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: ...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!

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!


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