A Small Moment of (Summer) Success

When the 6th grade boys keep working on their choreography over break time.

Sneak Peek: My Harvard Workshops

Oh, so excited!  In August I will be attending a Harvard Graduate School of Education professional education program called The Arts and Passion-Driven Learning (focusing on arts integration) on a very generous grant.  It's being led by Steve Seidel and members of Yo-Yo Ma's Silk Road Ensemble.  Today I got to pick my workshops, and I thought I'd share which ones I chose.

After looking at the entire selection of arts experience and classroom practice workshops, I decided to go with experiences that can potentially deepen or extend the inquiry in which I've been engaged over the last year or more. Specifically:

Computer Programming as an Expressive and Reflective Medium
Karen Brennan, Assistant Professor of Education, Harvard Graduate School of Education

What is evoked when you think about mediums for expression – music, text, video? What about computation? In this session, we will explore how code (the instructions that computers follow) can serve as an expressive and reflective medium by engaging in hands-on design activities with interactive media. Using the Scratch programming language, we will create interactive, reflective scrapbooks that document our experiences in the “Arts and Passion-Driven Learning” Institute. No prior experience with designing interactive media is required. Participants are expected to bring their own laptops; please do not bring tablets(iPad, Android, etc.).

I have been reading Seymour Papert's work all winter and spring.  His LOGO program and, by extension, MIT's online visual programming environment Scratch, has had me thinking deeply about constructivism / constructionism and the meaning and purpose of education.  I am also quite interested in how his work and thinking can help frame, support and strengthen the ways we think about and provide arts education.  A pencil and paper kind of gal, I will probably not be very good at Scratch but it will be a great challenge to be out of my comfort zone.

Traditions of the Middle East
Shane Shanahan, Silk Road Ensemble (percussion), Kevork Mourad, Silk Road Ensemble (visual art), Allison Trombley, teaching artist and former Silk Road Project Education Coordinator

How do Middle Eastern traditions in visual art and music mirror and complement one another? What can we learn about a culture through its art forms? Visual artist Kevork Mourad and percussionist Shane Shanahan lead participants through a hands-on exploration of the relationship between art and music. In this workshop, participants will work with both visual art and percussion as they consider the central theme of the connections between these expressive art forms.

I am very interested in this one because of the specific cultural context and the exploration of relationships/connections between two different art forms. I'm also hoping that Islamic (geometric) art will be included (hint, hint).  Can't wait.

Powerful Partnerships: Teaching Artists and Classroom Teachers Working Together
Elise Gallinot, Program Director, KID smART

The classroom teacher/teaching artist relationship is a deep and powerful tool for student learning, but what are the key features of successful partnerships? In this workshop we will explore some approaches to the co-teaching relationship, focusing on structuring planning and post-lesson reflection meetings for mutual empowerment and deeper understanding. We will discuss setting goals to help us discover and develop deeper ways to work together as colleagues and examine and develop tools and strategies to guide the co-teaching relationship. Throughout the workshop, we will focus on the following questions:

• What are the features of successful teaching artist/ classroom teacher partnerships?
• What tools do we need to make sure partnerships are vital and focused?
• How can we work together to assess quality integration focused on student learning?

I am hoping this workshop will give me some new insights into building, maintaining and deepening relationships with teachers, something that is still a work in progress for me since my time in schools is always so brief.  I generally do not co-teach Math in Your Feet but, more and more, I am meeting teachers with whom I would like to collaborate more deeply.  I also think this workshop may also be helpful in my quest to refine the way I present and frame my professional learning experiences for teachers.

At the date of this post I will be experiencing all this in a little more than three week's time.  I'm sure it will be incredible on a lot of levels and I plan to share and process my learning in this space.

Not All the Same

I'm telling you right now, understanding 'sameness' is hard for a kid.  It might not be hard for my adult brain, but for a six or seven year old, it takes a huge amount of concentration, analysis, and wherewithal to make it happen.

It's easily obvious to me that these slices of paper pizzas are not at all the same but you know what is really hard for me? Resisting the urge to rearrange those little pieces so this child can be 'successful' or get the 'right' answer.

When I resist the urge to correct or direct, I am able to help one child notice that he needs to select the same kinds and number of shapes for each piece of paper pizza.  When I resist the urge to rearrange, I can support the other child  who has mastered that step and now needs a chance to evaluate the position of the shapes on each 'slice.'

At some point, though, it's their project, and they can only move themselves so far in the short time we have. Sometimes just finishing is a victory.

This paper pizza activity I designed is deceptively simple because in one fell swoop it reinforces the math concepts of sameness, position, geometric shapes, pattern unit, transformation and symmetry. To adult eyes there is nothing to it. For a six or seven year old it is, I assert, the very best kind of challenge.

The activity gets an introduction with project examples and the briefest of instructions, and then the kids go at it.  Some might view my approach as flawed or, at the very least, unhelpful.  Perhaps, but how does one learn these things? I could talk until I was blue in the face about what they need to do; I could break down the making process into minute individual steps; I could do all the work for them, pointing out the next step every step of the way...and what would they learn?

Instead, I use my adult eyes for making observations. My adult hands to point out the lapses in visual reasoning. My adult mind to ask, "Does that look the same to you?" or "Does each piece have the same number of shapes?"

But at no time do I judge the work in terms of rightness or wrongness.  Most of these rising first graders 'got' it. Some did not, but each paper pizza is beautiful, not just because of the bright colors, but because it is a gorgeous snapshot into the how each individual child is thinking, at this particular moment in time.  Because no kid is the same as any other kid - and that is something to celebrate!

Beyond Linear

I started working with six, seven and eight year olds this week.  Two more weeks to go.  To start things out, the summer program I'm working with requires me to create and ask my new students a few questions which I'll also revisit at our last class.

One is "How can you make rhythm with your feet?" The other, "How can you make a pattern?"  The predictable and unsurprising answer to that one? 

Colors.
Shapes.

And that's it.  That's all they got.

My dream is to move kids beyond one-attribute linear patterns.  You know, "red blue red blue" or "circle square circle square."  I think those are fair places to start, but based on my experience last summer, even when kids get into upper elementary, they still give the same two answers as the 6 year olds. 

It's a wasteland out there. We're literally wasting kids' time on AB patterns when we could be engaging them in some truly exciting, interesting and beautiful mathematical pattern-based play, analysis and reasoning.

On my board after the first three days I have written:

"How many different kinds of patterns can we make?"

So far:

Rhythm patterns, in our feet, in our hands

"Recipe" (algorithm) patterns (and there I've noted the beginning 'recipe' for our Pizza Clogging choreography which we'll extend next week with our own favorite pizza toppings in our feet.  I also read them the fabulous book How to Make an Apple Pie and See the World).

Nature's numbers: The first nine numbers in the Fibonacci sequence including the one that showed up in the apple star I 'magically' discovered.

Also, in the slices of paper pizza we've been designing. More magic and transformation for the primary set. (The more math magic the better, as far as I'm concerned.)

Of course we'll also look into linear patterns too, but before we design pattern units and make our beaded icicles we'll  read The Lost Button (a Frog & Toad story) and investigate the attributes in our bead choices (color, texture, shape, size). 

Because, when you have more than one attribute you get to think deeply about similarities, sameness and differences, another thing I don't think little kids are asked to do often enough.  With more than one attribute you get a chance to evaluate, analyze, think, talk, make, dance, sing, tap and clap mathematics.

I don't have a lot of time with these kids, but I hope that the world gets a little bigger and their eyes open just a little more to the beauty and structure around them.  Because how will  they come to know and love math otherwise?  These are the basics, folks.  Just like 'literacy' is way more than decoding written words, so too is math.  A visual, kinesthetic, aural and expressive mathematical literacy for all elementary students.  That's my dream.

A Vision of Precision, Revised

Every day this week we've been playing with math dice. Enthusiastically.

I'm not going to name the company because not only do I not review or endorse any product on this blog for money or power (not that they asked) but it is also quite easy to go out to your local games shop and get your own set of two 12-sided and three 6-sided dice. (The rules are also pretty easy to figure out: multiply or add the two numbers on the 12-sided dice and then roll the six-sided dice and try to find a way to make the target number using as many operations as you know.)

Did I mention the enthusiasm?

My newly eight-year-old is enthusiastic about many things but has always been a little standoffish with her affinity for math, probably because, I think, she perceives it as my 'thing'. So, it's been nice to be able to truly enjoy a math game together.  (It's been a while -- we were heavy into UNO a couple years back which was super fun.)  It's clear my kid is on her way to a happy relationship with operations, but there's something even more interesting developing...

I had always thought my girl was not what I would call 'systematic' or 'precise'.  I know for sure she is prone to intuitive leaps of connection or understanding and lots of messy tinkering, none of it looking either precise or systematic to my eyes.

As I've been drafting and revising this post I've realized that maybe she has been those things, I just haven't been able to see it.  And, as we've been playing the dice game I've watched her systematically running through different combinations of the six-sided dice (by moving the dice physically to different positions) and  reasoning to herself out loud as she thinks through the different ways to use the hand she's rolled.

I guess I always thought that precision in mathematical problem solving looked, well, neat and orderly and on paper.

Anyhow, I am not (too) ashamed to admit that I was wrong. I think she's been precise and systematic in her own way for a while now. In retrospect, I realize I've heard this kind of  'talking herself through' a series of moves or ideas before. Systematically. In math and in many other contexts. For years. In a messy, verbal, highly enthusiastic way.

Okay, so I'm a slow learner I guess, but pretty open minded all the same. I think it's worth considering that there must be a difference in the way children and adults go about their reasoning. Or, at the very least, that I have a deeply ingrained image of 'what it looks like to do math'. I'm going to keep thinking about all this. If you have any observations or resources to share on this subject, I'd be tickled pink.

In the end, I'm super impressed that not only is she beating the pants off me but she has also created her own strategy for combining operations to reach a target number.  And it's all her.  The only thing I did was bring out the dice.