts.  But I wouldn't suggest teaching that from the beginning.  (#7 and #8 seemed very similar in nature)

So that's my 2 days in a nutshell. We talked a lot about giving "rich" problems (ala Dan Meyer, who was mentioned quite often), giving guidance but not answers, and the general idea of "Be Less Helpful".

It was a good 2 days; I brought away a lot.

HCESC (who led the program) has set up a blog and will be updating with different resources. Check it out.

One last thing - we were all given a ring of cards with questions meant to help you guide students in class. Looks like it has some good ideas on it.  The questions were included in the appendix of a manual that we received... if you're interested in a copy let me know - I'll try and scan my manual and email 'em out.

(They probably won't be pretty colors like mine, but you can deal with that.)

32 comments:

  1. Thanks for the post and link, Kristen. I'm part of a 4-member team supporting teachers with the new Common Core, so I try to gather as much info as possible. I'd love to get a copy of the questions if it's not too much trouble. Thank you!! (Glad to know your son loves the ball!)

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  2. good stuff. i've come to the realization that the Practices are the Core of Common Core...with good, rich tasks/lessons/problems - giving kids opportunities to experience the "productive struggle" and discuss /reason with their peers - getting back to the beauty of mathematics, in my opinion - not just the rote skill & drill

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  3. Would love to what that set of cards looks like! darren.burris@gmail.com

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  4. Fawn -

    No problem! I'll just need an email address to send them to.

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  5. I would really appreciate a copy of the cards that you were given at the training. Please send them to rebeccalzullo@gmail.com. Thank you so much!

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  6. I would also like to see the cards. My email address is prlowe@gmail.com

    Thanks!
    Pam Lowe

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  7. would love a copy too! lud5380@yahoo.com

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  8. I've sent out copies to everyone who gave me an email address. Let me know if you haven't received them!

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  9. I would appreciate taking a look at your Common Core card set. Thanks!
    baileyc@unionsd.org

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  10. A copy of the cards for me, too, please. Thanks!
    pwrichmond@gmail.com

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  11. Great post. I'd love a copy of the cards, too. jfjelstrom@gmail.com

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  12. I would love a copy as well.

    mccormickmath@yahoo.com

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  13. I would also love to see the set of cards -- they sound great
    adcyford@gmail.com

    thank you

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  14. Just sent out the latest batch! Let me know if you haven't received them.

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  15. If I'm not too late, I'd love to see the cards, too. This is a great post! mrsg.heartsmath at gmail

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  16. I would appreciate a copy of the questions.
    Thank you
    Dianne
    Dmbrandt@dps61.org

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  17. I'd like a copy of the cards if possible.

    jmunoz@magellancharter.org

    Thanks!

    ReplyDelete
  18. I would like a copy of the cards.

    dwhee3@gmail.com

    Thank you.

    ReplyDelete
  19. I've started making my own question stems, and I would love to see how similar they are to your card set. Would you be willing to send a copy to wornickcoker@yahoo.com?

    Thanks!
    Dawne

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  20. Are you still willing to provide a copy of those cards on the ring? If so I would love to have one.

    boodacious22@bellsouth.net

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  21. Can you still email a copy of the cards on the ring? They sound perfect for one of my teacher goals this year of improving my questioning toward the students!! Thank you!

    jaitoro@reddingps.org

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  22. I just shared them with you via gdocs. Hopefully that works!

    Kristen

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  23. Please send me the cards if you still can! Thanks! tara.humphrey@gravetteschools.net

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  24. Hi,
    Could you please send me a copy of the cards? kprichar@pasco.k12.fl.us

    Thanks!

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  25. I would love to have the cards! Can you email them to:
    kprichar@pasco.k12.fl.us

    Thanks!

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  26. Just found this post and I would love the cards and info!
    jlanphear@cranburyschool.org

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  27. I would love a copy of the cards! srhmajors@yahoo.com

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  28. I would love a copy of the cards. MA-Mitchell@wiu.edu

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  29. I too would like to see the cards you received. Thank you.
    labbem@portlandschools.org
    content teacher leader

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  30. @Fawn Nguyen -
    I too am part of a team supporting teachers as they begin to implement CCSS for mathematics. I would love to share resources.
    labbem@portlandschools.org
    http://k-12mathpps.blogspot.com/
    thanks

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  31. Hello, I am in search of Common Core MATH Question STems, I can find plenty for ELA but see that maybe you can direct me for MATH Question Stems! or Common Core Card Set!
    Thank you so much for any direction you can send me!

    Michelle Izzo
    michelleizzo@mgsd.k12.nc.us

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  32. I would love a copy of your questions! Thank you so much!
    lindaponton@gmail.com

    ReplyDelete