# Public Math

This is Molly.

This is Chris.

Molly is a math leader who lives in Vancouver, WA and started a project called Math Anywhere. Chris lives in Chicago where he supervises secondary math for the Chicago Public Schools and leaves math in places for others to find.

I met each of them through the work of this blog, and through Math On-A-Stick. We agreed that it would be fun to have some together this summer to brainstorm and prototype new forms of creative, playful math engagement for people in unexpected places.

One thing to know about me if we ever have the chance to work together is that I don’t work small or slow. One year I got the idea for Math On-A-Stick; the next year it was up and running at full scale at the nation’s second-largest state fair.

That tendency of mine turned an afternoon with Molly and Chris into a 48-hour extravaganza we’re calling the Public Math Gathering. With the generous support of Desmos and CPM, we added seven more amazing folks to our guest list and got started planning.

This is Morgan.

Morgan teaches at South High School in Minneapolis and runs a math circle at the Rondo branch of the St Paul Public Library each summer. We brought Morgan on board to help us plan and execute this work.

This is the whole team, including the four named above and our friends Aeriale Johnson, Manju Connolly, Lamia Abukhadra, Andrés Lemus-Spont, Amy Nolte, and Lara Jasien.

Together, this team includes designers, artists, elementary and secondary teachers, researchers, writers, and teacher educators.

Here’s how we have spent our time.

On Friday evening, we walked the boundaries of the Midway, Macalester-Groveland, and Frogtown neighborhoods of Saint Paul looking for opportunities for mathematical provocations. Here are some things we noticed and talked about.

On Saturday, we volunteered as a group at Math On-A-Stick, and then went off-site to do two pieces of work:

(1) Break down and critique our experiences at Math On-A-Stick, and

(2) Design new math provocations for new contexts.

Our reflections on Math On-A-Stick involved these questions:

• Who was there?
• Who was not there?
• How did you notice those who there engaging with the materials and the space?
• What are the affordances of the Minnesota State Fair as a place for designing math interactions?
• What are the limitations?

Our design work followed from this invitation:

Let’s design place-based opportunities for [X] to engage in math provocations that are [Y].

We filled in many possibilities for X and for Y. For some of us, X might be children or teenagers or families or the math anxious. And Y might be delightful or memorable or identity-changing or surprising.

We moved on to prototyping, and we’ll test drive some new ideas at the Fair on Sunday morning.

# Let the children play

Talking Math with Your Kids has been on something of a summer hiatus as I’ve geared up for Math On-A-Stick at the Minnesota State Fair. It has been a wild ride.

I have spent the last four days playing and talking math with kids of all ages for eleven hours a day.

My number one message coming out of this work is Let the children play.

Have a peek at our flickr photo albums to see what’s been going on. Here’s a sample (Thanks to Kaytee Reid for sharing these beautiful images).

I have been paying close attention to how children behave in this space we’ve built. I’ll just write about the plastic eggs today, but they stand in as an example for all of our activities.

When children come to the egg table at Math On-A-Stick, they know right away what to do. There are plastic eggs, and there are large empty egg cartons. The eggs go in the cartons. No one needs to give them instructions. (This is by design, by the way.)

A typical three- or four-year old will fill the cartons haphazardly. She won’t be concerned with the order she fills it, nor with the colors she uses, nor anything else. She’ll just put eggs into the carton one at a time in a seemingly random order.

But when that kid plays a second or third time, emptying and filling her egg carton—without being told to do so—she usually begins to see new possibilities. After five or ten minutes of playing eggs, this child is filling the carton in rows or columns. Or she’s making patterns such as pink-yellow, pink-yellow… Or she’s counting the eggs as she puts them in the carton. Or she’s orienting all of the eggs so they are pointy-side up.

The longer the child plays, the richer the mathematical activity she engages in. This is because the materials themselves have math built into them. The rows and columns of the egg crate; the colors and shape of the eggs; the fact that the eggs can separate into halves—all of these are mathematical features that kids notice and begin to play with as they spend time at the table.

We have seen four-year-olds spend an hour playing with the eggs.

I have observed that the children who receive the least instruction from parents, volunteers, or me are the most likely to persist. These are the children who will spend 20 minutes or more exploring the possibilities in the eggs.

The children who receive instructions from adults are least likely to persist. When a parent or volunteer says, “Make a pattern,” kids are likely to do one of two things:

1. Make a pattern, quit, and move to something else
2. Stop playing without making a pattern

We adults have a responsibility to let the children play. We can be there to listen to their ideas as they do. We can play in parallel by getting our own egg cartons out and filling these cartons with our own ideas.

But when we tell kids to “make a pattern” or “use the colors”, we are asking the children to fill that carton with our ideas, rather than allowing them to explore their own.

Here are some ideas children have explored in the last few days. I look forward to the next week’s worth of wonder. (Photos all shared by visitor and volunteers through Twitter and Intagram—handles are in the image titles. Many thanks to all for your generous sharing.)

# Help Wanted: Math on a Stick

UPDATE:

The updated post about Math On-A-Stick is here.

Here is the Math On-A-Stick page on the Minnesota State Fair website.

ORIGINAL POST:

I want to tell you about a vision of a beautiful thing, and I want to ask you to help make it happen.

Math on a Stick logo by Emily Bremner Forbes, who makes beautiful things. Many thanks, Emily!

Math on a Stick will be an annual event at the Minnesota State Fair (12 days of fun ending Labor Day!) that engages young children (4—10 years old) and their caregivers in informal mathematics activity and conversation using the Fair as a context.

• Parents will push children on a protractor swing so that together they can notice the angles and fractions of a circle the children travel through.
• Parents and children will use beautiful tiles to make shapes and intriguing patterns.
• They will comb the fairgrounds looking for groups of many different sizes, asking questions such How many mini donuts are in a bag?, How many sides does the Agriculture-Horticulture building have? and Why is it so hard to find a group of 17?
• They will notice the rotational and reflection symmetry in a wide variety of plants and flowers, then copy these symmetries by making a paper flower to take home.

Math on a Stick has four components:

1. The Math-y Midway
2. The Garden of Symmetry
3. The Number Game
4. Visiting mathematicians and mathematical artists.

Find out more about each of these below.

The major question now is whether Math on a Stick happens for the first time this year or next. The organizing body is the Minnesota Council of Teachers of MathematicsThe Math Forum is by our side. Max Ray and Annie Fetter from the Math Forum plan to come to Minnesota to help run the event. The Minnesota State Fair and Minnesota State Fair Foundation love the idea. We just need to convince all parties that it is possible to pull this off in the coming three months, and we need to locate the funding to make it happen.

We’ll need help with three things:

1. Volunteer hours this summer, before the Fair
2. Volunteer hours during the Fair
3. Funding

Of course I expect that most who heed this call will hail from the great state of Minnesota, but I encourage others to consider scheduling a visit. This will be a wonderful event, and the Minnesota State Fair is truly a grand spectacle.

## Volunteering

Before the Fair, we’ll need help finding and creating the things that will make the event go.

During the Fair, we’ll need help staffing the event. It runs 9 a.m. to 9 p.m. August 27—Sept. 7. We’ll have have about four shifts a day and we’ll require multiple people staffing each shift.

If we get Math on a Stick up and running this summer, one of our first orders of business will be to establish our volunteer website. Please check your summer calendars, pencil us in, and keep an eye on this blog for more information.

## Funding

If you (or someone you know, or an organization you are involved with) are in a position to help fund Math on a Stick, get in touch with the Minnesota State Fair Foundation to let them know you’d like to help make this happen. Our overall budget is on the order of \$20,000.

# The specifics

Here are specifics on the four components of Math on a Stick.

## The Number Game

The major activity at Math on a Stick is The Number Game. Adapted for math from the Alphabet Forest’s Word Game, children and parents are challenged to find groups of every size 1—20 at the fair. Examples: A corn dog has 1 stick, a cow has 4 legs, the Ferris Wheel has 20 carts.

Players receive a form they carry with them around the fair to record their findings, and can return with a completed form to claim a ribbon. Additionally, players can email, tweet, and post to Instagram, their Number Game fair photos. These are curated by Math on a Stick volunteers and posted to a public display that resets each day so that collectively State Fair attendees recreate daily a new visual answer guide to the Number Game.

## The Math-y Midway

A protractor swingset, tables with fun tessellating tiles, and images from Which One Doesn’t Belong? and a (forthcoming) counting book to play with and discuss.

## The Garden of Symmetry

Flowers are grown in planters along a path. As you walk from one end of the path to the other, you pass flowers with increasingly complex symmetry. Grasses (with one line of symmetry) are near one end. Irises are a bit further along (with three rotational symmetries), and sunflowers are near the far end (with MANY symmetries). Visitors to the Garden of Symmetry are invited to carry a tool consisting of two small mirrors taped together to investigate symmetries in the garden and the interpretive signage.

## Visiting mathematicians and mathematical artists

An activity area is set aside for a daily visit from a mathematician or mathematical artist. Each provides engaging, hands-on math activities during a scheduled period each day. We will draw upon talent from Minnesota, as well as nationally (budget allowing).

For full details on the event, have a look at our Math on a Stick white paper.

Hit me in the comments with any questions you have.

Get in touch with me through the About/Contact page on this blog.

# [Product Review] Candy Mega Buttons

This is our first audience-participation post.

I bought these at the Minnesota State Fair last summer.

When you open the package, here is what is inside.

(Click for larger version of this image, which you are free to download.)

I am curious how my readers would use these to talk with their children. Please feel free to post hypothetical as well as actual conversations in the comments.

There is no one right answer for this activity. See what fun you can have with them in your home, and report back!

# Summer project (3 of 3)

We went to the State Fair last week.

Having wondered about the height of the Giant Slide, and having developed a technique for measuring things, we needed to collect the information required to answer our original question.

The only problem? No one but me wanted to ride the slide. This is a big change from previous years.

I went up alone in the name of mathematics.

There are 104 steps to the top.

I asked a young woman employee how many steps she thought there were. She said 108. I told her my count and she was ready to believe it. I asked a young man employee how many steps he thought there were. He had no idea.

How can you work at the top of that thing and not be curious how many steps there are?

In any case, should someone wish to check my work next year, I got 1 set of 20 and 3 sets of 28.

I also took a kebab stick from Griffin’s dinner along with me. I broke it off at the height of one step partway up. I checked it against another step further up. Then I taped the stick into my notebook when we got home.

May not be actual size on your screen.

So then Griffin and I sat down one morning to finish this off. Recall our guesses of 40 and 45 feet.

It was a fairly conventional conversation, so I’ll just list the bullet points instead of trying to reconstruct our exact words.

• I asked him to estimate the length of the stick, which he did—4 inches.
• He measured the stick with a ruler—$4\frac{1}{2}$ inches.
• He suggested a calculator was in order.
• I suggested that this would not be happening.
• We sought to find $104\cdot4\frac{1}{2}$.
• He naturally subdivided this into $104\cdot4+104\cdot\frac{1}{2}$.
• His first answer to $104\cdot4$ was 408; on further reflection he got 416.
• I was a useful resource for remembering intermediate results (such as the 116).
• Half of 104 was easy for him.
• We ended up with 468 inches.
• He knew we needed to divide this by 12.
• I modeled an intelligent guess-and-check strategy for doing this by asking him to guess. I did the multiplication. You can see the results below.

For the record, I spoke aloud while doing these. E.g. “Two 45s is 90; ten 45s is 450, so 540” Et cetera

Upon completion of our analysis, Griffin wanted to know how high the Sky Ride is.

Success.