Recently, during a Number Talk, I wrote this problem on the board and asked students to show me a quite thumb if the problem made sense. Then, I encouraged them to try to find a solution using some of the strategies we have been working on.
26 + 10 = ________
Calvin mumbled something under his breath. Students started raising their fingers to indicate how many strategies they had used. Calvin crossed his arms and started to kick the air as he slunk down into his chair. I asked the students to whisper the answer on the count of three. I heard a chorus of “36”. I wrote the next problem on the board.
26 + 12 = ________
Calvin glared at me. He growled. He turned his back to me. Mrs. X went over to him and he whispered to her as I continued the number talk. When Mrs. X came back over to me, she whispered, “he’s mad at you because you won’t stack the numbers.” I nodded to her and continued on with the next problem.
26 + 22 = ________
Calvin glanced at me with angry eyes. Then, he looked at Mrs. X and snarled, “She’s not stacking it!” My quiet thumb dropped to my side. I took a breath, looked Calvin in the eyes, and responded, “Calvin, if you would like me to write the problem a different way, I can do that, but you need to use your words and ask me. I am happy to help you if you ask me to.” Then, I went back to thinking about 26+22. Calvin kicked the air and turned away from me. After some quiet think time, I collected solutions and asked for volunteers to defend them. Jason told us that he decomposed and added. I recorded his thinking as he spoke.
I said, “This strategy reminds me a little bit of the one Calvin likes to use. We don’t have it listed on our strategies menu, but I think maybe we should. Calvin, did you want to talk about stacking?”
Calvin turned around. His shoulders settled. He asked, “can you write the numbers so they are stacked? That is the only way I can do it.”
“Of course I can. Thank you so much for asking. I will write the numbers so they are stacked. Can you tell us how you would solve it?”
Calvin explained, “Six plus two is eight and two plus two is four. The first time I got 82, but then when Jason said 48, I figured out I was wrong.”
I rephrased, “So you added the six ones and the two ones and got eight ones. Then, you added the two tens and the two tens and got 4 tens.”
“No. It’s just four. Two plus two is 4. The answer is 48.” He beamed. “Can you write my name next to it, like you did for the other kids?”
I asked Jason if he noticed anything that was the same about his strategy and the strategy that Calvin used. Jason said, “we both decomposed the numbers. We both added the tens and the ones.” I asked Calvin if he understood what Jason meant. I motioned towards the similarities as Jason explained them.
Calvin smiled, “We both got 48.”
“Yes,” I agreed. “Calvin I am going to continue to write the problems horizontally, but I can also write them stacked, if you would like.”
“Yes,” Calvin replied.
This number talk took place about three weeks ago. I think about it a lot. I think about Calvin a lot. Usually, I get really angry when I think about Calvin. I’m not angry at Calvin. I’m angry for Calvin. Calvin wasn’t always in our district. He transferred here from somewhere else. Counting is challenging for him. His only experience with place value seem to be to “stack” numbers and use his fingers to tally up the digits in each column.
Calvin clings to stacking like a life boat. I picture him, tethered about 100 feet off shore, clinging to the lifeboat because no one taught him how to swim. I imagine, and maybe I’m wrong, that no one taught Calvin how to swim because they firmly believed that he couldn’t learn how to swim. They probably thought it was safer for Calvin to just cling to his lifeboat. I can imagine the types of conversations that happened in regards to Calvin’s potential for learning:
“Calvin is just so low.”
“Calvin just needs to be taught a procedure. He can’t think ‘like that’.”
“Poor Calvin. His life is so hard. It’s not his fault, but it makes sense that he is so far behind.”
“Calvin can’t be in class with his peers. He is just so far behind.”
“Math just isn’t Calvin’s thing.”
“Calvin should be tested.”
Who the hell are we to decide what Calvin can’t do? Maybe it isn’t Calvin’s problem. Maybe it is our problem. Maybe we need to ask ourselves, what can we do to help Calvin think deeply about mathematics?
After this number talk, I added stacking to our anchor chart of strategies. The week following this number talk, I wrote the Number Talk problems both vertically and horizontally. If I forgot, Calvin grinned and politely reminded me. Gradually, Calvin stopped asking for the numbers to be stacked. He still clings to his strategy, but he seems to be thinking about trying to count up by tens. Yesterday, we checked in on his counting skills. Look at his work and ask yourself, what CAN Calvin do?
Calvin can count forwards and backwards by tens, off the decade! He might not be able to do it all the time, but he can certainly do it. Now, we have to help him develop his place value understanding and connect it to what he knows about counting. I have been carefully observing Calvin during class lately. Here are some other things he can do:
- Calvin notices patterns when we do choral counts.
- Calvin always raises his hand when I ask if anyone wants to defend a solution.
- Calvin takes risks. Yesterday, one of Calvin’s peers used a compensation strategy to solve 19 + 19 = ______. Joey said, “I took one from the 9 and gave it to the nine in 19 and then I had 10+10+10+8 so I got 38.” I asked if anyone else could explain what Joey meant. Calvin’s hand shot up. He had a big smile on his face. I called on him. He thought for a while, smile never disappearing. He said, “I am not really sure.” I offered, “help or time?”. He asked for help. He loves being in charge of choosing who gets to help him.
Let’s start looking at all of our students in regards to what they can do. Let’s stop finding excuses for why we can’t teach students. Calvin is far behind his peers. He didn’t have the exposure to the math practices that his peers had, but Calvin has potential. Calvin has a voice. Calvin is capable of greatness. I will admit that Calvin terrifies me because it is going to require a lot of work and reflection for me to figure out how to help him think deeply about mathematics. I have a ton of questions:
- Should I give him place value blocks during the Number Talks?
- Should I give him Digi-Blocks?
- What if the other kids want to use them? Will it lower the cognitive demand of the Number Talks?
- How do I help Calvin connect counting to place value?
I don’t know exactly how to how help Calvin. I have a lot to learn about supporting K-2 students. So, I read. I try things out. I reflect. I ask for help and feedback.
Today, I tried to help Calvin, and the rest of the class, understand Joey’s compensation strategy. I put nineteen place value blocks in each of my hands. I asked Calvin to count them to make sure I was correct. Thank goodness he did because I was one short.
Then, I asked the class if anyone could use the blocks to show us Joey’s strategy from yesterday. Ben volunteered. Ben picked up one of the cubes from my left hand and said, “Joey took one away from the nine,” he placed the cube in my right hand, “and he gave it to the nineteen.” Calvin watched carefully. He looked up at me and said, “That’s a ten! We can trade it for a stick!” I smiled and asked him if he would like get the ten stick for us. He did. When he came back, he said, “that makes three tens. So it is 38!”
I said, “your darn right it is,” and I gave him the highest of high-fives.
All of our students deserve respectful, engaging, math instruction that requires them to think deeply. How can you help make this happen?
5 thoughts on “Let’s stop condemning kids to a life without math.”
Beautiful writing and teaching. I had two conversations this week with adults who (I believe) were concerned about whether I am overemphasizing math reasoning for kids who really need a procedure to follow. I love the way you not only stick to your guns about math reasoning and sense-making, but also help your students make the connections between concepts and procedures. But it’s also a little daunting that there’s already such a gap for K-2 students. Still, if they are all learning and owning math, maybe it doesn’t matter so much which exact parts each is learning and owning at this age.
Thanks Julie! I had multiple conversations last week that started with teachers telling me what kids can’t do. It is really frustrating. I have yet to work with a student who isn’t able to think deeply about math in some way. The gap you mention is what overwhelms me sometimes, but I firmly believe there is a place for Calvin Math class. We can learn from him. So can his peers.
A beautiful story that depicts the respect all children deserve for the work they do as they make sense of numbers and operations for themselves. Thank you.
Thanks so much for reading and I am so grateful that you could see the respect I have for Calvin.
Calvin is lucky to have such a supportive environment where he feels safe taking risks.
Thank you for sharing Calvin’s work! Will share with preservice teachers Math for Elem Ed later today.
Some very interesting thinking was captured…after 199 comes 1100…
Do you think dimes and pennies would help this student?
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