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:

http://www.insidemathematics.org/index.php/commmon-core-math-intro

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.