Pulling Language Forward: Notice & Wonder Day 6

After experimenting with Notice & Wonder last week during a Math in Your Feet residency with three classes of fourth graders I:

1. ...feel like I had more feedback about student thinking than ever before. I've always seen how children think with their bodies, but was never happy with their written reflections, which didn't really reflect what I saw them do while they were making their patterns. I have also not been happy with how hard it's been to help kids use and apply the terminology of the Movement Variables. I found Notice & Wonder to be a great tool at pulling the language forward in a way that was natural and meaningful for the students themselves.
   
2. ...noticed that each of my three classes last week moved from general noticings to much more specific noticings as the week progressed. Not only that, but they noticed more and more, and in great detail their own making process and the process of reflection; the math/dance pattern properties and structure (movement, direction and foot position); the differences between a reflected pattern and a non reflected pattern; and the process of unitizing two patterns into one larger one.
   
3. ...finally felt like students owned everything about the week -- their actions and the language they used to describe their own and others' patterns.
   
4. ...was grateful for the classroom teachers who made the decision to support the residency by making their normal math time a chance to explore the math we were using in the math/dance making. This was particularly important in terms of the angles/rotations and the idea of congruence. 

This week I'm back at the same school with three more 4th grade classes. Their Notices & Wonders today were really nice but, like last week, fairly general. I'm excited to see if they follow the same course as last week's students in becoming more and more specific, precise and descriptive with their noticings and pattern analysis.

And today I had a new Wonder: What if I bring a few notices and a few wonders forward each day (collected from all three classes) and put them in front of the students. They won't be identified by class or student.  Right now I'm thinking that it won't hurt to try and I'm curious what might happen.  Here are the student responses that I'm choosing to pull forward for tomorrow:

• I noticed all the different words you can use.
• I noticed all the movements, feet and directions we did today.
• I noticed you can combine different movements.
• I noticed we were doing the same pattern over and over again and I think we should choose something different.
• I noticed dance isn't just movement; it's feet, movement AND direction.
  
• I wonder what our pattern is going to be?
• I wonder how many 4-beat patterns we can make with all the things ups there [on the movement variables poster.]
• I wonder if I'll have better ideas tomorrow.

My original three wonders can be found here: INTRO/DAY 1

The rest of last week can be found here and, like I mentioned, document the progression of general noticing to much more specific and precise language: DAY 2 | DAY 3 | DAY 4 | DAY 5

Equivalence Relations & Spatial Reasoning: Notice & Wonder Day 4

Two girls in the process of reflecting their math/dance pattern. Different year, different school, different kids. Same tape. 

Today I took the noticing and wondering of my 4th graders from yesterday and used that information to restructure the frequently stressful last two days of my five day residency.  I will be going into more detail about how N/W has impacted my teaching after I finish the week. Today, however, it was clear that all three classes were noticing the math in their math/dance making more and more specifically.

ACTIVITY OVERVIEW
1. Students practiced/reviewed their A & B patterns. 

2. A body-based lesson on reflection symmetry and how to apply that idea to their foot-based dance patterns.  This included more discussion about how we were evaluating sameness. The classroom teachers have moved their geometry unit to this week so they can make specific connections to the MiYF work. I checked in with each class and asked them if we could use the word congruent to describe how they dance their patterns exactly the same as their partner. One boy said that our dances couldn't be congruent because all the 4th graders are different sizes. This led to a discussion about the relevant properties with which we assess sameness/congruence (all properties the same). FANTASTIC.

3. A chance to combine their A & B patterns into a new 8-beat pattern, otherwise known as unitizing.  All you have to do is read their notices below and you'll see how cool this is.

4th GRADERS NOTICED
The process of reflecting a 4 beat pattern across a line of reflection

• My pattern even looks good in a mirror
• Doing the reflection was pretty easy because it was like just doing the opposite foot. His foot was on the outside [away from the line of reflection] and I used my outside foot too. 
• The whole mirror thing was kind of tricky. I had to do the complete opposite.
• It was easier for my partner to be the reflection because normally when we'd do it she'd do the opposite anyhow. [So, she was well cast in the role of reflection?! lol] 
• It was hard for us to mirror each other and do the same thing, like opposite 
• When I was pretending I was a reflection I had to do the feet the opposite and it messed me up
• I noticed how people were doing the same thing being con-gruent (sic) 
• When you were doing the reflection not everybody was doing the exact same but they were pretty similar. 
• It was harder doing  reflection because [my partner] was trying to do the same as me like we did before and she is now doing the opposite 

Unitizing two 4-beat patterns into a new 8-beat pattern C [As you read, also put yourself in a spatial orientation/reasoning frame of mind]

• I noticed how we combined two patterns into one big one
• That we have a C pattern with eight beats
• That you have to take away one beat to make it Pattern C...[did you take away one beat or did you take away your starting position?] Starting position. 
• When we did B+B it was very hard because we kept getting confused with our moves and what to do because of our 180 turn. We were used to starting our pattern facing backward, and it was confusing doing the pattern [again] facing forward. 
• It was harder for us to do A to B because in our A we land in a split but In our B we start at a zero in the corner so it was harder to get there
• It's harder when you do same pattern twice, like A+A together because I finish over HERE and I have to jump to over HERE. It was freaky to put A+A together.
• When we did [our pattern] forward and then we turned and tried to do it the other way it was harder. We were facing this way the whole time and then when we tried to start from the other side and look this [other] way it was harder.

Properties & Structure

• I noticed lots of diagonals and turns
• When we were doing it congruently I noticed they [a nearby team] has a similar pattern. 
• I noticed there's yellow tape

Learning Process & Miscellaneous

• During the reflection it took like three goes and then we got it down 
• A lot of people were tired
• We did really good even though it was difficult.
• That everyone did Pattern A better than B...because we knew A better. 
• We can get through A+B a medium speed 
• [When they were working on reflecting their pattern] one person turned left the other person turned left and then the 15th time one person turned right and the other turned left

Heading into our final day I am finally seeing the process of math/dance making from the inside of the process. There is so much to notice from the outside in observing children's bodies thinking, moving and learning all at the same time. But having Notice & Wonder this week has taken my understanding of their learning to a whole new level. 

On Process & Properties: Notice & Wonder, Day 3

Kids practicing their math/dance patterns on my dance board before we started class this morning.

The room was hot all day. The kids were overly concerned about things being fair in terms of who got to show their work. They were also a bit squirrel-y (and my focus could have been better) but we all worked hard on the process of creating a second 4-beat pattern, Pattern B.

The math involved in today's activities included: 
- observing and comparing moving patterns and identifying relevant properties
- increased focus on using precise language to describe the math/dance steps
- increased emphasis on focusing/identifying one relevant property at a time in the dancing (movement, foot position, direction)
- continued growth in understanding and noticing sameness in the dancing (unison/congruence) including rights and lefts for foot placement and for direction of turns

My takeaway on today:
Compared to other days, this day was a huge challenge (in a good way). I have always known that Pattern B is challenging, even without hearing what the kids noticed. But their notices were so full of details today, way more than the first few days, about the process of making a new pattern as different as possible from their first pattern.

My wonder from today: 
I'm still pondering what to do with these noticings. It's already a great tool for assessing what and how they're thinking about the material. But I keep thinking there has to be something specific I can *do* with this information. And then I think that maybe that the explicit process of reflecting like this is helpful in itself for my learners, but I can't quite put my finger on why that might be exactly. So, for now, I will be content with what I have and look forward to the final two days of this residency.

In case you're interested, my original wonderings/goals re: adding Notice/Wonder to how I facilitate Math in Your Feet can be found here.  
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WHAT THEY NOTICED....

Observations on process
- We had to do two patterns so people had to know Pattern A and Pattern B and it's confusing...they have to know which one.
- [Me and my partner] would share our ideas and then we would do them all and then figure out which one was the easiest and the one we could do all together.
- It was hard because of the turns [So you gave your self a challenging pattern?]  Yep.
- Pattern B took more time [to make] because we had to come up with different ideas and if we had two or more turns we had to do less
- The first time I did it wrong and the second time I did it right.
- It's hard to do the same thing as your partner.
- We got confused a lot and we stepped on teach others feet and we got confused. [Why?] Because we kept on changing it and sometimes we'd remember A and mess up Pattern B.
- It doesn't take long to decide on a Pattern B if you talk and give ideas out to your partner.
- It was really loud in here when we were creating Pattern B
- Our Pattern B was very easy [to dance]
- We had to change our Pattern B because our first one was too hard. [What made it hard for you?]  We did all this tricky stuff and turned around a lot and crossed our feet a lot and it got hard so we changed it.
- Our slide had good sound but we need to work on the sound for the step
- People were making mistakes which is a good thing because if you make a mistake it's a FAIL which is a "first attempt in learning.
- I heard people being respectful to each other
- People were messing around

Observations on properties and equivalence (sameness and difference)
- Some people had jumps in Pattern A but in Pattern B they had turns and slides
- There was a lot of 90 degree turns
- We couldn't do the same pattern on Pattern B. We had to be different
- A lot of people came up with really different B patterns [compared to Pattern A]
- If people had lots of spins in Pattern A they did not do a lot of spins in Pattern B
- Everybody jumped at least once in Pattern B
- We did the same beats and the same feet for this pattern
- It took us a long time to get our B fully finished

WONDERS (similar to yesterday; I'm including the ones that stood out to me)
- I wonder what the rules are for [making] Pattern C?
- If every partner can agree with the other partner. [So, were you noticing that you were having some difficulties?]  Ummm...a little. [Did you guys come up with a Pattern B?]  Yeah.
- If everybody's A and B patterns will go good together?

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.

Making Learning More Visible: Notice & Wonder Day 1 (of 5)

I've noticed (ha ha!) over the last year or so the ways that math teachers have utilized the Notice and Wonder structure in helping kids problem solve and make sense of math. I've been wondering how N/W might play out in terms of helping kids make sense of their experience learning math and dance at the same time in Math in Your Feet.

Buoyed by a conversation with Suzanne Alejandre from the Math Forum I've been thinking more closely about how Notice and Wonder might be used to help my learners become more personally invested in reflecting on their math/dance making experience. In general, kids are already invested in the dance work, but I have always wanted them to make more connections between what they're doing and what they think about what they're doing with both the math and the dance.

This week I'm doing my first school residency of the school year. I'll be at this particular school for two weeks, working with three 4th grade classes one week, the remaining three 4th grade classes next week. Today I did Notice/Wonder with each of my three classes. I had them first talk with their partner about what they noticed and then share out to the group. I did the same thing with the wonder. I will likely keep this procedure the same each day.

At the outset of this little experiment I am wondering:

- How or will their noticing and wondering change over the five days we have together? Meaning, will they get better at it? Will they notice different things every day?

- How/will will Notice/Wonder implemented verbally/socially in my class impact their written reflection and word studies in their #miyfeet journals back in their regular classrooms?

- What will I learn about their thinking and how might that inform the way I facilitate their math/dance making & learning?

For context, today we started with learning what it feels like to make rhythm and patterns in our feet. The math connections were patterns and how we can make new rules to create variation, a lot of body-based spatial reasoning, language like center/zero/origin, and also some physical exploration of 90 and 180 degree turns in the context of the dancing. For this reason, a lot of their N/W was about the dancing.
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"I noticed..."
...I noticed jumping and different directions
...I saw movement
...It doesn't always have to be your feet your feet [that move], it can be your body too. You can twist your body around and your feet stay in the same place.
...there is a connection between dancing and math
...math and dancing can be combined-ded (sic)
....that clogging and tap are cousins
...there's a lot of footwork in clogging
...you hear different sounds when you're dancing
...you're using degrees when you dance
...there are different amounts of angles
...that dance and math work together well

A meta "I noticed..."
...I noticed that we made some mistakes and I, personally, stopped because I didn't understand it and I watched to see how it was done. [Me: was that helpful for you?] Yeah.

"I wonder..."
...how we're going to put all the beats and stuff together
...if you can cross your feet and go backwards with it
...if it's like a sport
...if I can do clogging on a tight rope
...if you can actually use math with dancing
...if we'll all actually end up being good at this
...if we're ever going to use the 360 degrees
...[wonders about how I dance so quickly, how long it took me to learn, etc.]
...is there a certain amount of beats you have to have in clogging
...could you dance for as long a time as you want
...why was clogging invented
...how do you do this for so long and not be tired?

I'm thrilled. This is already SO much more information about how the kids are experiencing the work than I ever had before.

Take-away from Day 1: Notice and Wonder is SOSOSOSOSOSOOOOOOOO much better than asking: "Do you have any questions?" lol