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.