Swimming toward Specificity: Understanding Pattern Properties

Today's work was to make a four-beat Pattern A. I structure each day/"lesson" as an activity progression with planned pauses to discuss certain key points of the math/dance making.  Today I recorded two similar moments, in two different classes, in the process of making Pattern A. When I transcribed the conversations this afternoon what struck me was how differently they unfolded. 

LESSON SUMMARY: My goal on the second day of my residency is to end the class with every team having a Pattern A they can dance the same way with their partner. We do this by watching individual teams demonstrate their patterns and then talking about what we see/notice about the pattern. This ideally means talking about the pattern properties that reside within the three different categories that build our patterns (movement, foot position and direction). Yesterday's notices made me think that the categories made sense to most kids. At the beginning of each class today we reviewed "what do we use to make our patterns" but when we started looking at the Pattern As I realized that though both groups were making nice patterns, both groups still didn't quite "get" what they were looking at in others' work.

The first story illustrates what it looks/feels like to work with a class that has a sense of what dancing "the same" might mean but is very far away from saying exactly what is the same (maybe the equivalent to van Hiele Level 1?)

The second story illustrates a class that is still learning how to interact with the movement variables but has what seems like a more flexible understanding the relationship between the categories and the properties within those categories (van Hiele Level 1.5?)

NOTE: In the two stories below my words are italicized, and the kids' responses are bolded. In both conversations many children contributed, I just haven't specifically noted change of speaker here.

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CLASS #1: Swimming Upstream
Let’s say what we noticed about that pattern (that the demo team just danced).  Kid:They’re both doing the same thing and they’re not off beat.

Okay, so by “same” do you mean same tempo? Did you mean same in any other way? (To class): [First kid] was seeing same in the tempo, the same speed. What else did you notice about their pattern? Let’s watch it again. That they’ve got a really good rhythm, like how they do it.

So we’ve talked about the tempo. What else did you notice? That they were doing it together they weren’t like one person wasn’t doing different things they were all together.

Okay, so “all together”  What does it mean? People were saying they were dancing together. So what does it mean to be "all together"? What words will help us describe a pattern that is "all together"? What kinds of things can we identify?  [Kids start picking words kinda randomly from our word board] Ooh! Symmetry. Interesting. But what have we been talking about how the patterns have been made? What kinds of things are we using to build our patterns that we could also use to say if a pattern was being danced the same or not?

Ummm. Transform? No…we haven’t actually talked about that yet. Reflect or…

You know, I've been spending most of my time when I’m up at the front of the classroom, near these posters.  This is the information that I’d like you to think about. What kind of words on these posters might help you describe these patterns? [Long pause] Movements? 

Yeah! [talking to the demo team] Did you guys do mostly jumps? Were the jumps the same on every beat.?[bringing the demo team back up to the ] Let’s say jump for each beat while they dance…Now there was another movement in there.  Look up at the list. The category of movement has a lot of movement words. Turn?

Turn! Right, let’s say jump, jump, jump, jump/turn. And how far did they turn? If they went from front to back? 180!

Now, let’s look at their foot positions. Let’s do it slowly. We can also describe the sameness of their dance by looking at their foot positions.  Right now they’re together. Do the first beat and stop. Is that split, together, right, left or cross? Split.

So let’s see their second beat. Ready, go. What are their feet doing now? Split. Where’s their third beat? Split. 

Good! You’re staying in this category of foot position…And where’s the fourth beat? Split! Did they do 4 splits?  My goodness. Let’s watch this pattern one more time and let’s talk about their direction.  So their beat zero is where? Center.  So first beat the direction is what? Diagonal.

Thank you! Is it a right diagonal or a left diagonal do you think? Right. Now let’s look at the next direction. They went to the…side. 

The right side!  And now the third direction? It looks like they went to a different kind of side with their feet to the right and left. Give them a round of applause! So what I’d like you to do right now is go back to your work with your partner and we need to make sure that everyone has the same pattern as their partner. You’re working together. 

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CLASS #2: Swimming Downstream

So what do you notice about this pattern? Let’s watch it one more time and see if you can come up with some words that can help us understand what you see in the pattern. What did you notice about that?  [inaudible] So you noticed a type of foot position which was…a cross. Okay let’s watch again and notice other foot positions.  

Tell me more about what you noticed? They really liked corners. 

(giggles from all the kids) What else could we be noticing? 

Okay before we watch this tell me what else we could be noticing? We noticed their starting position, we noticed that their feet were crossed at one point. What else could we notice? Feet?  Their left. Well, my right. 

So right now we’ve been talking about feet? What other CATEGORY could we notice while they’re moving?  

Step? They stepped backward? Yeah, but which category is that? Movement?

So let’s look at their movements...impromptu chorus of kid voices: Step, cross…

Well , what category does cross belong to?  Feet.

While we’re looking at the pattern let’s find words that describe what it is we’re seeing? They start with feet together.  Where are they?  Center center.

So if we’re looking at movements let’s see if we can figure that out. Step, step, jump, jump/cross…

We don’t say cross because we’re only looking at one category at a time. But this is challenging, I know that. So let’s say those movement words again. Step step jump jump.

Now let’s look at directions. They start in center and let’s do the first beat and stop. The first beat is where? Back left corner.

Where’s the second beat? Back right corner.

And where’s the third beat? Center.

And where’s the last beat? Front corners…

Me trying to talk over them: front, front…just front. Front corners.

Well, if they’re in both corners we’ll just say they’re at the front.  And what would be the foot position word that would describe the fact that their feet are in both corners?  Split.

So can you see how all three of those would…(to dancers) show us what your feet would look like if they were together in front.  So we would call that a together front. Now show us a split back…and a together back.  Do you see how that works? You need more than one piece of information to describe any one beat.

You Never Know Until You Ask: Notice & Wonder, Day 2

SYNOPSIS

1. I'm engaged in a week-long experiment with Notice & Wonder as a way to help kids in Math in Your Feet reflect on their body based learning and experiences. My Day One post is here if you want to get a sense of what my goals and wonders are.

2. For Day 2 I added a Notice into our observation of the math/dance patterns in progress, which led to increased student engagement and pattern analysis.

3. Make sure to read the Notices and Wonders at the end of this post. They are lovely and philosophical and insightful as to the creative process. They are also interesting evidence of children's processing around turns, degrees of turns, and combinations of turns. Why hello Trigonometry!

EPIPHANY: MORE NOTICE, LESS TELL

Today we started making a four-beat Pattern A. As part of this process I initiated a conversation to help kids focus more closely on the categories of foot position, movement and direction as resources for our pattern building and for noticing the structure of these temporal, moving patterns. Working on Pattern A also requires an emphasis on "sameness" -- making sure both dancers are dancing the same pattern and dancing it the same way.

Part of the work of making a math/dance pattern is about stepping out of the "actor" role (as the one involved in making the pattern) to observe others' work. This kind of stepping back can help you gain insight and perspective on your own work.  Today I tried something new during this observation time and had an epiphany:

Instead of directly guiding conversation by asking "What kind of movement (or direction, or foot position) did they use in that pattern...?" I decided (on a whim, let it be known!) a Notice. After a team of dancers would show us their pattern I would first ask something like: "What did you notice about their pattern?"  For the most part, children in all three classes noticed at least one relevant attribute without me prompting. And, even better, these initial noticings started interesting conversations during which I could contribute/introduce new ideas or observations and deepen the conversations.

The kids were more engaged in these discussions than I've seen before. Ever.

I'm beyond thrilled.

YOU NEVER KNOW UNTIL YOU ASK 
Since I only have five days max with any one class, I never have enough time to really figure out exactly what makes each group tick. Imagine having the first week of school over, and over, and over again. But, with the Notice/Wonder (first done in conversation with a friend and then shared out to the whole group) I am getting much more information from these 4th graders about how they're thinking about their work than I ever did before. 

Here are their Notice & Wonders from Day 2, but not all of them. I've combined all three classes' responses -- some of them were repeated in each class. Refresher: today's mathematical themes were sameness, problem solving, categories, and identifying attributes/properties as a way to make sense of pattern and structure.

I noticed...
- It was hard for us to do the same thing [move] on the same beats
- It was hard to make a decision on what we should do [while making their pattern]
- It was hard for us to go at the same rate.
- We did good when no one was watching and when people were watching we didn't do it right
- One of us was (crossing our feet) right over left and the other was going left over right
- That sometimes when we did it we'd get confused, or get messed up, and sometimes we had success
- Every group we saw had a pattern with jumps in it
- Every group had a pattern with a split [two feet apart] in it
- Everybody was doing the same dance/pattern as the other partner
- When people started in the middle [of the square]  and they jumped to the front part of the square they usually jumped out of the square so we thought they should start at the bottom part of the square and jump to the top. [Spatial reasoning]
- Every single dance pattern was different [meaning each team had a different pattern]

I wonder...
- Can I clog at home?
- If we can add some more moves
- If you could change a 360 degree turn into 314 degrees or you could choose your number from zero all the way up to 360?
- If we combined all the patterns in the classroom and then see what it looks like
- If you could do a 460 degree turn
- If everyone will remember their dance moves
- If we we'll actually be able to do the dance we made. [Me: So you're not feeling like you can do it right now?] Well...it's tough. We're still working on it. [Me, to class: How many other people feel like they're still working on their pattern, that they don't exactly have it the way they want it? (lots of hands). So, you're not alone. This is part of the process]
- If we're going to learn other people's patterns
- If our pattern will work out? [Is it not working out?] Well it is; we've wondered from the beginning if it would work out. [Okay, what do you think so far? Thumbs up?! Okay!]
- What's the difference between the A & B pattern is [They'll find out tomorrow!]
- Why your body and your mind control the pace you go in...why only you can control your pace.
- How we come up with the things (pattern) we came up with. [Do you have any thoughts about that?]  Well I think it's about how much you're creative and how much you do that thing. Like if you like to turn and that's your favorite thing and you do it all the time you probably would like to add that in to your pattern.

Bonus: 4th grade Teacher Wonder! ...What it would be like to make a math problem out of our turns...if we were adding and subtracting the angles as we turned, what the extent of that math problem would look like.

I can't wait to see what happens tomorrow.

Questions about Supporting & Extending Educator Professional Learning

I asked a question on Twitter yesterday that probably didn't make sense. I'm grateful to Joe Schwartz for asking me to clarify because our conversation led to a clearer undersanding of what I'm looking for. My original question was:

Has anyone used a Notice/Wonder like structure in #mathed professional learning sessions? Would love to hear more abt how you use it ... not w/ the math specifically but about their own learning experiences...

SOME EXPLANATION 
In my work I provide educators an experience of actually doing Math in Your Feet. I believe that as teachers we need chances to move out of our comfort zones and have experiences with new things, as learners.

In my workshops teachers experience familiar elementary math in a brand new context. We need to reflect on that. We also need to reflect on my approach facilitating the math/dance making which includes the flow of the lessons and how they build on one another, the conversations, the focus on language, and facilitating student collaborations in a moving classroom.

Because this is often new territory for teachers, I need and want make sure there is enough time for them to think about how they might approach using Math in Your Feet in their own classrooms. I want this reflection to be meaningful and useful.

Currently, I provide opportunities during my sessions for teachers to reflect on what the math/dance making they've been doing and what they notice about that learning. The reflection times are partly an adaptation of the Notice/Wonder approach which comes out of the Math Forum as a tool for helping students make sense of math. It is very similar to Descriptive Review, an arts education protocol introduced to me by my Teaching Artist Journal Colleagues. 

Overall, I am quite comfortable facilitating noticings and wonderings but...then what? What happens next? Neither myself nor my participants have been satisfied with me trying to quickly answer all their questions at the end of a long day.

IN A NUTSHELL
I've only got a maximum of six hours with any one group and I want to make it count. I believe in the power of the notice/wonder-like descriptive review as a tool for reflecting on an experience, but I want to know what the next step is. My conversation with Joe helped me clarify and refine my original question. What I'm looking for now is:

...an approach to experiential educator professional learning that helps participants not just learn "how to do" something new, but supports them in extending their questions into answers that will work for them in their own classrooms.

Unfortunately, organizations who bring me in are generally only willing to hire me for a day. Right now I see no possibility for developing longer-term coaching relationships.  I would greatly appreciate your thoughts and feedback!

Full-Day Educator Workshop in Michigan!

This just in! I will be teaching a day-long Math in Your Feet workshop at Grand Valley State University, Allendale Campus in Michigan on Wednesday, October 14, 2015.

More info HERE. Hope to see you THERE!!

Building Competence [#miyfeet Primary Project]

I've had some questions running around in my head about the Math in Your (little) Feet primary project/experiment. The one I'm pondering the most is: Why am I focusing more on the mapping aspect with the primary kids than in the upper ES version? After today, I think I might be closer to an answer.

Today, in all three of my sessions, the kids seemed to have settled into the dancing and by that I mean, compared to what I saw in the beginning, their bodies executed the (deceptively simple) dance moves with ease and accuracy, and we were moving more as a group. It truly was a beautiful, beautiful sight.

I believe this new-found ease with precision footwork has come about because I have also made a point to have them read and represent their foot work visually, even if it's challenging or not always "correct."  

Last week, instead of having the K-2 class build dance steps and then map them, I wanted to see what would happen if they could figure out how to dance a pattern starting with the map. It was clear at that point that reading dance maps and making dance maps are two different processes. I wanted to see if I could move those processes closer together. I decided to make a game!

The "starter kit" included yellow cards for the movements Jump and Step. Blue cards were direction cues; arrows for split feet (2 feet on the ground at one time), dots for individual feet. You could also use the backs of the blue cards to draw in foot positions as needed.

It created an interesting interaction between what you want to do and how it's mapped out in front of you.  Were you doing what was on the card? No? Do you want to change the card to match what you were doing? Instead of committing your ideas to paper (which sometimes needs erasing) the cards were semi-permanent, flexible, and interactive. 

I also was hoping that the cards would scaffold teams of kids toward real collaboration, maybe help them share ideas more fluidly, in a way that, up to this point, hadn't really been happening. I think part of the issue is that the dance goes by so quickly they weren't catching each others' ideas. I'm hopeful that these cards can and will support the development of some teamwork and idea sharing in the next three weeks.

The class was as focused as I could have hoped for given everything. It was an incredibly pleasant 45 minutes. 

Just like everything else I've tried so far, some kids loved the cards and some didn't. Upper ES kids don't need this kind of reinforcement to be fully oriented to the math/dance making. For the primary kids, though, my efforts to help create a visible connection between the dancing and the maps seems to be supporting them in building competence in both realms.

_________________

Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in Fall 2016.

Side Center Window Door: Map Reading with the K-2s [Primary Project]

I met with my K-2 group on Monday. This was our fifth session together. They have experimented with different combinations of steps and jumps executed in a variety of directions inside their square dance spaces. Their self-made maps are showing burgeoning competency in many students to think precisely about the location of their feet while they dance. It's amazing to see their growth from one week to the next. 

This Monday five of the kids had been out sick the Friday before; many were back but still under the weather, and four others were absent.  Because of this I realized we needed something different than the high energy math/dance making we had done so far.  I decided to switch things up on them. 

Could they figure out how to dance a pattern starting with the map?

This is the pattern I gave them, fully notated.  Take a minute to try it out.  It’s not hard, but it will help you understand what happened next as I led them through transforming this map into a real-live dance step:

By giving them this map I was challenging them to use their current knowledge of “what makes our dance pattern” in the brand new context of decoding visual/spatial information. Instead of translating from action to notation, I wanted to see what would happen we moved in the opposite direction.

But I didn't want them to be overwhelmed, so I broke the process down into a number of steps.

 

Step 1: Some of the information, not all of it

Me: Look at the whole thing. We’re going to spend some time looking, some time talking to our partner about what we notice, and then we get a chance to try it out.

As kids started talking to each other, some of them gestured the foot positions with their hands as they talked to their partners.  One kindy girl came up to me and told me, “Malke, you missed a dot…” meaning the single dot in Beat 3. My response? “Well, this is for you to figure out.”  Here’s what they noticed:

• Nothing in the front of the square 
• In the third square there’s not a foot up in that corner, there’s no diagonal 
• On the very last one there’s only one that’s colored in and one that is not colored in
• In the center on the first one it’s uncolored but the second one they ARE colored

Me: What do you think this whole thing is about? What do you think I want you to do with this?

•  It’s showing us how to write an example [of a math/dance map] 
• It’s giving you an idea of stuff. Because if that’s empty then that’s where you were [gesturing the starting position with hands together] but when you colored it in that’s where you are [gesturing the foot position on Beat 1, hands apart] [WOAH.]

Me to the class: Can you tell me more? What does that mean I might want you to do with this?

Kindy kid: Start there [pointing toward the center of Beat 1]

Me: And then what do you think you would do?

Kindy kid: Go to the colored parts [gesturing with her right hand, 2 fingers split to make a ‘v’]

Me: Okay, let’s all stand up with our partners and see if you can figure out what to do.

Step 2: Let them come to an answer that makes sense to them.

As they worked on decoding the dance from the map my basic question at this point was to ask both partners, “Does that feel like a good solution to you?”  My biggest goal at this point was to see how they were interpreting the map.  Some of the answers came back looking like this:

This was a solution that showed up in a bunch of teams.  Jumping so far has meant that the feet hit the floor either “together” (side by side) or “split”.  Presented with a single dot on Beat 3 makes no sense if you’re jumping so the only logical solution at that point was to put both feet together in that position. Two Kindy girls (one of whom told me earlier that Beat 3 was “missing a dot”) came up with a solution that was the closest to the intended pattern:

Another fascinating interpretation by others in the K-2 class, and also in the 2^nd grade class at my other school later in the day, was interpreting forward and backward from the map.  The original map shows two individual dots in the back L & R corners.  The team (whose work is pictured below) read that information and put themselves physically in the front two corners.  The reason this fascinates me is that most kids had oriented their physical selves within  the blue tape squares. They had also been successful writing out their own maps (which I could reproduce correctly). Nevertheless, many of these primary grade children moved themselves forward when the map read backward. Here's a representative example:

Step 3: Provide more details on the map

I wish I could say that by putting arrows facing “up” on the big math/dance map at the front of the classroom helped all the kids understand why they shouldn't move forward when the map read “back”.  Truthfully, what helped the most was adding one finally piece of information into the mix.

Up until this point not one kid had even thought to ask what movements they should use. They all just assumed they would jump.  So I said: “I on purpose did not give you all the information you needed in order to do this dance pattern exactly the way I made it. So, do you want to see what I'm going to put on now?  This is what the chart looked like:

I told the class “Take a minute to look at it, talk to your partner about what you noticed.” They noticed the Jumps and Steps. “But what does that mean?” I asked. “What does that mean is going to happen?

Kid: You jump and jump then step and step.

Me:  Okay. Does anyone else want to say that in a different way? [Silence] What does it mean when it says Jump under the 1 box?

2^nd grader:  OH! So it means you're jumping to the sides! [Gesturing: hands splitting apart].

Me:  Ooooh!

1^st grader:  And then we jump to the middle and then we step to the back corner and then you step to the other corner.

Me:  Okay! Let's stand up and try this with your partner! 

After a couple minutes I ask the class, “Let’s see if we came up with the same solutions for this pattern.”

A 2^nd grader and kindy boy show their work.  The boy watches his partner’s feet very closely and gets that he needs to be stepping in a back corner, but goes left instead of right. I ask them to go slowly and on Beat 3 ask “Which foot goes first, the one toward the window or the one toward the door? Toward the window? Okay, so we'll say Sides, Center, Window, Door while they dance.”

Everyone says it with me while they dance: Sides, center, windoooowww...door.

And they got it!

And, finally, Part 4: Use the understanding of a some to synthesize the understanding of everyone

Me: Okay everyone. Put yourself in the center of your square facing toward the board.  Point toward the window?  Point toward the door! [Correcting facing of some kids while I move to the front of the room. Then I have them “mark out” the dance steps with their hands while saying] side, center, window door.

Me: We've got it! What are we going to call this pattern? Side center window door? 

Class: Yeah...!

Me: Okay, one last time. Let's hear everyone's feet together. SIDE CENTER WINDOW DOOR!  Excellent give us a round of applause!

At this point I decided it might be good for them to map out this pattern.  I turned the classroom map over (out of sight) because I was just curious what would happen.  While they waited for me to get the papers I hear that S, a first grader, has “made a song” out of the pattern. She sings it for us, “Side center window door!” and we sing along...twice.

And, although not everyone was able to map out their foot positions on the outline I gave them, many of kids wrote out the words we used: “sides, center, window,  door.” 

And everyone hummed S’s tune as they made their maps. 

Position - Location - Direction [Primary Project]

This week was my fourth Monday with the K-2s (about 70 in all) and, without exception, kids at both schools finally had enough experience and understanding to take ownership of their work. Here's what I saw:

• Focused work in squares with partners
• Many of the not-quite participating kids finally digging into the independent tasks
• Good verbal and dance communication between partners
• A willingness to practice new skills
• A willingness to stay with the lesson flow (group work, observation time, individual work, written reflection)
• Emerging ability to bring both partners' ideas into the pattern they were making
• A sense of agency with the material -- the directions and movements make sense to them and we are all starting to understand the cool stuff we can do with these ideas
• More trust in the process: all these little pieces we've been learning can be used to make something new and interesting

All this is worthy of celebration!  It means that even with all my experimentation, my newness to this age group, and my not-quite-crystal-clear instruction, things are making sense to the kids!

My own gains/growth so far include being able to articulate an emerging conceptual framework for doing Math in Your Feet at the primary level. I'm using the same MiYF dance ideas as I do with upper elementary kids but, as I realized last week, K-2s need a different scaffold for the math/dance work.

Below are the elements that interact simultaneously throughout any one class. The challenge is to know which one to focus on at any one time. (And, just a reminder, no one said that teaching is easy! This kind of complexity is found in any classroom on a daily basis, whether a moving classroom or not.)

• Development of physical cognition and skills in the dance work
• Development of both dance and math/spatial terminology used in context (direction words and movement words in particular)
• Clear expectations and reinforcement about units, even if the kids don't quite have it yet
• Emphasizing sameness (for now this means: same four beats every time you dance it and having the same four beats as your partner)
• Written and visual reflections after every class. I can see already it's making a big difference in how they understand our work and interact with new ideas the next week.

I've illustrated this last point using student work, below.  

The three maps I've included represent student understanding of position/location/direction and are representative of what primary kids are capable of.  Remember, I only modeled a very basic way of thinking about the location of your feet in the square space. The kids themselves were the ones who decided where they needed to add in more information to communicate their dance patterns.

Seriously, I've been blown away by their thinking.

The "where are your feet" assignment is about assessing direction/location/position only. My thought after our 4th session was that we needed to add movement words into the mix. Later in the day I found this map by a 1st grader who had already figured out that she wanted to address this issue! Notice the word "jump" and a line connecting all four beats. On every beat you jump to the new position.

It's been super exciting to see how many different ways kids are representing location and direction. This 2nd grader used arrows to indicate the direction of the movement. 

This kindy girl is very clear where her feet are in the square. On Beat 1 the dot represents a step in the front left corner of her dance space. The exciting thing here is that she figured out a way on Beat 2 to be very clear about the fact that the left foot stays put and the it's the right foot that's moving into place. 

I think we're getting the position / location / direction thing down! And, next week? I think I'll work to bring "WHERE are your feet (location) and HOW did you get there (movement)" further into our collective consciousness.

_______________________

Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in Fall 2016.

The Power of a Good Reflection Prompt [Primary Project]

As I was musing over how K-2 kids come to understand what makes a unit, using the new and novel context of percussive dance patterns, the first and second graders at my second school were reflecting on it too. But, since we had last Monday off from school, I didn't get their reflection sheets until yesterday.

Overall, I am very happy with the reflection prompts I've created. They are doing exactly what I hoped they would do: helping kids settle into the idea of dance pattern units.  And, in addition to watching their moving bodies and listening to them speak in the moment about what they're doing, the sheets are providing me with a comprehensive view of what kids are thinking and understanding about the dance work. Take a look!

This one shows an understanding of the space, the movements we do in that space, and how they are sequenced.

Notice the arrows. Steps get down arrows, jumps get up arrows. Also, notice the chart he created to organize the sequence of events.  Plus, of course, the cool words!

 What I love about this one is that the kid in the picture has her hands raised! How exciting! And, this child was able to remember all the permutations of Jumps and Steps we made that day -- back in the classroom, from memory.

I'm glad they had fun. :-)

"Down jump" is a special term I use when I teach, grown ups and kids alike. It means that we're jumping up just enough to come down again on the beat. I love that the kid here remembered the term. I also love the leg articulations in the drawing. 

This child has created two different representations for "low" and "high" movements. This is not something I said anything about (except for the clarification of the "down jump".)

In case you're not fluent in 2nd grade spelling the writing reads: Jumping + stepping, low jumps, fun work out, movement pattern(s).

Requiring a written reflection may seem obvious, but you really do have to find the right prompt, which is why I'm really pleased with the responses I'm getting. Since the reflection prompts are fairly open ended I am also very excited and amused by all the different ways the kids are representing their understanding.

A different kind of scaffold [Primary Project]

Monday was a holiday but I got a chance to meet with the K-2 class on Tuesday. I had many thoughts about this class last week, primarily centered on issues of units and unitizing.  After leaving those thoughts and observations to simmer in the back of my head for a while I realized I needed to be more present in their dance making.

Because this is all just a big experiment for the moment, and my agenda wasn't really cutting it, I needed to see where their dance energy took me in terms of the math. I decided that I would purposefully not make a lesson plan for the next session. 

I can sense the room going silent, can't you?

You may be wondering how it went. Well, here's what I learned:

K-2s need a different scaffold for the math/dance work than in grades 3-6. This may seem obvious, but the first two classes with them made me realize this, and I went into the third class asking the right question:

"If my typical approach doesn't work, what will?"

Although I went in without a written lesson plan, I still had a *sense* of what I was looking to do differently.  I'll spare you the details but it turns out that I've hit on a lesson flow that I think might just work every time:

- Whole group instruction for warm-ups, including review of familiar steps and introduction of a few new dance ideas. We had already done jumps and steps in center with our feet together so I decided to introduce the idea of splitting your feet apart.  Throughout the class I used spatial language and more formal math language.  Out/in can also be sides/center. "Corners" was used interchangeably with "diagonal." My philosophy is that a rich use of language in context of actual doing is useful, effective, and generally assimilated.

- Whole group brainstorm: In this case to figure out how many different directions we can split our feet inside our squares. I also summarized our ideas on the board. 

- Release the group to work in their partner pairs...with the specific instruction to work on and practice these ideas with their partners.  In their first two classes I'd given similar specific instructions but was worried because it seemed that what I was showing them wasn't sticking. I couldn't figure out if it was because they weren't unitizing, or whether they were just so full up with creativity (hence the reference to unexpected poppies). This time I was super explicit and redirected kids every time with the statement "It's about practicing these ideas and THEN you're going to get a chance to try out new ideas."  

This didn't stop them, of course, but it did slow them down a little! After a quick group review of the stuff they practiced I moved on to the final portion: 

- Make a 4-beat pattern you can remember and repeat so that you have something to record at the end of class. They worked hard and their work was super awesome.  When most teams had something squared away I modeled how I might record my own pattern by drawing where my feet are in my square and then handed out my reflection sheet for the day.

My goal with the recording is to model one idea for representing foot position, but to allow the kids to figure out the way that makes the most sense to them. These are some great examples of the diversity of responses I got.

Overall both myself and the teacher were simply overjoyed at the children's creative work, their success with recording their patterns, and the flow of the class overall.  The video footage shows lots and lots of kinetic activity. It did feel a little frenetic to me in the moment but upon further review it appears it was as focused a lesson as one could expect in a classroom full of moving and talking 5, 6 and 7 year olds. After all, moving/thinking bodies and children talking to each other is the goal of this work.

But my biggest takeaway? That the scaffold IS the lesson plan. I'm excited to try out my new primary grades lesson structure in the coming weeks. Stay tuned!

The Road to Unitizing is Paved with Unexpected Poppies [Primary Project Day 2]

Day 2 of the Math in Your Feet primary project was super interesting and provoked a lot of thinking on everyone's part, myself included. (See my Day 1a and Day 1b posts for an overview of this project if you need some context.)  

I enjoyed myself and the kids were excited to do their work but throughout the sessions I had an odd sense of dis-ease. This sense was difficult for me to articulate until I transcribed the video footage from both schools but now I'm pretty clear: it's (mostly) all about units.

At the heart of our work in Math in Your Feet is the pattern unit and all the things you can do with it (make it, change it, compare it, transform it, perform it).  With my new audience of K-2 kids I'm getting to see what happens when I work with humans who are still developing a sense of wholes and parts.  It's especially interesting to observe their work when I challenge them to 1) dance a pattern the same way every time and 2) take a familiar-ish pattern and re-unitize it (which requires them to make different combinations/units using the movement pieces from the original pattern).  Here's an example from the K-2 class:

This group came up with [Jump Step Jump Step]

Me to class: I have a question. We have two different patterns up on the board. Let's do them w/ our hands...jump jump step step. Good. Now let's see if we can do the second one...Let's do it with our hands...jump, step, jump, step...[kids keep going...jump, step, jump...]  Oh wait! How many times do I do that? [This is where I really started thinking about units; they need to have a sense of where the pattern starts and where it ends.] I do Jump Step twice, so there are how many beats? [Kids say Four!] Let's try that with our hands together! [speaking and moving slowly] Jump...Step...Jump...Step.  

Me: Now. I have a question for you. Can you think of another way to combine two jumps and two steps to make a different pattern? 

The kids jump to their feet and start working enthusiastically. I stop the group after 2-3 minutes.

Me: Before we're done today, if everybody has a pattern that's new to them I want to get it down on the board. Who wants to show their work?

1st grade girls 1 & 2 (dancing and talking): Jump, Step, Jump, Step, Jump, Jump, Jump, Jump

Me: I put a line between JSJS and JJJJ. So really, how many patterns is that?

Girl 2: Two!

I write it on the board and then ask the girls: There's pattern A and there's pattern B. Nice! Give them a round of applause! Who's next?!

Jump Nod Step Jump Nod Step

Two little K girls (dancing and talking):  Jump Nod Step Jump Nod Step

Me at the board: So what was the first thing they did? [getting feedback from the class, writing down their pattern] And now my question is, is JNSJNS the whole pattern or is it two two of these [JNS]?

One of the K girls: JumpNodStepJumpNodStep.

Me: ...is the whole thing? (she nods) Okay, so we're going to call that one pattern and I'm wondering how many beats this pattern is? [Random answers from the group including TWO!]

Me: Let's count them (using my fingers while I say) JNSJNS...it's...?

Class: Two! Six!

Me: ...each time I say a movement it's a beat. J N S J N S. How many?

Class: SIX!

Me: It equal's six. And these [pointing to the JS combos written on the board] are four...Okay. 

At this point I should say that adding in movements other than the jumps and steps I've introduced has become a bit of a theme with all the Ks and 1s I'm working with. Although I am being as explicit as possible about What Makes A Unit (right now that means steps and jumps done in 2 or 4 beat combinations) K-1 kids have been extrapolating that to mean "Any move you can make on an individual beat."  I actually think this is kind of cool and am trying to figure out how to harness this in future lessons. But, I also think it might be related to the conceptual/cognitive development of both units and sets of things. 

After all, WHAT MAKES A UNIT?  To me, a 4-beat foot-based dance pattern is a unit that includes certain inventory of things you can use to decide:

- where your feet are
-how you move your feet, and
- the direction you move in.

And this is why it's fascinating to have these other moves (nod, clap, shoulder movements, toe touches, jumping jacks...some of them from our warm ups, some of them not) show up in the patterns like unexpected wild poppies in the garden. Gorgeous, but because they're prone to reseed like weeds, how will you deal with them in the context of your larger garden plan?

In other words, what's the balance between my agenda and their lovely sense of personal and creative agency?

None of this bothers me, by the way; I actually find their verbal and movement answers surprising and delightful. But it does make me wonder about my expectations for K-2s in general and these K-2s in particular.

But, the good news is, it's clear they've got the main point: we're using rhythm and movement to make our dance patterns; we can experiment and make new patterns; we need to remember and repeat these patterns; Malke asks us to notice things and talk about our patterns; there are special words we use to describe our work. To be continued...

I love that this girl drew the white board. It looks exactly the same as the real one!

Permutations in Your Feet: #miyfeet Primary Project Day 1, Part 2

The collectively created permutations using (mostly) steps and jumps.

[I am working to adapt Math in Your Feet to the primary grades. Day 1, Part 1 is here.]

Introductions

I have a weird name. Mall-key. Like the "key to the mall." Because of this I open every workshop with kids by teaching my name. I do it through clapping, because I also need to quickly assess multiple things about each new group (focus, interest, attention, beat competency, group-ness, etc.)

I clap my name because it's an easy way to introduce our upcoming work. I can clap my name with two sharp, hard claps, or two soft swishes from rubbing my hands together. I can clap my hands and then my legs ("up, down") or I can make two deep sounds by hitting my chest. And then I ask my new friends if they have any ideas for how I can say my name with claps. Whatever I do, my intention is to illustrate, from the get go, that there are many ways to do one thing, and that it's fun to experiment with ideas.  

How it started

I also tell them that any time I make a pattern forward, I like to figure out how to do it in reverse (or backward, or opposite) and then we have fun thinking how to "say" my name forward AND backward. Because this was my first session with 2nd graders I had no idea how things might go. So, imagine my excitement that this idea of opposite/reverse/backward actually became a theme that influenced the course of the class.

We started with me introducing two movements -- two-footed jumps and single footed steps, both done in "center" which I also described as "middle."

Me: What do you think would happen if we put two jumps together and then two steps? What do you think would happen?

[Collective shrugging of shoulders. I turn off the music as ask again: "What do you think would happen?” Kid in blue, in front of me, jumps twice, steps twice, but I don't notice. I ask the question again, and kid in blue dances JJSS again, but my back is turned and I don't notice him. He keeps doing it through the conversation, but I still don't notice!]

Boy: Um, it will be four?

Me, to the group: It will be four what?

Boy: It will be four...movements.

Me: Ah, four movements! What else could it be four of? Is there any other ways to describe the four?

Girl: It could be a rhythm.

Me: It could be a four ... what do we call what makes the rhythm?

Girl: Beats?

Me: Yeah, a four beat rhythm. Let's try it together. [Burst of inspiration] Actually, do you guys just want to try it in your little partner pairs? And see what two jumps and two steps look like and feel like?  I'll walk around and see what you’re doing.

[Kids work.]

Me: Who wants to show me jump jump step step? Which team wants to show me?

[At this point I'd just like to point out that I ASSUMED that because I asked what would happen if they put "two jumps and two steps" together that I would get a single answer. Silly me.]

Kid in blue: Can we do any pattern?

Me: ANY pattern? Did you come up with something else?

Kid in blue: Yeah...J, S, J, S

Me, walking over to our little white board: Wow. You know what, it's not up here on this board. This is from the first graders and look! Now I have a fourth pattern to put on here. You guys dance it and we'll say it and dance it with our hands while we're sitting.

Everyone says it with me: Jump, step, jump, step [rehearsing the steps with their hands].

Me: Who else wants to show what they've done? Who has JJSS? Boys do you want to show us? ... and they even used the same feet! Now who would like to play around with some ideas about different ways to combine jumps and steps?  Who would like to take a few minutes to do that and see what you come up with? [All hands go up.]

[2-3 minutes of experimentation]

Me: So, the first thing I want to see if anyone came up with a new combination that isn't on the board yet. And the second thing I'm going to do is ask you, and I want you to think about this ahead of time, what kinds of things you noticed about what we did today ...

Now who has a combination they want to show us? Let's turn our faces and bodies toward our friends [two girls in the back of the space dance SJJS but not in tempo so I ask the group to help me keep a steady beat while the girls dance. But there is suddenly considerable muttering in the room and I ask...]

Me: Did anyone else come up with that combination?" [The whole left side of the group raises their hands and continues to exclaim.]

Me: Shhh, sh, sh!! You guys, look at this!! In the other group [first graders] there was JSSJ. You guys were doing the reverse of that! It's the opposite. It's so COOL that you all discovered the SAME thing independently!  Okay, one more but it has to be a different pattern from that.

Two new girls dance SSJJ.

Me: And you know what? Our class pattern was JJSS but now you did the opposite [writing on board SSJJ.] We have discovered so many patterns out of steps and jumps, it's amazing!

Wrapping Up

Me: I asked you at the beginning to notice something about this space...now I'd like to hear about what kinds of things you noticed about what we just did today.

Dancing
Rhythm
"Well, we did do a lot of two plus twos."
"All of the rhythms had four beats.”
Opposites
Movements
[Me: and what were the movements we did?]

Jump
Step

[Me: And does anyone remember the direction we were doing the movements in? What do we call it when we're right here [gesturing to middle of my board]. Were we moving forward and back?]

"No, we were staying in the middle."

What I learned
I learned that even though second graders still have challenges coordinating their bodies, they can stay in rhythm as a group, work productively in teams of two, and do original (to them) mathematical thinking. On the first day!

p.s. I would love to hear your thoughts about the words opposite, reverse and backward. And, after this workshop, I somehow came across (w/o searching for it) the idea that inverses are important to permutations. If you have thoughts on that, I'd love to hear those too!

The Chart of Possibilities: #miyfeet Primary Project Day 1, Part 1

I had my first workshops with K-2s today! In all I'm working with about 80 kids, most of them first and second graders, every Monday through mid-March. My investigation focuses on the following initial questions. I'm sure I'll have more:

 How can the Math in Your Feet program be adapted for meaningful use in primary grades (K-2)?

What are the particular challenges and abilities of these younger learners (socially, physically, cognitively, mathematically) in the math/dance making setting?

What part(s) of the original MiYF program can/should be used with younger children?

How much of the established activity sequence and mathematical inquiry can be used in lessons with K-2s? 

How can we focus on sameness and change (symmetry) with kids where Left and Right is still a murky concept? 

Here's a conversation I had with one lovely kindergarten student about what she was doing on the reflection sheet I provided:

Me: So can you tell me about your picture?

Kindy girl: [Pointing to each little picture in the big square] There’s me, and there’s Oliver and then there’s you on that board over there. Then, that’s that camera thing over there. And that’s the thing that you were dancing on. [Pointing to the word] and there’s clogging.

Me: So that’s what *I* was doing!

Kindy girl: Yeah.

Me: Are you going to write anything else?

Kindy girl: No I was just learning new words that I haven’t learned yet.

Me: Awesome, thank you!

Here are a few more representative K-2 kid drawings (both from kindys, for some reason). Lot's of kids drew the layout of the space and/or themselves inside their square dance spaces.

I wrote a lot of new words on the board. "Center" (used in context with the less formal "middle") was a big hit with many.

Another thing that was true for all three groups I worked with (and also really similar to how upper elementary students think): When kids start to learn a few patterns in their feet, their interest IMMEDIATELY goes to making up their own. Crazy exciting.

At the end of the K-2 workshop I asked: 

"When you came in you noticed a lot of things about the space and you noticed a lot of things about my equipment. But now I'm wondering if you could tell me what you noticed about what we did."

Kid 1: Jump Jump Step Step

Me: Oh, so we did some movements! Cool!

Kid 2: We did a lot of jumping and clapping.

Kid 3: Jump jump clap clap, step step clap clap

Me: So what word up there says what that was? Does anyone know what it's called when you do something in order and you can keep doing it?

Lots of kids at the same time: Patterns!

Me: A pattern! Let's all clap that! [clapping out syllables] but we can also clap it in a new way (whisper, sliding hands). What other ways could we clap that word? (responding to a child's movement) Oh! We can go up and down! Let's all do that. Good!

Kid 4: Oh I know one! (flips hair) "Pa.." (touches nose) "tern" [We all do that as a class.]

Me: What else did you notice about what we did today?

Kid 5: Well I was thinking we could do jumping jacks and then then we could step.

Me: Okay you're thinking of other patterns we could do! Do you want me to show you something?  THIS is my Chart of Possibility. Next time I visit I will put it up. It will show you some more possibilities for making your OWN dance patterns. [Cheers from the kids.] Right now those possibilities are covered [with tape] but you will start to see that we will have all sorts of options for making new patterns in our feet in a way that a tap dancer and a clogger does.

Kid 6: Can we UNcover one of them now?

Me: Tell you what. Next week I will ceremoniously uncover the new words we are going to use!

Stay tuned for weekly installments through mid-March, including Part 2 of this post where 2nd graders investigate permutations out of their own curiosity! I can already tell it's going to be an incredible adventure.