Making Thinking Visible

Making Thinking Visible
Making Thinking Visible

Arts Integration

Arts Integration
Arts Integration

Stamina in the Math Classroom & The Twelve Days of Christmas

On the twelfth day of Christmas, my true love gave to me, twelve drummers drumming, eleven pipers piping, ten lords a-leaping, nine ladies dancing, eight maids a-milking, seven swans a-swimming, six geese a-laying, five golden rings, four calling birds, three french hens, two turtle doves, and a partridge in a pear tree!
Have you ever stopped to think about how much that poor lady received by the twelfth day Christmas? Year after year, my fourth and fifth graders have decided that the guy wasn't her "true love" based on the amount of fowl he bequeathed on the poor woman. 
I would've called the cops!
                                                     Fifth grader

Math investigations like this are huge amounts of fun, especially when we're winding down toward winter break. The kids are a little crazy. You're very tired, and everything around you is a bit manic. 

But, we still have to teach, don't we? Yes. We do. 

Marilyn Burns, math guru extraordinaire, has a wish list for math investigations in the classroom. Like Santa doing his list checking, I tried to check off Marilyn's when I designed my 12 Days of Christmas problem solving venture. 

Day One:Setting the Stage

We began by viewing some funny online versions of the song. They can be found on youtube. We watched a modern-day video performed by two men who acted out every animal in the song. 

Then, we viewed a wordless version, set in Victorian times,  that humorously pointed out just how ludicrous the gifts are in the song. We talked about the history of it (it's really old), and then we sang the it. We even wrote our own modern versions.

My students come from different backgrounds. Not all celebrate Christmas. That's okay. We talked about how it's a counting song for the Christmas season. It was a history lesson, not a religious holiday lesson.

Finally, we asked our math question: How much did she receive by the twelfth day? 

Math is Creative

Math is creative. There are many ways to investigate the same problem.
                                             - Ms. Willis
On day two, my students worked independently to devise a strategy for answering our question from the day before.  We used the Claim-Support-Question visible thinking routine to support us at this point. Some drew pictures. Others used tally marks. A couple of kids noticed a numerical pattern. Two or three students tried making a data table. I kept a close eye on my special education students and allowed them to work together on this part if it was necessary.  

I would not confirm their answers yet, because I wanted students to focus more on the process they were developing.  At the end of the session, they met in groups of four to share their strategies and the thinking behind them.  They were not allowed to share any answers. 

Your Brain Isn't Fried

Once tried doesn't mean your brain is fried!
                                                                                                 -Ms. Willis
By day three, most of my students had solutions.  Many, if not most, were incorrect. They wanted me to give them the answer. I refused.  Why? Because problem-solving stamina is important.  Our kids need to develop this.  We don't give up at the first sign of challenge. No. We. Don't.  They went back to their strategies. 

I asked questions to help them with their thinking. That is how I supported them. Students who had a correct solution were given the challenge of finding another way to prove their answers. Just like scientists who repeat experiments over and over again to justify their research, mathematicians search for other proofs, too.  This was an "a-ha!" moment for many students. 

The special education students I worked with also developed strategies.  Depending on the strategy they used, the amount of math it required, and their IEP goals and accommodations, I allowed some to use a calculator.  

Group Sharing & Celebrations

Finally on day four, students met in small groups to share solutions and strategies.  We identified the correct answer. We also created a mentor chart of the all the strategies tried. We named them after their authors. For example, "The Charlotte Strategy." We took a step back from the problem to discuss the type of thinking we engaged in. We use Ron Ritchart's Cultures of Thinking and Making Thinking Visible approaches at our school. Many students thought we were "uncovering complexities." Others thought we were "reasoning with evidence." The coolest part was discovering that we had traveled around the entire Understanding Map with this one math investigation!

Students ended day four with taking the song lyrics and math question home to their parents to challenge them to solve it. Their parents had homework to solve, and my students got to coach them on math strategies. 

I think Marilyn Burns would be proud of us. I know I am. 
The resources I used for this math investigation are below. You can try the Claim-Support-Question routine for free!

Psssst! Hey, yeah you! What does the Fox say? He says, "Be sure to follow Wild Child's Mossy Oak Musings. If you do, you get a monthly freebie in your mailbox EVERY MONTH!"


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