Vignette: Noticing, exploring, and discovering space with moving bodies

Today was my second of five days with three classes of 4th graders. Today Mr. C, whose class needs to be with me at 9am, smoothed out his morning routine and told them to come straight to the LGI room. Kids trickled in from buses, drop-off, breakfast, etc. In the absence of any particular activity the kids immediately started exploring the empty space. 

The activity mostly consisted of jumping from box to box and eventually led to discussion about which leap was the furthest and most difficult. 

I am a big fan of self-initiated explorations of space like this but after a while there were too many kids in the room to do this safely. Luckily one kid wanted to try out my dance board which led to a wonderful round robin of dancers, all being cheered on by their friends. So cute!

If you change a familiar space with tape kids will notice. When they notice they will explore this new structure with their bodies through movement. When they explore you will see how they are thinking. In this case their exploration was spatial and also mathematical in terms of magnitude and direction. 

Power

You are nine (or ten, or eleven). You have power.

You think mathematically while you move.  You make your own choices about how far to turn and in which direction, what kind of movement to use, where to put your feet, how to combine your patterns and whether to transform your pattern with symmetry.

Your choices are good, especially when they take time to perfect. 

You can enjoy the process...

...or not.

You can have fun and work hard at the same time.

You can be the one who usually gets sent around the building 'for laps' because you can't focus in class, and yet, in this case, you are the one who makes up the most fantastical, awesome pattern ever.

You marvel at how fast an hour goes.  Where does that time go?

It goes into your feet.

You have agency over your body, your brain, your ideas, and your learning.

Now that is power.

[It's also images of Math in Your Feet in action!  Photo credit: Ryan Richardson.]

Sneaky Math: You Know, UNO!

My six-year-old daughter is hip to my game.  You know, that I'm interested in stretching and deepening my personal understanding of what math is and how we make it.  She has become highly sensitive to moments where I might be trying to teach or show her something math related.  She's on to me.  She calls me, accusingly, "Math Mommy!" 

This is an attitude shift, actually.  Back in September, when she had plans to run away with her best friend, she very clearly relied on me to help her learn the math she would need for when they finally headed out into the wilderness. (Or, the elementary school playground, which has a huge field and lots of trees around the edges.  Whichever.)

Now, however, she wants nothing to do with me and my math.  And, after being quite self-motivated and curious about measuring, comparing amounts, comparing sizes, spontaneous chant counting by tens and twos, relationships between numbers, and relationships between shapes the whole summer and fall, her inquiry into all these things has slowed somewhat.

Except, she has become a W-H-I-Z at two person UNO.  We are UNO addicts; we play UNO every day, sometimes twice a day.  UNO perks us up: Having a bad day?  Let's play UNO!  Been in the same argument loop all morning?  Let's play UNO!  And, yes, I know there is math in this game but DON'T TELL HER!!!  Honestly, I have been giddy with glee that I now have an outlet to influence her mathematical thinking and move her math skills forward without her knowing!


Well, I mean, she knows she's adding up points, for example, but she wouldn't do it at all if I just asked her to outright.  She's already shot down my suggestion that maybe, perhaps, we could, let's say put down a 3 and 4 to match that yellow 7 that's on top of the pile?  "Math Mommy!  I just want to play the game!"  So, I've come up with my new 'sneaky math' approach.

What she doesn't know is that, faced with such perceptive resistance, I'm loosing on purpose (sometimes) and I'm quite gleeful about the way that it's working out.  I hand her my handful of lost points and say, "How big a win was it for you?!" giving her an opportunity to be very specific about the magnitude of her victory.  I'll casually say, "How many tens can you find?"  or "What's fifty plus twenty [Wild Draw Four + Skip cards]?"  As a result she's naturally skip counting by tens and sometimes fives, easily finding different combinations of numbers to make ten, adding numbers to sums way past twenty, using her fingers less and less and, in the process, improving her capacity for mental arithmetic.


Examples of different ways to make 'ten'.  I've somehow found my way to guiding her to find as many tens as possible and add those up first, which capitalizes on her love of tens, hundreds, and thousands.  We did get stuck today, though.  She found two 10's but then we were stuck with three 6's.  In the end I got out the paper to show her the 'easy way' to finish up the adding, thus sneaking in a little two digit addition on paper.  She balked a bit, but I said, "How are you going to know if you beat me or not??"  That was motivation enough!  (I'm still not sure, though, when to bring in a calculator.  I'm pretty sure being able to mentally calculate numbers is an important life skill in many ways, so I'll stick with fingers, skip counting and the occasional paper and pencil for now.)

She is quite publicly gleeful herself as she gloats about the magnitude of her victories.  Me? I am secretly thrilled that I've found a way for my incredibly enthusiastic and fiercely independent learner, enigma that she is, to enjoy her math without knowing her mama is enjoying (and influencing) that math along with her. 

For Christmas, since the kid is so into games these days, she's getting Junior Monopoly and the cube version of Quirkle.  Oh, and Mancala, plus some really cool fractal fridge magnets to go with our fridge tangrams.  I've got my sneak on, big time!

Kitty Census: Vet Edition

We have a LOT of kitties in our house.  And they're all real, too.  Most are stuffed, some are ceramic or plastic.  Others include a rare bookmark breed and one in a frame.  We also have an amazing example of the exotic puzzle breed, one who is an imaginary friend, an actual breathing, chipmunk-catching cat and, finally, one who is a special kind of human cat with white fur and a brown spot on her head.

When faced with multitudes like this, a mama's mind turns to math: Just how many kitties do we have and can we remember all of their names?  How many different types of kitties are living here?  How old are they?  Who is related to whom?

This morning the girl wanted to play vet.  I wanted to revisit the Kitty Census we started back in the summer.  As with many things, we compromised. 

ALL the cats went to the vet. 

I was the intake coordinator.  Each cat was registered by name, age, type/description, and malady.  Some of the issues included: "a little sad", "lying around, droopy whiskers", "smelly", "bedraggled", "music slows down at end" (that was the music box cat), and "hurt paw".  In the end, twenty eight showed up for well visits and eleven had some serious issues.  After a triage that took about an hour, we attended to the sickest first. 


This is the bunch that were there for their well-checkups.



We will revisit this data later.  For today we were concerned with 'sick' and 'well'.

Aventurine, of the rare 'puzzle breed', was assessed at intake as "needs fresh air and run around time without breaking."

First, the sick kitties, pictured above, all had a thorough examination, including temperature taking and whisker inspection.  Of the group, the Webkins family all had strep, two were afflicted by a 'fever' of undetermined origin, and two needed immediate whisker surgery.  Two others, originally thought to be sick ('lying around'), were determined to simply be acting like cats.

In the end, I think we simply set the stage for more questions about our brood.  I had her chart out the number of sick kitties compared to the well.  She was curious about how many kitties there were all together, and initiated a count starting at 28 (well) and counting up the sick column to find the sum total.

We'll revisit the intake records and mine it for more data in the near future.  How many family groups do we have?  How many different breeds and how many in each category?  What else do we need to find out about our household of kitties?

Until then, one thing's for certain: We've got a whole lotta' kitty loving going on 'round here.

"Mama!  Lucy's purring!"

The Importance of 'Doing' Math: A Conversation with Maria

Maria Droujkova, from Natural Math, read and commented on my recently published article about the development and use of Jump Patterns in the classroom.  Here are some excerpts from an interesting exchange we had today on the Natural Math forum based on her questions after reading the article:

Maria: Great article, Malke - thanks for sharing! I loved the photos, and especially the cool graphic organizers and visuals you use. Do kids like to use the charts? Does it depend on the person?

Malke: What plays out again and again in this program is that teachers are really surprised when they see how enthusiastic their students are when it comes to writing about their experiences in Math in Your Feet.  Recording their patterns using the one best word to describe each category of each beat *is* challenging, but they are motivated toward accuracy because it is *their* pattern.  Also, it usually plays out that within each team of two, one person is more comfortable in the 2D realm of the page than the other, and one is more comfortable moving than the other -- it's a team effort, which makes it more comfortable for everyone. Once the kids do the tough work to record their pattern using the descriptive words, it's actually quite easy for them to plot their feet on the simple grid.  I still think there is a better, maybe more mathematically accurate way to do this, I just don't know what it is yet! 

There are, however, whole groups of kids who still just need the physical portion of the program (more and more, sadly).  These are kids who never had a chance to develop spatial reasoning in preschool, for instance. They don't have enough math, even in 4th or 5th grade, to use the program to take them further -- I find that they begin to understand the math concepts as if it's the *first* time they've ever seen or heard about them.  In these cases, I require just the minimum in their workbooks, and I purposefully stay in the physical realm.  It may be the only time they will ever have to just 'play' with math.

Maria:  Mathematics is "embodied" in that its grounding, basic metaphors come from bodily experiences and observations. You can't skip over that and go into formal math. Even working with adults, I find that you need to go through folding, building, mirroring, measuring and other physical activities and/or stories if math does not make sense to them.

Malke:  This is great to hear, and I believe it wholeheartedly based on what I see kids do in my program and in my personal math (re)learning...I just gave a very well attended 90 minute hands-on presentation at the NCTM [National Council of Teachers of Mathematics] annual meeting and it was surprising how many of these adults were really quite challenged.  It has nothing to do with being 'good' at dancing and everything to do with not having enough experience working with and within a physical realm.  I attended a session on the van Hiele Levels [for developing geometric thought] and realized that this probably applies to adults as well -- experience is key to understanding.

What is interesting to me is that my 'hunch' eight years ago, that there might be math in what I did as a percussive dancer, is now more true than I initially imagined.  At that point in my life I believed, as most of us probably do, that math is primarily symbolic.  I realize now that the math I bring to children in the form of rhythm and dance is some of the experiential math they may not have ever had, and that they need this kind of experience to move forward.  I've heard that only 10% of us will understand the symbolic realm of mathematics without needing to first have, as Maria says, "...bodily experiences and observations".  Just this fact alone makes DOING hands-on, experiential math that much more of an imperative.

Here's the link to our full conversation on the Natural Math forum.

Play

"The artist is accustomed to working in the open spaces of creativity, ambiguity, uncertainty, opinion, and personal story.  Woven into this relationship with the discipline is a sense of play.  Play may be a key to understanding how people learn and how artistry and scientific thinking are linked. [...] The playfulness of artistry can be absorbing, exuberant, intense, and transcendent.  It can provide temporary perfection and sanctuary of mind that is a refuge from the mundane banalities of ordinary existence. Playing often involves rules, but it also includes freedom, imagination, risk unanticipated outcomes, and the possibility for  participants to become deeply immersed in the activity."

From Mark A. Graham's article "How the Teaching Artist Can Change the Dynamics of Teaching and Learning."  Teaching Artist Journal 7.2 (2009): 89.