There are many things that I love about our Kindergarten Program Document, but the way that math is embedded through play might be one of my favourites. It’s really about making math authentic. I think about the value of this as children continue to progress through the grades. As a Board, we’ve spent a lot of time looking and talking about Jo Boaler‘s work on Mathematical Mindsets. I can’t help but wonder if the key to changing children’s perceptions of themselves as mathematicians rests in noticing and naming the mathematical thinking that students engage in on a daily basis, while continuing to focus on the Process Expectations. This does not mean that we negate the value in computations and learning specific skills, but we also need to help children view themselves as mathematicians, so that they regularly think, problem solve, and approach life through a mathematical lens.
I think of the math that happens daily in our Kindergarten classroom. For everything that we do, there’s a lot that we don’t do.
- We don’t do math centres.
- We don’t do a Problem of the Day.
- We rarely use traditional math manipulatives, and even when we do, they’re rarely used in a traditional way. Just look at how the dominoes are used in this house. Mind you, there is still a lot of mathematical thinking in their design.
Trinity and Milla made this PicCollage on their own as I was on duty today. Look as they decided on the pictures to include and even sounded out each word to add. Milla told me when I got back, “You missed the most amazing PicCollage!” I might agree. ❤️ SWIPE ⬅️ FOR MORE. #teachersofinstagram #ctinquiry #iteachk
- We don’t require the completion of specific activities for kids.
This does not mean that we just wait for children to become interested in math, and then develop the skills. Nor do students just happen to stumble upon the math, and we wait (fingers crossed) for this to happen. We make a lot of deliberate choices around the materials we put out, the location of these materials, the questions we ask, and our morning meeting provocations, with the intention of developing math thinking and knowledge. Even the little finger plays we do each day are done with math in mind. Here is what we do to get children engaged in thinking mathematically and developing skills, all within the context of play, inquiry, and everyday experiences.
- We spend a lot of time observing and listening to students. Most of our time is spent with kids. Recently, a teacher told me that I never sit down. I’m not sure about that. I think that my teaching partner, Paula, and I do sit frequently, but never on our own. We’re always with a group of children, or standing back, and listening carefully to what children are saying. It’s when we listen that we can often make the connection to math and can “name” this math for kids. Some might argue that this math talk interrupts the play, and at times, we both wonder if it does. But then we see how children take what we’ve named, and use this language and share this thinking in their play … without us being the push. This makes the observing and listening well worth it!
Had some branch talk outside this morning. What could we do with this branch? Led to a good opportunity for some subitizing. https://t.co/z6rwzDf5as
— Aviva Dunsiger (@avivaloca) April 14, 2018
Edward really wanted a big block, but we didn’t have any more. He wrote a note (a good opportunity to work on letter-sounds and look more at consonant blends) to Ms. Lantagne asking to borrow a block. He borrowed two because of the size (and explained his measurement thinking). Trinity then piped in about subitizing. We re-examined what this term means and explored it with some of Edward’s math thinking. Math is also everywhere. ❤️ SWIPE ⬅️ FOR MORE. #iteachk #ctinquiry #teachersofinstagram #engagemath
This light table drew some students today. While they told some stories around friends and hotels, it was their math thinking that really got me here. From the subitizing to the beginning subtraction and 1:1 correspondence, there were a lot of interesting discussions in this space. Slowing down to count seemed to be key. It’s not always easy to do. And of course, at the end, a few students were excited when they could make the people have a “group hug.” I kind of love the little ❤️ here. SWIPE ⬅️ FOR MORE. #iteachk #ctinquiry #teachersofinstagram
- We make our outdoor learning time about way more than recess. When on duty at recess, it’s hard to do anything besides supervision, but with our outdoor learning time, a smaller group and a bigger space allow children to really settle into play. This gives us an opportunity to go around, observe, listen, and talk with kids. We do not structure this outdoor time. Students decide what they want to do and where they want to play (within boundaries of course), but even so, there is so much math that happens authentically outside. Measurement talk is often huge in this space, but sometimes, there are also discussions about geometry (particularly shapes) and number sense (often counting, addition, subtraction, and subitizing). Again, after naming what we’re observing, students begin to use this language on their own.
Paula said, “Comparing similarities and differences in Ella’s stick collection. We chat about about length and size. And discuss how we need to be sure the sticks start at the same point in order to get a correct measurement ❤️❤️❤️” https://t.co/LMJh7eGJMd
— Aviva Dunsiger (@avivaloca) March 23, 2018
The measurement continues with Paula Crockett today. Ensuring that the sticks are at the same spot as Ella measures and compares them. https://t.co/uWa7fVsYS4
— Aviva Dunsiger (@avivaloca) March 23, 2018
They found big sticks today. Led to some measurement as they competed the stick to the branches on the tree and how tall they could hold them. Then I pushed for a little estimation, which led to a little sharing of subitizing too. Math through free play in the forest. It happens. pic.twitter.com/YhCN9S98oX
— Aviva Dunsiger (@avivaloca) March 1, 2018
They created some mud today. Comparing their two versions had us looking at which container had more, and what they put in them. What made the interesting colours? I love Ella’s comment about the “yogurt balls” … “just two.” Some subitizing perhaps? 🙂 SWIPE ⬅️ FOR MORE. #iteachk #ctinquiry #teachersofinstagram
- We think carefully about our transitional times. We don’t transition a lot in our room. With a long outdoor time followed by a long block of play in the classroom, our biggest transition is around mid-day when we come inside and have our meeting time. (Since eating happens all day at an eating table, we don’t heed to the nutrition breaks, which also reduces the number of transitions.) Getting 27 Kindergarten children undressed and organized is a challenge in itself, especially with this never-ending winter, so usually Paula oversees this (she’s amazing), and I connect with the kids as they come into the room. We often use this time for some phonological awareness activities, but also, some math talk. When we noticed that our children really needed to develop their subitizing skills, we created this Google Presentation that shows examples of subitizing in real life. Discussing these examples provides a great opportunity to get children thinking about subitizing. We also play some simple games that have children considering subitizing. I like to use the finger play, “Open them, shut them, give a little clap. Open them, shut them, give a little tap. Open them, shut them, fold them in your lap.” Now I’ve changed the words, and give a specific number of fingers for children to clap or tap. For example, I might say, “Open them, shut them, give a two and three finger clap.” Initially, I focused on doubles, but one child suggested I try an uneven amount, so I changed to this. Children then tell me how many fingers they’re clapping or tapping. Simple, but effective! I also use fingers for children to show me different amounts. This only takes a few minutes, but it’s really worthwhile. Having children discuss how they determined the correct total also provides a great option for communicating math thinking.
Looking at other ways to make 6 with this finger game. Will be playing these games again. A good way to also build subitizing skills. pic.twitter.com/o1ZxdHM7b8
— Aviva Dunsiger (@avivaloca) January 18, 2018
Looking at how to make number amounts in different ways using our fingers during a transitional time this morning. A fun option to play at home. Discuss how kids know they’re correct. pic.twitter.com/ZSyuqQxDao
— Aviva Dunsiger (@avivaloca) February 28, 2018
- We’re intentional about what we put out and where we place items. During the course of the day, just about everything in the classroom is moved around, but to start, Paula and I think very carefully about what we’re going to put out and what learning and conversations these materials might lead to. We had a Math Night a couple of months ago, and as a Kindergarten team, we decided to really showcase math through play. In this document, we highlight different areas of the room and how we connect math concepts to these areas. In our room, we try to make more authentic links to data management, and now students come up with all kinds of their own reasons to survey friends and interpret data. That said, this document still shares a lot of different examples of math in the classroom, as well as extension possibilities for home. This home/school connection is so important, as then parents can also provide these authentic math opportunities, and help children see themselves as mathematicians.
She engages in some Lego math at the Math Night tonight. She figured out that she could make a 1 out of 9 Lego bricks. I wondered if she could make other numbers also out of 9 bricks. She made a math sentence, & problem solved when the 8 used more than 9. https://t.co/bkfs1hUeNH
— Aviva Dunsiger (@avivaloca) March 1, 2018
When playing with the kinetic sand during our math night tonight, Milla noticed the two groups of 6 in the tray, and realized there were 12 hearts altogether: “6+6=12.” Her mom is helping her see the connection to multiplication, but she’s not interested right now. She did look over at the muffin tin though, and realize that there was another example of “6+6=12.” ❤️ SWIPE ⬅️ FOR MORE. #teachersofinstagram #iteachk #ctinquiry
He continued to create taller towers at our Math Night tonight. He was comparing his measurement to the height of the two towers when they fell down. I wondered how many blocks taller the biggest tower was as compared to him. This was a hard question to answer. We’ll need to use this language more as we build in the coming days. Our new block space should help with this. #teachersofinstagram #iteachk #ctinquiry
Usually a similar group of children end up in this block space, but today, some different children played here. Trinity and Addison created a house for the dog. When I pointed out a label on one of the blocks, they started to label others. Pretty soon, everything was being labelled. Great to hear Addison’s increased confidence in reading and writing. She was reading what Trinity wrote (using letter-sounds) and vice versa. I love when kids realize they have the knowledge and skills to read everything … & they attempt it. ❤️❤️❤️ They also added a number to the dollhouse. This allowed us to look at place value and how we read different numbers. SWIPE ⬅️ FOR MORE. #iteachk #ctinquiry #teachersofinstagram
Joshua decided to do a survey for what colour we should paint our new big canvas. He sounded out the title and the colour choices. Then he went to ask his classmates. We will look more closely at tally marks next. Then Olivia and Carly wanted to start the painting. They washed the jars and mixed the paint. More children joined them as they started painting. Love listening to the quiet conversations as they paint. ❤️ SWIPE ⬅️ FOR MORE. #teachersofinstagram #iteachk #ctinquiry #art
As I think more about math in the early years, and really just math in general, I wonder if the traditional math manipulatives and tools make math learning any better. I had a conversation recently with various Kindergarten and Grade 1 teachers. They were surprised that I didn’t use ten frames. We may not use the traditional ones, but we explore the same concepts in different ways. Is a ten frame better than an ice cube tray with 10 spaces in it? What about a muffin tin with 10 cups? When our Kindergarten students first started in our class, many of them wondered when we were going to “do math.” Without a workbook, a blackline master, or a separate time for math learning, play didn’t seem like math. But now, with the amount of math talk that we do, more children realize that math can — and does — happen everywhere, even around the eating table.
And even better, children see themselves as thinkers and doers of math: true mathematicians. Isn’t this one of our goals as educators? I realize that embedding this authentic math through play can be harder as children move up in the grades, but then I see examples such as the many ones here — what a Grade 6 teacher in our Board does — and I realize that it’s still possible. I wonder how many of these students view themselves as mathematicians. Does this change their mathematical mindset? Imagine if we all started the school year telling students that they are mathematicians, and helping them believe it. Would something like this make a difference to how students see themselves as mathematical learners? I know that I teach some of our youngest children, but maybe there’s something that we can all learn from the Kindergarten Program Document. What do you think?