Saturday, October 12, 2013

Four = Eight (almost)

I am taking part in the Exploring the MTBoS challenge.  This week's challenge had two different prompts: share my favorite rich problem or share what makes my classroom unique.  Since most of the really cool, rich problems I am currently doing have been shamelessly "borrowed" from other people, I thought I would share what makes my classroom uniquely mine.

If you have read the book The Four Agreements by Don Miguel Ruiz, you may recognize these signs that hang above the window in my room:

For years these have been the four rules of my classroom.  During the first day or two, we go through them and decide what they might mean in the context of being together in this classroom and in our friendships and relationships outside of the classroom.  These have had the added benefit of tying in nicely with the math classroom.  Ask any student in my room, especially the Geometry students, how many times I have just POINTED to rule number three as they worked.  "Oh, right...."   

In the last 2 years I have been trying to really incorporate the Eight Standards For Mathematical Practice in all aspects of my classes:

List of Common Core Mathematical Standards

What I have noticed is how well these eight standards match up with the Four Agreements.

Be impeccable with your word
MP 3:  Constructing viable arguments and critiquing others' reasoning requires a great deal of thought. Students must learn to put together words and thoughts in a logical manner: both to present their arguments, as well as to refute the arguments of others.  All the while, they must be careful to attack the thought process, not the thinker.

MP 6:  We are asked to attend to precision.  That means we need to use the best possible language to describe what is going on.  No longer will I fill in the words for the students. They use the word boards, the magnetic theorems and postulates hanging up, and or their notes and or their phones, but the responsibility lies with them.  For me, I may need to look long and hard at all the little "cute" ways I refer to parabolas (happy vs sad) and instead help them identify what transformation has occurred - a reflection (not a "flip"!) across the x axis?  I know this will be a challenge for me!

MP 7, 8:  Both of these require excellent communication skills along with precise language.

Don't take anything personally:
MP 3:  When someone has inadvertently NOT been impeccable with their word, know that they are not attacking you as a person.  They are attempting to say something about the logic chain you put into play.  We remind each other how to use more precise wording, and use "I" instead "you".  

Don't make assumptions:
MP 2: It is too easy when we first begin to reason abstractly to assume something is happening, say, in a pattern, without really probing.  Students frequently want to make the quick jump, but often they need the manipulative first, which allows them to SEE.  From there they can talk about the assumptions they made and how that led them down the wrong path.

MP 6:  Lack of precision in a drawing (neglecting tic marks, right angle markers) can cause another to go astray.  Assuming that those lines are parallel because they LOOK parallel can lead to disaster. 

Always do your best:
MP 1:  Make sense of a problem and persevere!  No giving up!  Keep plugging away!  I teach at a vocational school and I often tell the students that as tradesmen, frequently they will  be stumped by a broken down car, a furnace that isn't working, or a patient that is not responding to physical therapy.  It is their responsibility to pose questions that will lead to answers.  Just saying: "Sorry, I don't know why your burner won't turn on!", is not an option and will not lead to a paycheck!

MP 7:  Some days students will not want to find the pattern, will not want to "guess the rule", will not see that 16x^4-9y^4 is just a difference of squares!  They will not want to stretch their brains, and we will find it easier just to tell them, or at least give them so many hints we might as well have told them! But if we do that then we have not allowed them to do their best.  Since this applies to me, as well, if I give in, then I have not done MY best either.


  1. I am also using the 8 week challenge. Otherwise I might not have found your post. But it resounds with me. I work with the non traditional learner as well. This is my first year to have even heard of the 8 standards of mathematical thinking. But I find myself constantly referring to them as I encourage my students to persevere on a problem. I had to chuckle at your reference to "'humanizing" terms. I do the same and this year I have made a concerted effort to use both words.

    I am definitely heading to the library to pick up The Four Agreements. Thanks!

  2. Those are really great to live by! I love how you can just point to the assumptions one for your geometry students. I need to have that!

  3. I apologize if this ends up appearing multiple times. At first I tried commenting on my iPad and it seemed to keep vanishing. I gave up and moved over to my laptop. Hopefully you can delete any extras that went through! :-) On to my comment...

    Thanks for sharing! I love how you're tying rules to live by with rules to do math by. Very clever. I especially like that it ties them together instead of making the students feel like there's one more thing to memorize. With your population, I'm sure it is especially useful, but I don't doubt that other teachers would appreciate this approach.

    1. Hi! It didn't come through twice. Thanks for the comment! I have always loved the Four Agreements and as I was making posters of the 8 Standards of MP, I was amazed at the correlation.

  4. Yes, I love the way you tied your four agreements to the Standards for Math Practice! I'm going to try this with my class rules and see how they correlate.

  5. Really love this idea of having just 4 things to rule them all!