The Cute-Purposeful Dichotomy

Cute.

Activity.

These are two words that I hear a lot as a kindergarten teacher, and they make me cringe.

Language is powerful, and as someone who is deeply interested in how teacher language affects the way children form identities as mathematicians and define for themselves what it means to “do math,” I spend a lot of time thinking about words.

Now, if you’re a user of “cute” and “activity” you may have stopped reading already, but I hope not. Because recently, I’ve been wondering if I’ve created a dichotomy between cute and purposeful where perhaps there shouldn’t be. So maybe you can offer me some new thoughts.

I have always defined cute as the antithesis of purposeful and meaningful. When a visitor comes into my classroom, looks at what my children are doing and responds, “They’re so cute.” “What a cute activity! You are so creative!,” I usually give them a piece of my mind.

I sometimes have to restrain myself from stepping up on my soap box and saying, “All of the work I plan and the invitations to mathematical play I extend come from serious consideration of what message I am sending about math.  I think, “When I ask my students to work on this problem, what message are they walking away with about what math is?” When I question their thinking and ask them to explain their thoughts or listen to the thoughts of others, I think, “What am I showing them about what it means to be a mathematician?”

Cute is not the message I’m looking to send. Activity, to me, means purposeless work with no real meaning behind it. Now I’m sure I’ve lost a few readers. But if you’re still here, keep reading on, even if you disagree.

This week my mathematicians and I have been talking about different ways to measure. During our Explore time, our kitchen has been converted into a vet clinic as part of our study of heroes and power. During one investigation (I much prefer this word over activity) we measured the length of the stuffed animals from our vet clinic using Unifix cubes. As I planned this investigation, I thought to myself, “What message do I want to send about measurement as a form of mathematizing? I want to show them the usefulness of measurement.”

Our stuffed animal measurement became a “Make a Bed” investigation. ”Some of these animals in the vet clinic may need to spend the night in the clinic. They’ll need beds, but in order to make a bed you’ll have to figure out how to make one that fits the animal.”  So, away they went. Measuring, recording, and taking their recordings and Unifix cubes over to the Lego table to construct beds for the animals that would accommodate the length of the animal.”

The kindergarten mathematicians were beside themselves with this investigation. They made the animals talk as they measured them beds. “Don’t give me a small bed,” said an alligator through her puppeteer.

To a kangaroo one boy at the Lego table said, “Let’s see. Your bed is now eleven cubes long. As now I’m going to add some flowers to it, because all kangaroos like flowers.”

As I watched the measuring and constructing of beds, I felt a word bubbling up. A word I detest. Cute. Don’t worry, I didn’t say it aloud. Banish the thought! Is it possible for mathematicians or their work to be simultaneously purposeful and cute? Is cute always a way to belittle the importance of someone’s thoughts or work? Or is it simply a nod to the importance of aesthetic and play in our work? The talking alligator? The kangaroo’s flower bed?

I’m not sure yet, so I haven’t yet said the word aloud. Instead I said, “You really thought about how that alligator would feel in a bed that was the right length for him.” “You’re thinking the kangaroo wants a bed that is the right size and looks nice.”

So, you tell me, is there a dichotomy between cute and purposeful? I’m still figuring it out. And for now, that’s an ok place to be.

 

Math Explore-Investigate-Choice

My colleague Katie Keier, over at Catching Readers Before They Fall, has written a wonderful series of posts on Explore, a time for meaningful, rich play that is full of learning and teaching opportunities.

Katie’s post on  Literacy Explore, the term she uses for the independent practice time in which children are ”engaged and playing in a literacy activity of their choosing” got me thinking about what that time looks like in my math workshop.

This year, as I went back to the classroom as a kindergarten teacher, I did a lot of thinking about the structure of my math workshop. I knew I needed  a structure that would ensure that 1) children were given lots of time for meaningful exploration, investigation, and play within the math workshop, 2) this time would be (eventually!) independent so that I could meet with small groups for Math Exchanges daily.

I’ve gone back and forth with the language I use  for this part of math workshop. “Math Explore,” “Math Investigations,” “Math Choices.” I still don’t know what feels right, or if what I call it is even important.  I do know, however, what it is that is happening during this time that is important to me.

1) Element of choice–Mathematicians of all ages should have the right to choose work that is important to them.

(Are these presents shorter/longer/the same length as the present boxes?)

2) Purpose–Every time I plan a station/investigation I ask myself, “What is the purpose behind this?” “What message am I sending about math and what it’s all about with this investigation?”

(Which containers hold the most/least water? How can you prove it?)

3) Balance of collaboration and working by oneself–I want my students to learn how to work/negotiate/play/collaborate with a partner or group, but I also want them to have time to reflect on their own. I want this for my own work. And I want it for theirs as well.

4) Balance of open exploration and guided task–room for open play, coming up with one’s own questions as well as time to work on a specific task that needs figuring out.

(Who has more on their cards? Who has less? How do you know?)

I end each workshop with a short reflection time. Sometimes I have focused, content-related questions. And sometimes I ask the open question, “How did you work as a mathematician today?”

Subversive Teaching

This post started out very differently. I planned to write about how three of my kindergarten mathematicians solved the problem, “Three kids have a mug of hot chocolate. They are going to put ten marshmallows in each mug. How many marshmallows will they need altogether for their three mugs of hot chocolate?” Someday I might write that post. (The pictures of the kids in action on this problem are still here) But here’s a bigger idea I’ve been thinking about.

Children are powerful mathematicians. This is something I’ve written about often, here on my blog and in my book. It may seem like a simple statement, but I believe it speaks to the kind of advocacy we, as teachers, need to commit to for our learners. All children problem solve, our brains are designed for it much in same way that our brains are designed for language learning. We expect our babies to learn to talk, our children to learn to read and write, and yet, in many ways the expectations for mathematical problem solving are not the same.

Recently someone asked me if I missed my former position as a math coach, and why, when I chose to go back into the classroom, I chose kindergarten. The answer to that question is, of course, not  simple. I chose to go back to a classroom position because I missed the community aspect of having my own classroom and being with the same group of children all day. I missed teaching reading and writing (I’m more than just math ) The mathematical answer, however, was that kindergarten is a place where the informal problem-solving strategies that children develop (as early as when they are babies) can be developed and guided in amazing ways. Kindergarten is a rich environment  for instilling the idea, “You are a mathematician.” “This is what mathematicians do.” “How were you a mathematician when you…?” “What do you wonder about? And how can we figure that out?” Children can become agents in their own learning, feel a sense of ownership from the beginning of their educational career.

And yet, kindergarten is often a place where math is watered down to rote counting, number writing practice, and inappropriate (in my ever humble opinion) memorization of facts. There are textbooks and programs making lots of money off this idea that kindergartners are empty slates who must first learn to do x, y, z before they can be problem solvers. Many teachers are asked (by schools, by districts, by our federal government) to commit to these kinds of practices. I know sometimes, in some places, it feels like there is a constant struggle between teaching responsively in the way you know is best and teaching what has been dictated.

And so, here is my truest answer about why I went back to the classroom. I say this with the caveat, that this was only the right choice for me. There are amazing math coaches (I get to work with several!), specialists, and administrators that advocate amazingly for students and teachers. But the classroom is where I belong. For now.

The classroom is really the grassroots of education. Despite the fact that we teach in a time in which many teachers feel powerless to the greater forces at play in education policy, I maintain that the classroom is a powerful place for change. It’s a place to be subversive. To teach what children need. To be responsive to every child. To problem solve with your kids. To push limits. To push back when you are asked to teach/test something inappropriate.

When people ask me what I do for a living and I reply that I’m a kindergarten teacher, I often hear, “Oh how cute, you get to sing and play with kids all day.”

“Yes, I do.” And while I’m singing and playing I also help them to think about the world, to question gender roles and power, to inquire about mathematics and determine pathways to solving problems, to understand the power that comes with being able to read, to negotiate, to argue fairly.”

Some of this is in the written curriculum, lots of it is not. I hope more and more teachers consider themselves powerful advocates for their students–that we continue to be subversive in our teaching (even in small ways) in times of ever-increasing standardized education.

So, teach on, amazing educators out there. Keep up the hard, but always worthwhile work.

 

 

 

 

 

Hot Chocolate Play

My brilliant kindergarten colleagues Lauren Nye and Courtney Carroll recently came up with another engaging way to practice counting in a playful way–making pretend hot chocolate.  This counting task mirrors our Halloween Trick or Treat play in which children counted to a specific number, a different kind of task than when children are asked to count all of a collection.

Children were given a set of plastic holiday cups each marked with a number 1-20, indicating the number of marshmallows that a customer would get in their pretend hot chocolate at the hot chocolate shop. The kids loved getting into the play of it. “Oh, this person is so sad, only two marshmallows!” or “You are the lucky one. Twenty for you.” “Seven for you, nine for you, looks almost the same.” Playful, mathematically rich conversation.

As I watched them work, here are the mathematically significant information I was looking for:

1) Does the child recognize the numeral on the cup automatically? Or does she use a tool (number line, number grid) to figure out what number word/quantity the numeral corresponds to?

2) Does the child maintain 1:1 while counting the marshmallows? If not, where does he lose the 1:1?

3) Does the child understand that she needs to stop adding marshmallows at the numeral written on the cup? Early counters will often not yet monitor for the stopping number, but rather continue counting.

4) Is the child consistent in number word order? Watch for children who get lost in the teens or meld 13/14 into one number, forget the decade numbers.

Extensions:

As this task was occurring mostly while I facilitated math exchanges with small groups (with some check-ins from me), I wanted to make sure that the task was truly independent.  This task was a good fit for most of my students. For more struggling students I limited the number of marshmallow cups and taught them to use a number line or ask a friend to help them identify the numeral. Here are a couple of ideas for those who complete this task with ease.

1) Extend the hot chocolate task to larger numbers, 20-30, or 50-60. Do they start organizing in any way (by tens, perhaps) to make sure they don’t get lost in the counting of the higher numbers?

2) Give the child several different size cups. Ask: “Which cup do you think will hold the most marshmallows? The least? Can you test your estimate? When the child has filled the cup half way, “Do you want to stick with your original estimate or change it? Why?”

3) How many marshmallows do you think come in one bag? Is there an easy way you could figure that out?

Leading Into Problem Solving

And, of course, with all counting tasks, I like them to lead into problem solving. Here are some problems we will be solving when we get back from winter break.

1) ___ friends each have a mug of hot chocolate. They put ___ marshmallows into each their mugs. How many marshmallows did the friends use altogether? (Multiplication)

2) Ms. Wedekind has ____ marshmallows to put in Avery, Miguel, and David’s marshmallow mugs. She wants to make sure each child gets the same number of marshmallows. How many marshmallows will she put in each mug of hot chocolate? (Partitive Division)

What counting and problem solving tasks are keeping your mathematicians’ brains warm this winter season?

 

Number of the Day Routine

I was recently reminded of the Number of the Day routine from Jenny Orr and her first graders.

In Chapter One of my book I talk about number sense routines being a daily part of my math workshop structure, but I hadn’t done many Number of the Day routines this year. I decided the time was right for some of these.  While the charts of our conversations and thinking only show part of the picture, here’s what they looked like:

 

 

One of my mathematical purposes in using Number of the Day is to get into conversations about how numbers can be composed (built from their small parts) and decomposed (broken apart from the whole into their small parts). The conversations about “breaking a number apart” and “putting it together” were really powerful.

“Seven can be four and three and it’s still seven. Like four fish and three dogs. It’s all seven animals.”

I also asked them (idea from resource below). When would this number be really small? When would this number be really big? At first they weren’t really sure what I was talking about.

“How about if you draw a really big 5?” (see chart). That would be big.”

Then through multiple experiences with this routine over several days (that’s the power of routines!) they expanded and deepened their thinking.

“If someone had eight houses all for himself, that would be big. Eight marshmallows can fit in your hand. That’s a small eight.”

“Seven dinosaurs would fill the room. But seven tiny rocks is small.”

Exploring ideas of decomposing/composing  number and relative magnitude of numbers has broadened their understanding of how numbers work. And it’s a simple routine they love doing for five minutes a day over a period of several days. We’ll be returning to this routine many times throughout the year.

For more on this routine, check out Jessica Shumway’s book, Number Sense Routines, where she writes about using and expanding upon this routine for children in grades K-3.

Robber Bird

Now that my kindergartners have been working on acorn counting collections for a while both during our math workshop and our Explore play, I decided to add another problem solving component to this familiar context.  One current focus in our math workshop is exposing children to different types of problem and helping them internalize the structure of various problem types. I use the mathematician statement “Mathematicians listen to the story and tell it again to help them solve the problem/figure out the story.” I chose a Separate-Result-Unknown problem because I noticed that some of my students tend to automatically combine quantities in story problems without thinking about the action in the story. So, here I am back to the  idea that the math we do with our children must be 1) contextually relevant and 2) mathematically significant.

I believe the story telling aspect of problem solving is crucial for all students, but especially English Language Learners (which most of my students are). While traditional thought tells us to simplify language for English Language Learners, I actually think that the story context and story telling is even more crucial for English Language Learners in understanding story problems. Here’s the story I told about the squirrels and the Sneaky Robber Bird, and some of my teaching language from my recent math exchanges. I used a couple of simple toys to tell (and help retell) my story to help students understand what is going on in the problem.

“The squirrels have been busy collecting nuts for the winter. Show me with your body how squirrels collect nuts for the winter. The squirrels put ___ acorns in a hole. But a sneaky bird, Robber Bird, has been watching the squirrels from up in a tree. The Robber Bird swoops down (Whoosh!) and says ‘I’m gonna get me some of those nuts!’ (I have a funny voice for this line.) You say that part with me. The Robber Bird swoops down and takes ____ of the acorns (I use nuts/acorns interchangeably because I know my kids know both words) and flies away. How many acorns are in the squirrel hole now?”

“Now you tell me that story again.” (facilitate retell the story before solving the problem.)

“Now let’s figure it out. Would you like to use your notebook to draw a picture? Acorns? Cubes? Fingers? Which tool will you use?”

And later I use the reinforcing language “When you listened to the story and told it again, that helped us solve the problem.”

I’m hoping to take a video of a Robber Bird math exchange tomorrow, so stay tuned! What stories have you been telling with your mathematicians? What is your mathematical focus?

Honoring the now

I’m always looking ahead–for myself and my students. What is the next goal I will work on? What is next learning I will ask my students to take on.

Often I have to remind myself to slow down. Honor the child’s current understanding. Hover in this moment to really understand it? What is it that the child really understands? How do I know this? What questions can I ask to clarify his thinking rather than impose my own? These are difficult practices. But teaching, like yoga or art, is a practice. Commit to the practice, to the moment.

Erica Jong’s “You Are There”, which hangs in my class, reminds me of this.

You are there.

You have always been

there.

Even when you thought

you were climbing

you had already arrived.

Even when you were

breathing hard,

you were at rest.

Even then it was clear

you were there.

Not in our nature

to know what

is journey and what

arrival.

Even if we knew

we would not admit.

Even if we lived

we would think

we were just

germinating.

To live is to be

uncertain.

Certainty comes

at the end.

Imaginative Mathematical Play

In my book I talk a lot about how math exchanges must be both contextually meaningful and mathematically significant. Many times “contextually meaningful” means relevant or useful to the life of the mathematician solving the problem. However, this year with my kindergarten class I’ve been exploring the role of mathematics in the imaginative play of the five year old mathematicians.

In Virginia the days are getting cooler and we’ve been taking fall walks to look for signs of seasonal changes. We’ve noticed lots of squirrel dreys (nests–I didn’t know this word before I came to kindergarten!) in trees, but we haven’t spotted a squirrel on our walks yet. (Perhaps the squirrels see the parade of curious five-year-olds and head for the hills!?) Yesterday we set up a squirrel feeder with corn and nuts in an attempt to attract squirrels, so these critters have been on our minds.

Today I introduced some little containers covered in fabric alongside some of the acorns we have collected on our walks. “We know squirrels collect acorns for the winter. We could do some pretending with these containers. They could be dreys or holes in the ground. I wonder how many acorns will fit in these different containers? You could try figuring that out today.”

“I’m a busy squirrel!” “These are my nuts. I’ve got to get a lot for winter. Maybe even more than 30!” “Hey, 33 nuts and 31 nuts are almost the same. They look the same, but 33 is two more.”

I try to find ways to invite curiosity, play, and imagination to mathematics. Is counting acorns contextually relevant for my students? I think so. Not in a solve a real problem kind of way (We work on lots of those kinds of problems too!), but certainly in a math is playful and creative way.

And let’s not forget that math exchanges must be mathematically significant! Context is important, but it is nothing if you’re not helping kids grapple with the big ideas of mathematics. Counting (1:1, number word sequence, cardinality, number identification and writing), estimation, and comparing numbers and quantities (Which container will hold the most? Why do you think that? If this container holds 30 nuts, how many will this bigger one hold?) are all ideas that are important for kindergartners to explore deeply. These  imaginative math exchanges and contexts will lead into some story problems we’ll be working on in the next few days in which I’ll be taking a closer look at students’ strategies for various types of problems. (Stay tuned!)

So, how are you making your math exchanges both contextually meaningful and mathematically significant?

 

Math Is Storytelling

Just returning from the NAEYC annual conference in Orlando,  my head is swimming with ideas–ideas that both extend and challenge my previous beliefs. I love that hopeful and refreshed feeling of returning to my classroom after an amazing conference feeling ready to take on the world!

I want to share an abbreviated version of my presentation, “Mathematics is Storytelling: Bringing Play and a Sense of Narrative to Problem Solving” with you all. And while the slides only tell part of the story, I hope they give you a sense of all that is possible when you build a culture of problem solving and live a rich mathematical life alongside your students.

So, how are you bringing play and a sense of narrative to problem solving in your classroom?

A peek ahead…

Next week I travel to Orlando for the annual NAEYC (National Association for the Education of Young Children) conference. My presentation is called “Mathematics is Storytelling: Bringing Play and a Sense of Narrative to Problem Solving,” and it is all about using storytelling to strengthen children’s understanding of problem solving.  I thought I’d give you a sneak peek at a couple of pictures from the presentation.

This kindergartener explores counting collections and expands her ability to tell a mathematical story through Trick or Treating play.

Two kindergarteners solving a difficult problem type using an imaginative, familiar context, The Gingerbread Man.

 

 

Ahmed records his thinking for the problem, “The Gingerbread Man needs to cross 13 stones to get across the river. After hopping on the tenth stone he takes a rest. How many more stones does he need to hop across to get to the other side of the river?”

 

 

 

Ahmed records his strategy and says, “Ten stones and three more is thirteen. I just saw ten and three more!”

 

 

For those of you who will be in Orlando next week at the conference, please join me at my session on Saturday, November 5th from 1-2pm. For anyone else interested, I’ll be posting the presentation on my blog and tweeting from NAEYC sessions (@kassiaowedekind) as well!