Yesterday, we were all involved in PA Day sessions around math. We looked closely at **Van de Walle’s book**, and worked in our PLCs (Professional Learning Communities) to design tasks and choose activities that would better support our students in learning math. I’ve read a lot of **Van de Walle’s work before**, and was familiar with many of the key ideas before digging into this book yesterday. It was the challenge though of a critical friend that got me to think differently today.

Let me explain. As part of yesterday’s PA Day, we were encouraged to choose something from **the book** to try out in our classrooms. There are many key ideas about math that we already use in our room, but often these activities look different from the ones designed in * Elementary and Middle School Mathematics*. Listening to what other people chose to do and thinking about the needs of some of our students caused me to have a moment where I questioned if we should veer from

**the play-based Kindergarten Program Document**that we support,

*and believe in*, so strongly.

My **teaching partner, Paula,** was away sick yesterday, so in the midst of our planning time, I texted her to ask for some advice. Looking at the topic of subitizing — *which I thought would support some of our math learners* — I wondered if we should create a set of dot plates to use during transitional times. Children could talk about the number of dots on the plate, and I thought that if children heard what others had to say, they may also develop their own subitizing skills. In her reply text, Paula reminded me that we do approach the topic of subitizing outside with the collections of sticks, the groupings of burrs, and even the groups of children who sit on the fallen log or ride the tree branch around like a horse.

But all of that being said, she didn’t say “no” to the idea, so I got caught up in “doing something from the book” and I made a list of what I needed to create dot plates. I even added a **subitizing resource to our class blog**. On my way out for dinner last night, I picked up the items for the dot plates, and then when I got home, I created them.

I’m not going to say that the idea sat perfectly with me. *It didn’t. *Paula and I work hard to create authentic reading, writing, oral language, and math experiences in the classroom, and this subitizing option did not seem authentic to me. After posting the Instagram picture though, I got more “likes” and “comments” than I do on most of my posts, and I started to wonder if maybe this was the right decision.

This was until a fellow educator sent me a Direct Message on Twitter, and pushed me to think differently. She told me that she saw the subitizing plates, and while she sees the purpose of them, she loves real-life examples. She gave me a few ideas, and asked what I thought. *Yes! *This was my big problem. Learning to subitize is important. It helps with developing a stronger understanding of number, and even lends itself well to addition and subtraction math talk, with a real emphasis on the benchmarks of five and ten. *But why does subitizing need to be done with dots, five-frames, or ten-frames? *There are lots of great examples of subitizing in the real-world.

I thought about this even more when I went out for brunch this morning and had way to much fun building milk towers.

Then I came home and did a little searching online for images that connect with the numbers from 1-10. I thought about the **dot plate formations**, and found examples that aligned with these formations. I created a slideshow with a different image on each page. We can still look at subitizing during transitional times, but now, maybe we can do so with more authentic examples.

We all need people that challenge our thinking. Grateful for somebody that did this for me today, & led to the creation of this "real world subitzing" document. I see math talk potential! https://t.co/PdBYlR0t5R cc @john_gris

— Aviva Dunsiger (@avivaloca) December 2, 2017

*Sorry for my “subitizing” typo!*

I even started to wonder if we could make more subitizing links through play. Yesterday, I thought about the use of muffin tins and ice cube trays in the sensory bin to lead to some discussions with anchors of five and ten. *But what about in our dramatic play block space? *Children regularly turn at least half of the block area into a house. *What if we added a few materials into this space to help with subitizing, such as an empty egg carton, a few plates and cups for table settings, and maybe even a muffin tin? *This doesn’t have to be something that we do on Monday, and I haven’t even talked to Paula about the idea yet, but I’m starting to wonder what else is possible.

I will admit that I’m tempted now to throw out the dot plates and **change the link on our class blog**, but I think that I’ll wait. I’m hoping that we can use the real-world subitizing examples this week, and add **this link to the class blog for next weekend**. The dot plates still may go, but I wonder if we can show the link to kids between these plates and the real-world examples. *Does this link matter? *I’m not sure.

Yesterday, we were encouraged to choose something from **the book** to use in our classrooms. I’ve been thinking today that we may not have done exactly that, but we did pick an idea **from the text** and make it more relevant to the kids and the pedagogy in **the Kindergarten Program Document**. There’s no question that Van de Walle knows math, but his book was written well before the update to **our Program Document**. I wonder if/how his ideas would have changed to align with a play-based approach. Since John Van de Walle is not around to make the change, we’re going to need to create it on our own: *merging perspectives, contemplating the developmental levels of the children, and holding true to the pedagogy explicitly outlined in our document. *I think it’s possible to do this, but maybe just with enough of a push from critical friends that remind us of why we do what we do and the value in this approach for children.

**What do you think, and what do you do?**Many thanks to this educator that reminded me to hold true to my “

**educational troublemaker roots**,” and what I know (

*and believe*) about kids and learning. I hope I’m not alone!

Aviva

Love it! I cannot tell you how much it means to me when you work this through in front of all of us, such as it is. I know lots of us wrestle with this kind of questioning, especially with math. How do I make it real? And dots are awesome, but I’m never really going to run across a plate with dots on it in my real world. Cheerleaders in pyramids yes, dots on a plate, no. I will share this with my math p.d, group if it’s okay with you.

Thanks so much. And give your critical friend my thanks. They are an invaluable gift to us, those voices. Genuinely hard to find.

Thanks so much, Lisa! You can definitely share this with your Math PD group. I’d love to hear their thoughts. And your cheerleaders in a pyramid example is making me wonder if I need to find another photograph to add to the slideshow. 🙂 It’s amazing how many real-world examples there are of subitizing, and we can have the same conversations around them as we have with the dots. I guess that we could use the dot plates along with some of these real-world examples to help “notice and name” the math the that children are demonstrating: a key component of the K Program Document. My teaching partner and I continue to text about this, and we’re still trying to work out what to do. I think we’ll be figuring it out along the way.

This same critical friend helped me out even more tonight when she sent me some more real-world examples to add to the slideshow. The comment that she made with the photographs is really quite invaluable. She said that the dot plates are a right/wrong answer, where these real world examples actually lead to math talk. Light bulb moment for me! Yes!! This is why I like these examples even more, as there are multiple right answers, and so many genuine ways to talk about math. Her examples were even more diverse (largely added after slide 31), and even inspired me to Google the spider and the pants examples that I added at the end. This makes me think about Lori’s (@firstgradelori on Twitter) Math Talk Mondays, and the value in having open-ended photographs to discuss under a math lens. There’s often more than one example of subitizing in these photographs, so even more to talk about.

Yes, these critical friends are truly invaluable, and this particular one has been in numerous ways today! Thanks for getting me to think and talk even more about this, Lisa!

Aviva

For me these days in math, it’s kind of coming back to that question of “what do you notice, what do you wonder?”

I found myself taking photos on my recent trip to Ottawa with all kind of geometry in them. I want to use them as a notice and wonder activity. I like the idea of using slides to put them together and let my students talk about them. Your lightbulb moment is exactly it. Let’s just let our students talk, and see what happens in the learning. For some of my students, not assuming it’s math will be an asset.

Thanks Lisa! I agree. What you’re sharing here aligns with the Kindergarten philosophy of “noticing and naming.” This may also help students see math in the everyday — and even think mathematically more — but also realize just how much they can contribute to these math discussions. This could even change their mindset of themselves as mathematicians. I think of Jo Boaler’s work, and I think your point could align with her research as well. Another great reminder that this kind of math talk is as important for Kindergarten students as intermediate students. Thanks for continuing this important discussion!

Aviva