In chapter 8 of Taking Action: Implementing Effective Mathematics Teaching Practices, the authors remind us that we can use “evidence of student reasoning and understanding (or misunderstanding) to **inform teacher actions *** during instruction *as well as to assess students’ progress in learning”.

When planning with a kindergarten class, we began by looking at their data. That data told us that these students were organizing collections greater than 10 and tell how many after counting them. Most students were creating equivalent sets. We decided to plan a subitizing lesson. During the lesson, students would participate in a number talk with arrangements of dots and later be introduced to rekenreks using combinations and totals of 5.

As the **number talk **began, students struggled to answer both *“How many do you see?”* and *“How do you see them?”* I was doing all the talking talking talking! So, I stopped talking and suspended the number talk. I chose to move to the rekenrek part of the lesson.

Here is the rekenrek plan.

Below, from an earlier blog post, is an explanation of the rekenrek introduction.

*“I started with a context. In the book Bunk Bed and Apple Boxes by Catherine Twomey Fosnot, the author connects the rekenreks two rows of beads to bunk beds. In The Sleepover, Aunt Kate invites friends for a sleepover. The guests arrange themselves on the two beds. When Aunt Kate brings treats for her guests, she places treat cups matching her guests’ arrangements on the bunk beds. But each time she leaves to rearrange the treats, the friends move around on the beds, making different arrangements and confusing Aunt Kate.*

*Rather than read The Sleepover aloud, the class acted out the story. Creating bunk beds with tape on the whole group carpet, six friends arranged, and later rearranged themselves on the beds, with some students sitting on the top bunk and some on the bottom. An additional student in the class played the part of Aunt Kate (or Uncle Charlie).*

*Next, students used the rekenreks to retell the story!*

*Before putting the rekenreks into students’ hands, I introduced this “new to them” mathematical tool. Red and green stickers were positioned at the top. The red one showed students where beads would rest. To be ready to begin a math challenge, all the beads rested on the red side. The green sticker marked the go side. When showing math thinking, the beads slid to the green side. To help me (and their teachers) see their “good math thinking”, rekenreks rested on the rug in front of them as they worked.”*

For this **kindergarten** class’s lesson, our story had **5** friends on the bunk beds. Making arrangements using 5 beads, students used their rekenreks to retell the story. Then they used their mathematical tool to play “Guess My Way”. I made a combination of 5 on my rekenrek and and students had to guess the way I had arranged my beads. The original plan would have concluded with students guessing each others’ “way” while further exploring their rekenreks.

However, responding to the information gathered during the number talk, I made the instructional decision to connect their rekenrek combinations to recordings. Students were asked to show 5 in different ways on their rekenreks and then choose their favorite “way” to share with the class. I would record some of their “ways” for all of us to see. And as I recorded, I asked students to “see what they noticed”.

Here is the recording.

**What did students notice?**

“*Mine is the same! I have 1 on the top and 4 on the bottom like that one!”*

“*This one has 3 on the top and 2 on the bottom and this one has 2 on the top and 3 on the bottom.”*

“*These two boxes have the same- 4 on the top and 1 on the bottom.”*

“*Oh! I can’t have 5 on the top and 1 on the bottom. Then it wouldn’t be 5 altogether!”*

Takeaways:

- We (teachers) must listen for understandings but also misunderstandings during a lesson.
- Even when we think we have accurately anticipated student responses, based on data, we might be surprised.
- Understanding learning progressions and developmental learning trajectories are helpful when planning, anticipating, and responding during instruction.
- When I’m doing all the talking, I’m the one learning. During the number talk, I had to stop, and look for a plan B.
- This time, Plan B was offering an opportunity, during the lesson, for students to connect acting out (with the bunk bed story) and constructing combinations (with the rekenreks) to the recordings that represented those combinations.