# Summer PD: Day 2 Mathematical Flexibility

Summer Literacy and Mathematics Professional Learning
June 5-9, 2017
Day 2 – Mathematical Flexibility
Jill Gough and Becky Holden

Today’s focus and essential learning:

I can demonstrate mathematical flexibility to show what I know in more than one way.

(but , what if I can’t?)

Learning target and pathway:

Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people (Boaler, 58 pag.)

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.  (Boaler, n. pag.)

UED: 8:45 – 11:15  / EED: 1:15 – 2:45

Resources:

# estimate and reason while dancing, singing, and playing

How might we promote peer-to-peer discourse that is on task and purposeful? What if challenge our students to estimate and reason while dancing, singing, and playing?

Andrew Stadel, this week’s #MtHolyokeMath #MTBoS Effective Practices for Advancing the Teaching and Learning of Mathematics facilitator, asked us to use visuals to engage our learners.  In his session, we used Day 127 How long is “Can’t Buy Me Love”?, Day 129 How long is “We will rock you”?, and Day 130 How long is “I feel good”? from Estimation180.

Here are my visual notes from class:

Our homework was to estimate  How long is “I feel good”? and to try visuals with students.

I asked Thomas Benefield, 5th Grade teacher and FSLT co-chair for 10 minutes of class to try Day 127 How long is “Can’t Buy Me Love”? with 5th grade students.

How might we make sense and persevere when making estimates? What is our strategy and can we explain our reasoning to others?

Students were asked for a reasonable low estimate, a reasonable high estimate, and then an estimate for how long the song is based on the visual. My favorite 5th grade response:

Well, you asked for a low estimate and a high estimate, so I rounded down to the nearest 5 seconds and doubled it for my low estimate. I rounded up to the nearest 10 seconds and doubled it for my high estimate.  For my estimate-estimate, I doubled the time I see and added a second since it looks like almost half.

#Awesome

It was so much fun that they let me stay for How long is “We will rock you”?, and How long is “I feel good”?, and they asked for Bohemian Rhapsody. Wow!

Andrew said that you know you have them when they start making requests.

As you can see, it was a big hit. They were dancing in their seats. This quick snapshot of joy says it is worth it for our students.

What if challenge our students to estimate and reason while dancing, singing, and playing? What joy can we add to our learning experiences?

# Boost Conceptual Understanding & Procedural Fluency with Rich Number Sense Tasks with @mr_stadel #MtHolyokeMath

I’m taking X.MTHED-404: Effective Practices for Advancing the Teaching and Learning of Mathematics (K-12).

Here are my notes from Session 4, Boost Conceptual Understanding & Procedural Fluency with Rich Number Sense Tasks, with Andrew Stadel.

Notes from previous sessions:

# Mistakes: it’s what you do next…

Mistakes: everybody makes them; the key is what happens next.

In his #CMCS15  session, Making Math Mistakes and Error Analysis: Diamonds in the Rough session, Andrew Stadel (@mr_stadelDivisible by 3, and Estimation 180) challenges us to make our thinking visible and to seize opportunities to deepen understanding.

• Math mistakes are a valuable window into student thinking
• Analysis of mistakes can help drive instruction, curb student misconceptions, and strengthen formative assessment.

How might we strength formative assessment to spur action?  Knowing is not enough.  What if we bright spot work found in the mistake to show something was going well?

Do we practice?  How often do we reflect on our struggles? Knowing what went well and where we struggled, how might we consider taking new tack in what we do next?

Do something different… It’s what happens next.