Sunday, June 28, 2015

Learning to Fish

     The 2014-2015 school year is now over.

      And while the year held its share of challenges, there were also many highlights:

Much better than the status quo.

Andrew Stadel made me figure out how many times a swing's chain would wrap around a pole.

The faculty lounge coffee drinkers had to go without sugar and sweeteners for a few weeks.

How much do you think I could get for this on ebay?

     But overall I am most proud of my PLC.  This past school year, it consisted of myself, my co-specialist Theresa, our two fifth grade math teachers, our fourth grade math teacher,  one each of our third and second grade teachers, and one of the district's elementary TAG (Talented and Gifted) teachers.  My supervisor also sat in on several of our meetings.  We met once a month, for about an hour, alternating before and after school.  Our stated objective was to gain a deeper understanding of the Danielson Framework's domain 3b: Using Questioning and Discussion Techniques, but informally, I thought of our sessions as MTBoS 101.

     In September, inspired by Justin Lanier's course Math is Personal, we examined our own personal relationships with mathematics, and reflected on how those relationships impact our teaching practice. 
     In October, we watched Annie Fetter's Ignite talk, Ever Wonder What They'd Notice (If Only Someone Would Ask), discussed the benefits and advantages of using the noticing and wondering prompt as a way to open up student thinking in math class, and left with a homework assignment to use the prompt in class and report back the following month.
    During the November meeting, participants shared their experiences using the notice and wonder prompt, in subjects ranging from math to science to social studies.  We used this crib sheet from The Math Forum during our debriefing.
    The December meeting was a highlight.  I engaged the PLC participants in Andrew Stadel's File Cabinet 3-Act, asking them to work out the aspects of the task while at the same time keeping notes on their reflections, comments, and questions.  I was a little nervous during this one.  My supervisor was there, and was using the session as one of my two observations.

The group enjoyed sharing their solution strategies.  And my supervisor loved it.  It was his first experience with a 3-Act, and he later told me he used it during a department meeting at the middle school.

       At the January meeting we debriefed the File Cabinet 3-Act.   Several of the participants expressed feelings of nervousness and anxiety during the experience, and we discussed the importance of putting ourselves in the place of our students and maintaining empathy for their emotions.  The feedback was overwhelmingly positive, especially for the thinking required during Act 2, where the students need to develop questions.  As one participant said, "It forces kids to use different muscles."  Yes!  The PLC also liked the fact that 3-Act tasks embed many different skills in a single problem, and expressed excitement about the prospect of integrating more 3-Act tasks into their practice.
     We kept the 3-Act momentum  going in February.  We used this comprehensive guide from the Georgia Frameworks as our discussion text, and focused on different ways to put students in collaborative groups during Act 2.  Participants were given time to explore the trove of 3-Act tasks created and collected here, here, here, and here.
     We spent the following month taking and submitting pictures that might inspire notice and wonder prompts, estimation activities, or even 3-Act tasks.  I collected them in a file on the district's shared drive, and during the March meeting we took a look at our efforts.  Some samples:

Jane submitted this picture, taken at her son's birthday party.  The group felt this had the potential to spark a lot of mathematical thinking, including: How many slices?  Unit cost per slice?  How tall is the stack?  How about categorize by topping and find fractional part of whole?

Jeff submitted this picture...

...followed by this close-up.  This also generated a lot of mathematical thinking, from: How much trash can the bin hold?  to: How much milk would you have to drink to make a trash can?

I encouraged the participants to continue taking mathematically inspiring pictures.  Our cell phone cameras are powerful tools!  My supervisor framed this activity in a conversation we had soon after this session by quoting for me the old saying: "Give a man a fish and he eats for a day. Teach a man to fish and he eats for a lifetime."  He made me realize just how empowering it is to be a creator of content, not just a delivery mechanism.  I wanted the PLC participants to feel that power.
     After the long, cold winter, the PLC was relieved to see signs of spring.  In April we explored the rich discussion opportunities afforded by Which One Doesn't Belong? tasks. We started with one that I made:

and discussed an example from Christopher Danielson's book:

The enthusiasm was contagious.  Several days later Larissa was proud to show me one that she had created...

...and I encouraged her to submit it to the site.  She learned how to fish!

     In May we dipped our feet in Jessica Shumway's book, Number Sense Routines:

I like this book so much that I had my principal order copies for all our primary grade teachers to use in our PLC next year.
I was interested in exploring the use of counting circles.  We started by doing a counting circle of our own, starting at 1 and stopping at 18 (there were 18 days of school left.)  Theresa recorded the count on the board, and the group noticed some interesting patterns.  We looked at several examples I had collected during the school year:

Grade 1

Grade 5

Grade 3

      During the June meeting, the PLC took a reflective look back and shared their important "takeaways".   Listening to the discussion, I could only hope that the teachers would carry their enthusiasm for noticing and wondering, 3-Act tasks, and an all-around more student-centered, engaging approach to teaching mathematics into the following year, that they would make these activities an integral part of their practice, and that they would take them and make them their own.     

And everyone got a present!

Thursday, June 11, 2015

"Nobody Puts Kindergarten in the Corner!"

    If the MTBoS has a signature teaching move, it's got to be the 3-Act.  It incorporates so much of the MTBoS ethos: noticing and wondering, estimating, premium student engagement and student-directed learning, collaboration, low floors and high ceilings...a good 3-Act wraps it all up in one beautiful  package.
    Created and spread by middle and high school teachers like Dan Meyer, Andrew Stadel, and Kyle Pearce, until somewhat recently the pickings have been slim for us primary grade folk.
    Enter Graham Fletcher.  Graham has worked on developing 3-Acts for the elementary school set, and he hasn't neglected kindergarten.  One look at Shark Bait and I knew I had to give it a spin.  So last month, armed with some baskets of unifix cubes...

...I set off for kindergarten.

ACT 1: The Question

Seated on the carpet in the front of the room, the kindergartners engaged immediately.  I mean, aren't worms right in that 5 year old wheelhouse?    They clamored for another viewing, and another one after that.  I had them do some noticing and wondering:
  • The worm is long!
  • That worm is disgusting!
  • Why is it raining?  
  • Is that worm real?
  • I saw a really big worm once!  Bigger than that one!
and, finally, the focus question:
  • How many cubes will it take to make that worm?

I had the kids make some estimates, which got recorded on the board:

ACT 2: The Work
     I explained to the kids that I was going to give them some clues to help them figure out the answer.  In a true 3-Act, the students would need to request the information; here I decided simply  to provide it.  It was their first experience, and I did not want the task to become too overwhelming.   Here's what Graham provided for Act 2:

I showed this to their teacher several days before the lesson.  She was concerned that the kids might not be able to read all the words.  She made a suggestion...

...and Theresa  modified it by adding some color hints.  She ran off a bunch of copies and laminated them.

Their teacher and I had discussed whether or not to read it out loud.  The teacher felt the students still might have some difficulty, but I wanted to see what would happen if we just handed it out.  So I asked the kids to go back to their tables, distributed the clues, and let them have at it.

They got right to work.

There was very little problem.  The struggling readers got help from their classmates.

They compared their worms.  Some kids were a little short.

ACT 3: The Big Reveal

     The kids brought their unifix cube worms back to the carpet for the reveal:

We counted the cubes, both by ones and by fives (plus 2) and established the correct answer as 22 cubes.  The kids who had forgotten the extra oranges went back to their baskets and retrieved the missing cubes, and kids that had too many put the extras back.  Again, they insisted on viewing the video several times, and paid careful attention at the end as the worm began to extend.

ACT 4: The Sequel
     What's a 3-Act without a sequel?  For this task, I wanted the kids to draw and then measure their their own worms, using whatever combination of cubes they wished, then record the results, using whatever way made sense to them.  They dug right in!

A standard response.  This student made a worm 22 cubes long like the worm in the video.

This student made groups of 5 and included an addition number model!

This student used a different method.

Worms have segments, right?


Because he did not group like colors together, this student had a counting challenge.  Can you figure out his method?

.  My favorite worm.  It's partly underground!

 It was time for me to go, so I had the kids come back to the carpet for a final activity: a counting circle, from 1 to 22 and then backwards from 22 to 1.  To follow up, I encouraged the teacher to try having the kids order their worms from smallest to largest.

Act 5: The Reflection
   I had several thoughts looking back on the lesson:
  • The task was perfectly suited to kindergarten.  
  • I was glad that I hadn't helped them read the clues in Act 2, but that I had provided them with the color hints.
  • Maybe I should have pushed them more in Act 2 to come up with what they needed to answer the question, instead of going straight to the clues. I've admitted that my feel for kindergarten isn't all that great, although it's gotten better this year because I've spent more time there.  I think it's time to level up my expectations.  As one of our great kindergarten teachers likes to say, "Nobody puts kindergarten in the corner!"
  • I was struck by their resourcefulness.  I told their teacher that I was impressed by how well the kids spelled the color words; that I thought they would need more help.  Turns out they were copying from the clue cards, as well as from the color words that were posted on a wall in the back of the room. And I loved that there was so much diversity in the ways they used the cubes to measure, and in the way they recorded their results.
     One final reflection: The 3-Act lesson, which reflects so much of what's good about MTBoS project, has another huge selling point: its adaptability.  So while the mathematics of the task changes to reflect the competencies and standards attached to the particular grade level, the core template remains the same.  From kindergarten through high school and beyond, it's something every math teacher should have in his or her tool kit.