Sunday, November 11, 2012

Living Math Monday: The Button Box

"When Tigger (one of our new kitties) is curled up like that, she looks like a spiral," Brian, my four year old, this morning observed. And she did indeed look like a spiral, the tip of her tail curling around the curve of her thigh and her nose tucked under her hind paws.

It could be that Brian's sudden and intense interest in mathematics is simply a natural development appropriate to his age. And I do think that is part of it. But the fact that his participation in mathematical conversations began in earnest about the same time Dorothy and I began our living math journey, I believe is indicative of something more than mere developmental progress.

Before we embraced living math, mathematics was a subject that Dorothy toiled at mostly alone at the table with a workbook and a set of manipulatives. I would give Brian some manipulatives to play with while Dorothy worked, but he usually tired of this quickly and would go back to his Star Wars figures. But then, we began reading Fred, and of course Brian wanted to know what Dorothy was giggling about. And all those living math books, many of them story heavy, drew Brian in. More often than not, when we sit down for a good read, he'll bring me a book from the math shelf. He especially loves the picture book bios of Albert Einstein and Pythagoras.

One book that both kids love is The Button Box, a sweet story about a little boy who loves to play with and sort his grandmother's button collection. This little story is loaded with rich mathematical fodder. What makes this story especially inviting to my children is that we have our very own button jar, which belonged to my great grandmother. And of course, with each reading of the story, we must dump out the buttons. Which naturally leads to sorting. Which leads me to Fred.

In about the middle of the first Fred book, the author introduces set theory, something which I vaguely remember from high school math, a concept that I never could make heads nor tails of. It was just another process to memorize.

In chapter nine, Fred is looking out over the campus lake, and notes the absence of alligators and ocean lines in the lake. He also notices that there are zero birthday cakes floating on the lake. He then goes on to say that while it might be difficult to name a set which contains exactly 5 members

{Monday, Tuesday, Wednesday, Thursday, Friday}

it is easy to think of a set containing zero members. He then goes on to list a host of sets which contain zero members. Thus, Fred introduces the young reader to set theory, a concept which Fred returns to again and again. Dorothy and Brian enjoy playing a variation of I Spy, in which Dorothy or Brian names a set and I must guess the members of the set. For example, Dorothy says, "I'm thinking of a set with 3 members in it." I throw out a few guesses, "The number of televisions in our house." Wrong. "God the Father, God the Son, God the Holy Spirit." Wrong again. "The number of cats in our home." Third time's the charm. Right I am.

The Button Box fits right into Fred's obsession with sets. Although the book never uses the term sets, it is very natural to point to the page with shoe buttons and call the buttons a set instead of merely a group. This is one of the things I very much love about Fred. Grouping, a skill usually introduced at the elementary level, is given the term "set." On page after page, sets are written out complete with brackets. It is my hope that one day when my kids are introduced to set theory in higher mathematics, they will remember Fred's musings and our "I'm Thinking of a Set" game, and set theory will make perfect sense.

The past week, we've played with buttons quite a bit. Dorothy and Brian love making their own little piles, shifting them around from set to set, changing the parameters. Brian pulls out all the blue buttons, which drives Dorothy mad because he must borrow from her cloth and metallic button sets to do so.

One day last week, I had Dorothy sort the buttons into sets, a task which took her nearly an hour (there are a lot of buttons.) When she finished, I told her to pick 4 sets, and then write out each set's description ala Fred. I was amazed by her description of one set in particular. The third set contained three members: buttons with a pattern of concentric circles and three parallel lines. And yes she used those exact words.

We put the buttons away, but the last set, the set containing 27 metal buttons, I pushed into a Ziploc. The next day I shook the metal buttons from the Ziploc and told her to make sets from the metal buttons. She played with them for awhile, pushing them into piles, then shifting them around. When she finished, she had three sets.

{Metal Buttons with 2 button holes} 4
{Metal Buttons with shanks} 14
{Metal Buttons with 4 button holes} 9

We discussed subsets for awhile and I pointed out that all of her sets involved how the button is connected to the fabric with the thread.

Then I drew this for her, showing how sets can be shown with pictures. The largest circle represents the jar which contains the buttons. Within that set their are a multitude of sets. I explained how each circle can intersect as each set might contain buttons with the same properties as buttons from another set. I showed how each subset could be broken down, broken down, broken down. I also showed how each set could be contained by a larger set, which could be contained by an even larger set. For example, the button jar sits on the table and the table sits in the dining room which is only one room in the house which is only one house on our street . . . She said, "It's just like in Zoom," an ingenious book that starts with a narrow focal point, and each page pulls back just a bit giving the reader a wider perspective, until the reader arrives at the last page which shows the earth, just a tiny speck in the universe.

Then I found these pictures on her desk last night.

A veteran elementary math teacher once told me that the sign that a child really understands a concept is that they internalize it and are then able to apply that concept to areas outside the given parameters. I think these drawings are a good indication that Dorothy has a pretty good grasp of the concept of set theory and shifting perspectives.

When my Memaw removed buttons from shirts and overalls all those years ago, she could have never imagined to what use those buttons would eventually be put. But I do think she would have approved.

I can almost imagine the years rewinding,
or zooming backwards,
the set parameters moving
ever inwards

until my minds eye arrives

at that moment when

the first button


the glass jar


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