Happy Anniversary!

...and I nearly missed it.  Just this week I was thinking, "Gee, I think I've been blogging for about a year now.  I should go back and check the date."

I remembered just now, and good thing, too.  It's been exactly a year today since my first post.  I had just submitted my article for peer review to the Teaching Artist Journal and felt I had more to write.  And write I did.  When I started I didn't really know if anyone would read this blog; I haven't had a ton of readers, compared to other blogs, but am so grateful for the folks who have subscribed, followed, checked in, and commented. 

This blog has been a chance for me to illustrate and explain my work integrating percussive dance with elementary math topics, describe my work as a teaching artist more fully, and make connections between math, dance, and other similarly creative pursuits.  It's not really all over the 'map' but I do recognize that this might be categorized as a 'multi-topic' blog. That's fine with me -- I enjoy having multiple interests that intersect in sometimes fascinating ways over time.

This space has also been a way for me to connect with really interesting and smart folks in the mathed world, folks who have been really patient with me as I ask questions, share my ideas and generally expand my understanding of math thinking, topics and practices.  Sue VanHattum at Math Mama Writes, Maria Droujkova of Natural Math, Julie at Living Math, and Bon Crowder at MathFour have all provided wonderful support, forums, and conversations as I explore the world of math education.

It's been a whole year, but I feel like I'm just getting started.

Supporting 'Math Values in a Rich Context' / Origami as Math

I see a lot of geometry in origami but have always wondered what other math you can find in this kind of paper folding. 

Here is what Maria Drujkova had to say about origami during a recent blog post about the activities in her Natural Math Club:

Origami has the same values as mathematics, such as precision, modular reasoning (“bird base” as a group of folds), attention to detail, modeling, algorithmic thinking… Thus origami can be used to support math values in a rich context. The same goes for music.

I love the idea of supporting math values 'in a rich context.'  I love even just the idea of a 'rich context.'  I think all learning should happen in such a place.  Onward.

Book Giveaway: Square Cat

Over at love2learn2day there's a fun giveaway of the book Square Cat, by Elizabeth Shoonmaker.  You can find a review and lesson plan of the book there as well.

I just had to repost this because we are all into cat-based education here at our house.  There's more to this story but, for now, I will just say:

Check back soon for the results from the KITTY CENSUS.

Conversational Math: Part Two

In trying to capitalize on the kid's penchant for 'talking math' I recently decided to try a game with her that I found in the booklet that came with our set of Cuisenaire Rods. 

The game is called Build What I Have.  One person describes a design they are making with their rods and others try and reproduce that design by listening closely.  One of the main points in this game is to introduce and/or reinforce math vocabulary.

The suggested age range for this activity is 2nd-8th grade; even though the kid is a young six I knew we could still get something out of it.  I decided that, to start, I would capitalize on concepts she already knew (parallel, points, edges, top, bottom, sides, etc.) and introduce some new ideas (perpendicular, horizontal, vertical). 

The rest we'd muddle through somehow, I figured, but she did surprise me by knowing her lefts and rights.  "We've been doing that in ballet class, Mama," she stated mater-of-factly.  Fabulous.

To start, we hid our designs from each other.


This is the first design.  I led and she followed, trying to make her design match mine by following my instructions. I started by saying: "Lay your blue rod parallel to the bottom of our work surface."  She already knows the concept of parallel really well, often times finding and noting examples of parallel lines when we are out and about.  "Then," I continued, "take your green rod and place in perpendicular [holding the rod in the air] up and down like this, and place the end in the middle of the blue rod."  Success!  Our designs matched!

This is the game she led.  To start she told me to put my orange rod parallel to the bottom of the workspace, but about an inch up.  The second orange rod was to be 'a couple' inches above the first one, but when she told me to put the blue rods on the sides to 'make a rectangle' I clarified the distance.  "Looks more like three or four inches, to me," I said.  I asked her to clarify the placement of the blue rods -- do they go on the outside ends of the orange rods, or inside?  Notice that this design is mostly made up of parallel lines, a concept she is most familiar with.

This is the second design I led.  I said, "Take your three light green rods and put them so they are together and vertical, up and down, in your workspace...Oh look!  They make a nice little cube!"  At first she thought she needed a fourth one to make it a square, but I clarified and said we're not making the outline of a square, but a solid shape.  When we revealed our designs to each other we saw some differences! 

This is how she recreated my instructions.  The white cubes are essentially in the right areas, but I had actually challenged her to put each white block 'point to point' with each corner of the light green square.  The dark green rods are essentially in the correct place; I knew that was somewhat complicated to execute.  And, I just noticed, the light green rods are horizontal, not vertical.

This is the last design in our session, which she led.  Perfect!  She wanted to use a bunch of different rods, but everything is still parallel here.
 
Here is what I find fascinating:  

My daughter's designs were much simpler today than normal and I think it might be because she had to describe what she was doing as she built them.  There is an equivalent experience that I find to be true in my work with 4th and 5th graders as well.  Often times I tell those kids that they are doing complex mathematics in their bodies and grade-level math on the page; they understand more math in their bodies than they can communicate through words or symbols.  Sometimes it is impossible for them to notate their Jump Patterns because they are just too complex for their current stage of symbolic mastery.

Often kids can do, know, and understand way more than they can communicate symbolically.  If we only judge a kid by her output on paper, we're not really seeing the whole child.  There are many ways represent comprehension: we need to listen and watch carefully for other indications of understanding as well. 

It wasn't too long ago when I brought the word 'parallel' into my daughter's universe.  It will be exciting to observe her body and conversations show me she's 'got' the concepts of perpendicular, horizontal and vertical. 

Conversational Math: Part One

Being able to use math terminology freely and appropriately is a big goal in elementary math education.  In my opinion, there's no way you can really use math vocabulary intelligently unless you've first had a chance to experience the concepts in a concrete manner.  This is a huge part of what happens during a Math in Your Feet residency -- I am never surprised when an astonished teacher tells me: "I can't believe how easily they're talking about math!"  It would not be an exaggeration to say that most of us need to do math with our bodies in some way before we can talk about it.

Much of the math my daughter and I do together is hands-on and verbal; as a learner, she is best served by conversation.  We'll be in the car on the way to somewhere and she'll spurt out some new computation she's been working on in her head and with her fingers.  She may only be working with numbers one through twenty but, based on the frequency and variety of these kinds interchanges, she seems to be going pretty deep into her questioning. 

The other day I wrote Maria Drujkova from Natural Math with a (very) basic math question: 

"My daughter is telling me all the different ways she can 'make ten'," I wrote, "what's that called in math language? You know, 2+8, 6+4, 9+1...?"

Maria, being the awesome person she is, got right back to me:

"These are called 'number friends' by elementary teachers. 10 is important as the base of our number system. She is playing with a newly-discovered idea of an 'equivalence class.' You can try it with other things. For example, numbers whose difference is her favorite number (10, 2, whatever) - like 15-5 or 12-2 or 99-89. It's a road to ratio and proportion, too - which come up a lot in music signatures and dance!"

Thanks to Maria, it appears my daughter and I will have a lot more to talk about, well in to the future! There are other ways we are talking math these days, as well.  You can find out more in Conversational Math: Part Two.