Math in the Age of Distance Learning – Part 2

Image credit: Math With Me MN; annotations show student thinking

Recently, I came across a Twitter question that asked Kindergarten teachers about their favorite virtual routines or ways of interacting with students online. It got me thinking about what felt the most successful in my distance learning with Kindergarteners. I’d been spending so much time thinking about the fall, and about what hadn’t worked or needed to be better that I had not paused and simply reflected on what did feel successful.

I was surprised the answer came to me so easily. It starts with a picture.

The Power of a Photo

I hadn’t realized so many of our math routines followed the same structure: show some kind of photo on Zoom, look at it together and talk about a specific question (“how many?”; “what comes next?”; “what shapes do you see?”; “which one doesn’t belong?” amongst others). Then students would take their own pictures, in their own contexts, and answered or talked through the same questions we’d examined as a group.

What do you notice? What do you wonder? What shapes do you see? How might you describe a shape that you don’t know the name of? Image link.

As a class, we examined the photo on the left for shapes. We’d already been talking about shapes – both 2D and 3D, though some students were less sure about 3D shapes. My goal in selecting this picture was to give students 1) the opportunity to examine a lot of shapes, some that have clear names and some that are perhaps more complex, and 2) to show a picture with a context that might be meaningful or familiar to some students.

The photo appears to be an outside kitchen/stand in South Asia – many of my students are Indian and have travelled there, and I recognized the metal pans and colorful beans as part of my own childhood. Embedding students’ math exploration in a variety of contexts shows that math is everywhere, and pushes back on the defaulting to the same objects and contexts over and over.

When students described the shapes they saw, they found circles, “small circles”, cylinders, squares, and a box or cube. One student said that if you turn the jars sideways, you’d see a rectangle (note the slight angles present on one of the jars!) To follow up, students looked for shapes around them. They found square walls, rectangular mirrors and round (spherical) balls. I missed an opportunity here for students to grab some paper and draw a representation of a shape from the photo, or from around them – but we did get to see students’ thinking and representations live while exploring visual patterns, as I’ll show below.

Student work – In The Moment

A student holds up their drawing while explaining their thinking. They’ve extended the visual pattern & numbered each step.

With a little Zoom finagling, this setup works pretty well. We were exploring a visual pattern, and students had been told to bring something to write on and something to write with. I was sharing the image from my iPad, and annotating it, while looking at all my students in the “gallery view” on my laptop. After I annotated some of our noticings onto the pattern, I asked, “what comes next?” Students drew the pattern as they saw it, and what they thought the next step would be. What was interesting about this pattern is that the “next” could come in a few different places, so students’ drawings did not necessarily look identical.

Students were able to hold their work up as they spoke so their classmates could see what they’d drawn. This method would work fairly well for certain types of routines, including representing patterns, shapes and counting collections. Another option would be for students to come prepared with a collection of objects and count, recreate a pattern or identify shapes live. This gives the opportunity for students to directly respond to each other’s thinking in the moment.

Student Work – Follow Up

If the live work is meant to extend on a single image (or group of images) we all examine together, then the follow-up is meant to give each student an opportunity to carefully select and explain their thinking behind our focus. One of the first activities our class did was to look at a scene or collection of various things and ask “How Many?” (I wrote about this more in my previous blog).

This image has an empty alt attribute; its file name is 2020-05-15_79c1ee15-4506-4b2b-8d49-6988e2a78ce4.jpg
A student’s photo for the prompt, “How Many?”

Giving students the opportunity to create or find their own image, and explain in their own thinking all the different things they might count in it gives teachers (and students) a better idea of how well they can take what they learned live and apply it to their own context. The student on the left, for example, found a collection of legos and other objects. There are SO many things we could count in this picture – and when it’s captured in an image, it’s easy for both teachers and students to revisit and learn from.

The follow-up doesn’t have to be a photo – photos are great, but so are videos of students explaining their thinking, or showing how they counted or built something. Students might also submit work that shows how they represented what they counted, for example.

Students also created their own “Which One Doesn’t Belong?” images, after exploring the book together on Zoom. Students recorded themselves and a family member each explaining which one they think doesn’t belong and why.

Some student examples of Which One Doesn’t Belong? In the video, a student and his family talks about which one they think doesn’t belong from a student-created set. Students submitting follow-up work allows them to engage family members or caregivers with the math.

The Rest of It

I want to make sure I mention some of the other activities and tasks we did that I think are interesting and worth revisiting, but in the interest of keeping this blog as concise as possible, I will be brief and include links to student work around these ideas.

First of all, during a couple of our Zoom meetings, we tried an Esti-Mystery and a Splat!, two routines from Steve Wyborney. Esti-Mysteries involve students estimating how many objects are in a container, and revising their estimates as clues are revealed. Splat! requires students to think about how many objects were hidden under the “splat” using what they know about how many there were to start with, and how many are left.

To see more of what this looked like, follow these Twitter links:

We also thought about how chickens could be arranged inside and outside of a coop. This activity was adapted from one that Bethany Lockhart uses with her Kindergarten class.

Towards the end of the year, students built structures out of paper and talked about what shapes they saw, how many sticks they used, and how they would use their structures. This was an idea from Chapman University’s #MathPlay series, and it was amazing to see their creativity!

What’s Next?

This fall, I’m teaching 3rd grade, so I’m adapting what I’ve learned and thinking about the needs of slightly older students, and I’m also waiting to hear specifics of what fall teaching will look like in my district (aren’t we all?!) But in the meantime…

  • Routine is key. I want to remember to set up a routine (just like in class!) where students engage in a warm up, problem solving and discussion, even if we are virtual.
  • I’m very curious about having a virtual “Hands Down Conversation” (from this book) with students about math (and literacy!)
  • I want to do 3-Act-Tasks both synchronously and asynchronously with students. The fact that photos worked well as a jumping off point for mathematical discussions shows me that with proper preparation, watching a video together could be even more interesting! And maybe students could create their own…
  • Social Justice and math are intertwined, and I want to explore this much, much more next year. A good jumping off point might be having discussions around slow reveal graphs and students collecting data which we can then analyze together.
  • As I mentioned above, I’m trying to make sure that when I bring in an image, or story problem to students, the contexts are meaningful and go beyond what we think of as “neutral” or “default” (i.e. White, Western, European). However, I need to get better at spending just as much time with students unpacking the contexts and how they connect to them – because just throwing in a “diverse” picture (cringe) does absolutely nothing.
  • I want to make counting collections and choral counting more of a regular routine, even in 3rd grade. Going back and really thinking about place value and base ten will be important for students, especially in light of inconsistent experiences this spring.

I’d love to know what you are thinking about for this coming school year!

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