Wednesday, January 28, 2015

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.

Tuesday, January 27, 2015

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.

Wednesday, January 21, 2015

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!

Wednesday, January 14, 2015

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: 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)'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!

Saturday, January 10, 2015

Math Poetry Project: "Which one doesn't belong?" [Part 1b]

This is the second part of the activity I did using Christopher Danielson's new book project "Which one doesn't belong?" It's the math provocation/experience in a new math poetry project I'm developing. 

If you haven't already, make sure you read the first conversation I had with this 3/4 class here. You're gonna' want to because you will get to see me exert considerable energy helping the kids develop a concept of sameness and then nudging them on to similarity. This post is gravy compared the first 20 minutes of class!

I debated whether or not to summarize these conversations, but as I was transcribing my recordings I found the progression of ideas really interesting (including my own struggles to figure out what the kids were saying and what they meant!)  That's all to say: here's another transcript! Enjoy!

Me: Let’s make a list. I think, from going around the groups, I think everyone had similar reasons but let’s just make sure. Who had the blue background? It’s the blue with green shapes. And it’s interesting that we had talked about color being a way to sort out differences but that’s not an option here, so you had to think about it a little differently.  If you didn’t have this card, I’m going to put it here on the board so you can get a sense of what we’re talking about.  Who wants to start?

Kid 1: Well, three of them have six sides and one of them had five.

Me: Great. Who else wants to share another way they sorted out one that didn’t belong.

Kid 2, pointing to the three hexagons: Well, these are all diagonalish, and the other one is not.

Me: So I’m going to write on the board “three are diagonalish’  Aweseome. Who else has something to share.

Kid 3: Three of them were made out of original shapes.

Me: Can you tell us about that? What do you mean?

Kid 3: Like pentagon, hexagon and the other one is made out of squares. 

Me: Oh, so looking at this (pointing to the fourth shape)…

Kid 3: That’s NOT a shape.

Me: So if I write…I’m going to bracket this because that doesn’t include three of them, you’re not excluding one. These and these you recognize as shapes.

Kid 3: Yeah, that’s made out of squares…and that isn’t.

Me: Oh I see!

Teacher: It’s not like an identifiable shape.

Me: Made out of squares….okay I’m going to un-bracket that, now I understand! Thank you! What else.

Kid 4: One has an odd number of sides, the others have an even number of sides.

[And typing this out, I realize that in this second half of class as I recorded their findings that I was writing down the three that make the inclusive group, not the shape that was excluded. I wonder why?]

Me: Who else had this picture? Does anyone else want to add some more?

Kid 5: One will never, no matter what you do, whether you add or take away parts, will never be a standard shape.  [We talked about this a little, but it really was just a reiteration of the earlier conversation. I left it in because this kid was so emphatic and expressive about his belief!]

Kid 6: Another one is that three have obtuse angles.

Me: And what do you mean by obtuse? [I asked this because I’m pretty sure most of the other kids didn’t know but it was also good to hear her thinking about this as well.]

Kid 6: What I mean is that on the paper, only the one with the squares have right angles that are kind of like perfect almost. The rest of them are more open and obtuse. 

Me: Do you guys understand this? We could do that with our hands really quick. If you have  a right angle [making one with my hands] they’re like all around us, they’re what makes our walls stand up straight, and so I think what she’s saying is that they’re actually wider than that [opening my hands up wider]. Does that make sense when you look at that picture? Now we have this one…

Kid 7: One of the rectangles is the only one with an outline.

Me: So the other three are…

Kid 7: solid.

Me: What’s another category for this one?

Kid 8: Three of them have right angles, one of them does not.

Me: What else?

Kid 9: These three are not like this one.

Me: Okay, I want to take a minute to talk about this because I think a couple groups mentioned this. There are three are not like the square, but when you look at the three? Can you see why they’re putting them into that group?

Kid 1: Well they’re all longer.

Me: Oh, longer is an interesting reason. What were you guys saying about it?

Kid 10: Well…

Me: Did you basically tell me, although it took me a long time to understand what you were saying, is that they are not squares. So that the thing they have in common is that they’re a negative. They are not squares.  Anything  else?

Kid 11: Okay, so, one has three sides and the others have 4.

Kid 12: One is red and the rest are blue. 

I am so impressed with your thinking! This was SO fun! Here’s what’s going to happen …next time we’re going to take this idea of sameness and difference and we’re going to write some poems [pdf of project description here].  And do you remember the c rods we used to make our faces? We’re also going to use those to design our poems.  

Friday, January 9, 2015

Math Poetry Project: "Which one doesn't belong?" [Part 1a]

I'm working informally but collaboratively with some math teacher friends to develop a math poetry project. My goal is to provide K-6 kids with authentic experiences with both mathematical ideas/thinking and poetry composition. I want the math activities to inspire rich and generative conversation. The poetry should extend those mathematical ideas and thinking into the larger world of interests, thoughts and actions of each individual child.

The first project is about comparison (the pdf of full lesson is here). Comparing one thing to another to find similarities and differences is at the heart of mathematical reasoning and equivalence relations. One thing can be described many ways depending on what you choose to focus on. In this first activity, we will focus on sets of shapes with many different and interesting properties. This activity uses the visual provocations from the new book Which one doesn't belong? by Christopher Danielson (you can download the free (for now) pdf here).

I did this activty with my daughter's grade 3/4 class today; 24 kids grouped into small groups of 4. Initially I thought I could tell the whole story in one post but after transcribing the rich (and quite fascinating) conversation we had around the first (warm-up) image, I realized I needed more than one post to tell the story.

Part 1b of this lesson is here.


I love hearing what kids think and why. What was fascinating to me was that although I was clear that the goal was to find "the one that doesn't belong" out of the four shapes on the page this didn't seem to make much sense to them, at least initially. Their small group reasoning showed me that they were thinking of only one general property/attribute: the shape.

But the most fascinating thing of all was that they were, initially, only finding differences and very little in the way of sameness.  I know that was the question, but in fact, more than one group was convinced that NONE of the shapes were the same as each other. As one girl said: "They are all unique in some way." It seemed that by focusing on difference kept them from grouping the rest into a set. In this introductory portion of the lesson I spent considerable energy supporting them toward a concept of sameness and then a final little nudge toward similarity.

Like I said -- fascinating.

I gave all groups the same image for the first half of the activity. Here's how it played out:

After about 5-7 minutes of letting the small groups look at and talk about what they were noticing and letting them get started with figuring out "which one doesn't belong" I said:

Me:  So I have walked around the groups and it’s very interesting. There are a bunch of groups that are saying that none of those little shapes belongs in a group.  I will tell you, if there are four shapes, the question is which one doesn't belong to that group? And there will be more than one answer. We’re thinking of them as a whole group, not as individual shapes. There are different ways to look at this. It’s not just the shape. What other things tell you something about them?

Kid 1: The color.

Me: So what is one thing that three shapes have in common but one shape doesn't?  Let’s make a list of the kinds of groups of three you made. What was the first thing you noticed that three of those shapes had in common?

Kid 2: They’re all squares in different sizes and shapes.

Me: She’s saying three are squares and one is not? What’s another way you could group those shapes together?

Kid 3: All of them have four edges.

Me: So that’s a way of saying that they all belong, because they all have four edges. We’re going to start a different category over here. What else?

Kid 4: One of them is at a different angle.

Me: [Because a LOT of kids were calling the turned square a diamond I pressed the point a little further using their language.] I’m wondering what you think about that little blue shape. Is it a square or is it a diamond? Can you look at that blue diamond-y square. What would happen if you tried to put it right on top of that red square? 

Kid 5: It depends on the way you turn it.

Me: So your definition of a diamond is that it depends on the way it’s turned.  But what if you turn the page? Does it look like a square? Can it be both a square or a diamond?

Kid 6: Or a rhombus!

Me: Oh, hmmm. A rhombus (drawing one on the board). Who think this looks more like a diamond. [kids exclaim: yeah!] So if you can turn that little blue thing and it looks like a square when you turn it so the bottom edge is toward you, is it a square or a diamond do you think? [kids agree, it's a square]

Me: What other ways can you look at that picture and say ‘these things definitely belong together and this one doesn’t’?

Kid 7: So, the rectangle…all of these can make a square or a diamond, but this one [the rectangle] doesn't

Me: Okay. Is there any other property...

Teacher: Remember last year we were talking about attributes...?

Me: Yeah, the things we can use to describe something. We can describe them by their shape but how else can we describe them?

Kid: Color?

Me: So which one doesn't belong if we’re looking at color?

Kid 8: the little red one.

Me: Right now we have color and we have shape as the categories. Are there any other categories that helped you make your decision?

Kid 9: Um, size?

Me: Tell me more about that.

Kid 9: Three are small but one is huge.

Me: Any other way to think about this?

Kid 10: Well I already said that one of them was at a different angle. It will ALWAYS be at a different angle than the others b/c you cannot turn that shape without turning the whole paper!!!

Me: Got it! So we will say the word “position."  So we will say that ‘three are parallel to the edge of the paper’. Does that make sense to you? [class says yes]. Is there anything you want to add to this list?

Kid 7: I don’t think any of them belong together. Because they’re all different.  They all have something special about them.

Me: So you’re saying they’re all different from each other in some way. Can you give me some examples?

Kid 7: Well, one is red and all the others are blue. One is a different shape from all of them.

Me: Can you give me one example of how they’re all different, like how is that red square different from the blue one?  Compare them to each other? [Kid 7 starts moving counter clockwise around the page, comparing one shape to the next, the second shape to the third...]

Kid 7: This one is smaller than that one, and that one is angled differently…[fades off]

Me: And how does the angled differently one compare to the one at the bottom?  How many people understands her reasons? [lots of kids raise their hands]

At this point I knew they were at a good enough place to take this introductory experience and move on to  more challenging images. I need to listen to the audio to decide if I'll report on the second half of this class, but I know that this first 20-25 minutes supported the forward movement of their reasoning in the next section with new images. I definitely heard a lot more descriptive language, both formal and informal, and they seemed more certain in their analysis. Best of all, with some small exceptions, the kids' energy was really strong for the entire hour and they were really listening during our group discussions.

Next week I'm moving on to the poetry portion. You can look at the lesson plan here, but imagine writing poems around topics like:

Vanilla OR chocolate?
Endermen OR Slimes?
Circles AND Spirals

You get my drift? My hope is that our work in the shape comparison portion will inspire some really interesting writing. Cheers.

Part 1b of this lesson is here!

Tuesday, January 6, 2015

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.]

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 I'd like to hear about what kinds of things you noticed about what we just did today.

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


[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!

Monday, January 5, 2015

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.


Related Posts Plugin for WordPress, Blogger...