Tag Archives: Effective Practices for Advancing the Teaching and Learning of Mathematics

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:

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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.

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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!

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Andrew said that you know you have them when they start making requests.screen-shot-2017-03-04-at-7-43-06-pm

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.

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

Deep understanding: visualize, connect, comprehend

We need to give students the opportunity to develop their own rich and deep understanding of our number system.  With that understanding, they will be able to develop and use a wide array of strategies in ways that make sense for the problem at hand.  (Flynn, 8 pag.)

Let’s say that the essential-to-learn is I can subtract within 100.  In our community we hold essential I can show what I know more than one way. 

Using our anchor text, we find the following strategies:

  • I can subtract tens and one on a hundred chart.
  • I can count back to subtract on an open number line.
  • I can add up to subtract on an open number line.
  • I can break apart numbers to subtract.
  • I can subtract using compensation.

What if we engage, as a team, to deepen our understanding of subtraction?

Deep learning focuses on recognizing relationships among ideas. During deep learning, students engage more actively and deliberately with information in order to discover and understand the underlying mathematical structure. (Hattie, 136 pag.)

In his Effective Practices for Advancing the Teaching and Learning of Mathematics class last week, Mike Flynn highlighted three advantages  of using representations to deepen understanding.

  • Representations build conceptual understanding and help assess comprehension.
  • Representations serve as a tool to make sense of the task and the mathematics.
  • Representations help develop proof of generalizations.

What if we, as a team, prepare to facilitate experiences so that learners can say I can subtract within 100 by deepening our understanding with words, pictures, numbers, and symbols?

Context: Annie had some money in her “mad money” jar.  Today, she added $39 to the jar and discovered that she now has $65. How much money was in the “mad money” jar before today?

2ndgrade65-39

Can we connect the context to each of the above strategies? Can we connect one strategy to another strategy?

If we challenge ourselves to “do the math” using words, pictures, numbers, and symbols, we deepen our understanding and increase our ability to ask more questions to advance thinking.

How might we use Van de Walle’s ideas for developing conceptual understanding through multiple representations to assess comprehension and understanding?


Flynn, Michael. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, Maine.: Stenhouse, 2017. Print.

Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L. (2016-09-16). Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series). SAGE Publications. Kindle Edition.

Van de Walle, John. Teaching Student-centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K-2. Boston: Pearson, 2014. Print.