THE BENEFITS OF TEACHING LIKE A DUMMY

Saturday, September 19, 2015 / 3 comments

I had to laugh at myself today as I stood in my classroom facilitating a discussion.
Today's lesson was about missing addends and trying to make connections between different strategies and representations while trying to link addition to subtraction.



I was currently in the "Connect" portion of the 5 Practices of Orchestrating Productive Discussions.  (If you've read my previous blogs, you would have seen this book title before.)

I had three other adults in the room at the time as well: a one on one aide, a push in classroom aide (I have many special needs in my room this year.) and a parent volunteer who was assessing kids on sight words for me.  I could see the adults smiling.  I could hear them chuckle now and then.  I could even see the eyebrow go up on the parent helper when she thought I couldn't see her.  Now, my one on one aide has become accustomed to my antics, especially when it comes to math, but the other two... not so much.  From the outside looking in, it may have been alarming.  I mean, imagine you're the parent and you grew up  copying what your teacher did learning math the way nearly all of us did...
My child is in a classroom where the teacher is completely clueless.  She doesn't show them how to
do anything.  She doesn't model for them and then have them practice.  She displays 4 to 5 different student samples that she doesn't even explain herself, nor does she let the same student explain their own work.  I don't think she even understands the student work!  She's always scratching her head and saying she doesn't understand so she asks other students to do her job!  Did I mention she doesn't even give timed tests?!  How on earth is my child going to learn all of these crazy common core standards?!

From the "Dummy's" perspective (that's me)...
Before the lesson:
Anticipate ways students might think, including misconceptions.  Plan questions ahead of time.  Keep them open.  Steer away from answer getting. Choose a contextual task that provides the opportunity for all of my students to have access to the math from angle.

During the lesson:  
Daro, presenting at NCTM Boston 

Give students a task. Encourage discussion on what tools might be useful for this particular task in groups or with partners.  Give students time to solve.  While they’re solving, monitor the class for common misconceptions.  These misconceptions are the “canary in the mineshaft.”  (Thanks, Daro) This does not include that one kid over there who made a computational error.  Those can be fixed on their own through reflection. Give students time to talk to each other about how they solved the problem.  
Some ideas:
Carousel Museum Walk – Students walk around the room and look at each person’s work.  Mark it with a :) or ?   Interesting discussion after – group representations that have either a lot of :) or a lot of ? and ask the students, “Why do you think so many people understood this work?  What do you think was confusing about this work?  How could they make it more clear?”
Musical Math – Works similar to musical chairs, but without removing a chair.  I play music and when it stops they sit in someone else’s seat.  Then, they have to explain to their new group how they think that person (the desk where they’re sitting) solved the problem. 
Around the World – When I call out “Around the World” students have about 30 seconds to find a new desk to sit in.  Then, they have to discuss with their new group how the person (the desk where they’re sitting) solved the problem.
Table talk – discussing with their own group
Partner talk – talking with their partner


After small group discussions, give students time to go back and reflect on their own work.  “Is there anything you would like to add or change in your work?  Is there anything you can do to make it more clear or precise?  If you weren’t there to explain your work, would someone else be able to understand it?  Did you remember to jump back into the context of the story problem and see if your answer makes sense? Did you answer the question fully?”

SELECT & SEQUENCE a handful 3-5ish student samples that range from concrete to representational to abstract.  It is a good idea to include a common misconception as one of the samples you are using if you see it as a common theme.  I have found that students often learn a lot, and sometimes even more, from these misconceptions.  All you have to do is put it up and say, “Prove it.” or “What do you notice?”   Why do you think I didn’t say, “Boys and girls, what went wrong here?”


Display student work.  I usually move from the lowest level thinking to the highest.  (CRA - Concrete, Representational and Abstract)  As for when the misconception fits into that sequence, I don’t have a definite answer.  If you do, please share it with me.  Right now, I try to sequence the misconception where it fits in the progression from concrete to representational to the abstract. When I display student work I do not ask that same student to explain their work to the class.  It is not show and tell!  Instead, I ask other students to explain and critique the work. Hello SMP 3!
The most important part of the whole lesson, in my opinion, falls in this chunk of the lesson.  This is where we are asking students to make CONNECTIONS between the different representations.  Why would that be important?  Well think of it this way…  What if you only displayed the equation because that was your end goal, but not all of your students understand the equation or where the numbers come from?  Who is left out? 












What if you followed your curriculum company’s advice and only showed the kids the counters? Who is limited?
Tape diagram
number line
120 chart
equation
Part part whole mat







By looking at the images above, whose 
understanding would you say is stronger?


Following the math lesson we reflect on what we learned.  We often use this time to write in our math journals.  We may work out problems or we may reflect on what discoveries we made that day.  (I wish I knew how to attach a document to this blog.  I would attach my math journal templates for you.  If you want them, leave an email below and I'll share.)  Sometimes I get so excited about what we are doing that I keep pushing until I don't have time for math journals.  If that happens I add the math journals into one of my literacy centers.  Hey, I'm putting writing together with math, right?  :)

So...  I guess from an outsider's perspective I may look like a dummy, but there is actually a lot going on here... and none of it is on accident.  
My child is in a classroom where the teacher is completely clueless.  I wouldn't have it any other way.
She doesn't show them how to do anything.  Why would I remove the reasoning and problem solving?
She doesn't model for them and then have them practice.  Too many kids left out.  They don't think like I do and they need to build from their own conceptual understanding.
She displays 4 to 5 different student samples that she doesn't even explain herself, nor does she let the same student explain their own work.  Kids need to critique the reasoning of others.  They are far less likely to take on the teacher than they are their peers.  When a kid explains their own work the class shuts down and disengages.  Allowing others to explain and critique the work promotes reasoning and making connections.
I don't think she even understands the student work!  Sometimes I don't. :)  Again, I act a fool.
She's always scratching her head and saying she doesn't understand so she asks other students to do her job!  Again, I act a fool.
Did I mention she doesn't even give timed tests?!  Why would I want to create an environment that would possibly breed anxiety and a poor disposition toward math?
Wish I could remember who shared this at NCTM Boston... 
I assure you, it was someone smarter than myself.


How on earth is my child going to learn all of these crazy common core standards?!  They will... by doing everything I just explained, and in great depth.


By the end of the lesson my brain hurts, but my throat doesn't and my kids are solid.  I'll take that.











3 comments:

  1. This "Columbo" style of teaching is right on. It's like a teeter totter. Teacher goes down, kids lift way up. You have created a vacuum for them to fill. I love it. The musical chairs and other similar techniques speak to your intention.

    In the end, the students feel respected, because they know you trust them to pave the path to articulating the common intelligence of the group.

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  2. Thank you, Arjan! I like the idea of the teeter totter, such a good analogy! I put in a lot of effort to create a "safe" environment, or to encourage a growth mindset to use today's buzz words. :) I love the musical math and the carousel museum walk because it really heightens their attention to detail in their work. I always remind them, "Will your classmate be able to understand this without you there to explain it to them? Did you answer the question fully?" Things like that. Thanks again for your thoughtful response! I learn so much from you!

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