Fun While it Lasted

The first group (sixth graders) arrived in my classroom after what appeared to be an intense recess. They were, all of them, either drenched in sweat or nursing some kind of injury.

I surveyed the carnage. Turns out half their class was absent this day as well.  I decided that dancing was not in the cards.

"Okay guys," I said, "come sit down near me. Let's talk about our options for today."  I outlined my plan. They had played around with the straws and pipe cleaners last week and loved it.  I had given them a chance to figure out for themselves how the materials worked and they loved the experimentation and play, even going so far as to exclaim "This is better than Xbox!"

Today, I wanted to challenge them.  I showed them a sheet with pretty good but not overly helpful illustrations of the Platonic solids.  I told them they could work individually or in teams - the goal was to see if, as a class, they could make at least one of each solid.  Most chose the octahedron, surprisingly. But by the end of class when the three-person team was finally, after a lot of muddling and helpful argument, finishing up their icosohedron, a bunch of other kids decided they wanted to make one too.

Since class was almost over at that point, it was a race down to the final possible minute.  Because once you make an icosohedron, you also have to spin it!

I love how certain aspects of this solid are made more obvious through...movement!

Later that day the fourth and fifth graders were more up for dancing but they also got a chance to work a second time with the straws and pipe cleaners.  Their particular challenge this time was to build something using an odd number of edges in their starting shape.  This essentially meant three (triangle) and five (pentagon) as the base shapes.  They grumbled. Some made squares anyway.  I reminded them of the challenge.  They grumbled some more but then...

Play Power

Although I know it already, it never ceases to surprise me just how true it is.
 
Learners of all ages need the opportunity to experiment with a new medium before putting it to its more formal or expected use.  Often this kind of activity is called 'playing around' which I often perceive as a derogatory term in relation to learning.  But, in my experience, if you observe children at play long enough and really pay attention you will be astounded by the myriad of ways they are representing their knowledge, understanding and mastery of a subject.  Play and exploration are not wasted time.  In fact, I think it is exactly the kind of activity that builds the foundation of real understanding.

Here is a case in point from a recent Math in Your Feet Family Night.  Having finally found success using straws and pipe cleaners as a math toy and building material with my own first grader, I decided to include it in the Family Night for the first time.  I made some models of polygons and polyhedra, gave the station volunteer a quick orientation, and left the materials to be discovered.

Immediately, it was the most popular station of the eight offered that night.  As the children descended, the adults followed, providing lots of helpful advice and some modeling...

...which the kids politely and assiduously ignored as they confidently forged ahead.

This initial inclination to explore the materials on their own terms was fortified by the fact that this was not officially 'school time'.  There was no pressure to do things 'right', or follow the rules, or learn and use proper technique. 

As a result, most kids cheerfully ignored the formula for folding a pipe cleaner in half and making a nice right angle before inserting it as a connector between two straws, and instead found their own twisty or unequal ways to make it work. 

Most also ignored the nice models I had made and created their own.  I had never heard of a hexagon cube, for example, but there it was! 

They were having a grand time 'playing around' when I noticed something amazing happening.  After a very focused exploration period, they started discovering the rules on their own!

This little one, two years old according to her brother who sat beside her, had been methodically putting pipe cleaners into the straws, one after another.  It looked like a little gallery of Q-tips, someone joked.

She was working on her own.  She must have been at it for thirty minutes and then...she started connecting straws together!

Voila!  A hexagon.  No one, I suspect, expected much out of a girl so young.  And yet, there she was discovering the materials and watching others around her, ultimately creating something for herself.  I'd wager that if someone had insisted on sitting her down and showing her how to make a hexagon, she might have been less interested, engaged, focused and, ultimately, successful. 

Children much older also experienced this same progression.  Check out what her brother was building, below. 

Kids kept coming up to me wanting to know if they could have the dodecahedron I made as model for the night.  Sort of like a door prize?  I said, "Well, no, that one's mine.  But you could make your own!"

Only one girl decided to make one for herself; she also really wanted me to sit next to her while she figured it out.  I provided moral support for about five minutes, and then had to 'go do something...'  A few minutes later, she came and found me with a question and, still later, enlisted support from another adult so she could finally finish it.  But you know what?  She did all the work, she just needed help 'seeing' the structure and pattern.  If we had had more time she and I could have talked  how to make all the angles congruent so it would be more regular but, still...what a prize!

So, what kind of learning was happening during all this 'playing'?

I heard a teacher mention that this activity reinforced the learning they were doing in class about corners and sides.  Yes, and so much more.  

The side of the shape becomes a shared edge.   You only need one straw for each edge.  The more you build on to your initial shape, the more this aspect of intersection and sharing is apparent.

A vertex can be created from the intersection of two, three, sometimes even five different lines/edges.

Depending on what polygon or polyhedron you're making, the pipe cleaners need to be bent at different angles.  An equilateral triangle's angles are different from a square's which are different yet again when you create a hexagon, or a pentagon.  These are properties you might not truly understand unless you had to make them yourself.   And, when every angle in a shape has to be the same, and you're the one who has to make them that way, you truly build a new understanding of 'sameness'.

And that's just the math stuff and just what I noticed while watching them build.  I'm sure there's more.

All in all, a good evening's work.  I think my new definition of success is when my project idea is just the starting point and, over the course of the 'lesson' not only do multiple right answers emerge but the children are satisfied with their efforts. If the resulting mess is any indication, I'd say it was an entirely satisfying evening. 

Our New Math Studio

We've had a bunch of visitors in the last few days.  We show them around our house.  They see the ten million stuffed kitties.  The see the kid's collection of old books, including the 120 year old speller and the 80 year old (very cool) atlas.  They see the fantastic, never-ending headstand (hint: not mine).  And then they walk into our sun room.  "What is that?" they ask.

Why, it's our new math studio, of course!  Here is the inside view for those lucky few who can fit in the door:

This is what you'd look like from the outside if you were sitting inside it.

Here is the new math studio in use:

And, here is an example of something that might be made inside.  In this case, start with a cube and, um...square it?  Cube it?  Make a cube out of cubes?  (We're both still learning about this math stuff.) 

"I want the inside to be a different color, Mama, so you can see where the middle is."

We have what we call our 'making studio' in another part of our house, and we make a lot of math these days, so it makes sense the kid would think of our new installation as a math studio.

How did we make this wonderful structure, you ask?  Lots of newspaper, tape and pipe cleaners. You can read all the details here.

And the Award for Favorite Platonic Solid Goes to....

After constructing all the Platonic solids out of straws and pipe cleaners (some with my daughter's help) our favorite platonic solid is hands-down the icosahedron.  I made this one with one green pentagon end, and one yellow pentagon end.  It 's strong and sturdy, spins well, like a top, and is fascinating to look at from every angle!

Here's another view:

In a past post, I observed that illustrations of these solids are rarely to scale.  I wondered how a icosahedron would compare to the unwieldy dodecahedron I made.  Here's a family portrait of all the platonic solids, all constructed with six inch edges.  See what you think:

Yup!  Looks like a family, to me (Papa solid, Mama solid, sister solids, baby solid, lol)!  But, clearly, the icosahedron, despite more faces and the same number of edges, is smaller than the dodecahedron.  For what it's worth, I guess I have my answer about the scale issue. 

Hmmm...I wonder what I should try next?  And, here's a question: if the kid's not involved in the making, would my obsession be considered parental neglect, do you think, or could I just call it 'enriching her learning environment'?   I'm thinking about one of these (source), something truncated or stellated...

Making Math: Big Dreams of Building

We are going to build a cottage.  That we can live in.

We are building it out of straws and pipe cleaners.  We started with one cube and attached another to it.  You should have seen the kid's jaw drop -- it was like magic.  And, did you know that after the first cube you don't need to make a complete cube ever again?

I quickly figured out my methods, but it was hard for my six year old to keep up with the precision.  To attach the straws use half a pipe cleaner folded at each end, then bend it into a 90 degree angle and slide the straws on. 

Unless of course you are attaching your cubes together.  In that case you make one folded end for the open straw, and slide an unfolded end into the attachment point. 

But that's just what I discovered and, honestly, half the fun was in trying to figure it out!  I suspect there are a lot of right ways to go about doing something like this.  If you decide to try building like this I'd love to see pictures of what you make!

In the end, the kid and I worked as a team for a while and then she left to rehearse her show which opens with the song "The Moral of the Soggy Hat" (an original number).  I imagine this building activity continuing mostly on mama power, but that's because I have ulterior motives.

I get to do a ten-day version of Math in Your Feet this summer for some inner-city programs for kids ages 6-12.  In addition to rhythm and pattern in the feet and hands, we'll be exploring what else you can do with a pattern unit, which includes building!  I can imagine, over two weeks, the older kids will have built something really cool.  And if they get really good at it, I might suggest trying to construct something out of tetrahedral units just for fun!  But I think I should try it out first, just to get a sense of what the pitfalls might be. 

As for my girl?  She's all for building something she can live in, even if it's made from drinking straws. "But Mama,"  she said, "Will I have any privacy?"