Tag Archives: #MtHolyokeMath

#LessonClose with @TracyZager at #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 8, Lesson Close with Tracy Zager.

Tracy’s session connects, for me, to a practitioner’s corner in David Sousa’s How the Brain Learns.  He writes

Closure describes the covert process whereby the learner’s working memory summarizes for itself its perception of what has been learned.  It is during closure that a student often completes the rehearsal process and attaches sense and meaning to the new learning, thereby increasing the probability that it will be retained in long-term storage. (p. 69)

How might we take up Tracy’s challenge to “never skip the close?” What new habits must we gain in order to make sure the close is useful to the learner?

Sousa continues

Closure is different from review. In review, the teacher does most of the work, repeating key concepts made during the lesson and rechecking student understanding.  In closure, the student does most of the work by mentally rehearsing and summarizing those concepts and deciding whether they make sense and have meaning. (p. 69)

What new habits must we gain in order to make sure the close is helps them reflect on learning, make connections, and/or ask new questions? In other words, do we plan intention time for learners to make sense of the task?

Closure is an investment than can pay off dramatically in increased retention of learning. (Sousa, p. 69)


Sousa, David A. How the Brain Learns. Thousand Oaks, CA: Corwin, a Sage, 2006. Print.

Building and Sustaining the Culture of Problem Solving in our Classroom with @FawnPNguyen #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 7, Building and Sustaining the Culture of Problem Solving in our Classroom, with Fawn Nguyen

I am struck by Fawn’s initial purpose. Building and sustaining a culture of problem solving in our classrooms demands vision with plans and commitment with continual growth through feedback.

How to we make use of structure in our planning to narrow our resources to build and sustain coherence and connectedness? Wen we plan, are we intentionally connecting to standards and intentionally stepping away from them to promote problem solving, visual learning, and deepening understanding?

What tasks do we select? How much time do we spend? And, most importantly, how do we show faith in our learners to promote productive, creative struggle?


Notes from previous sessions:

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Harnessing the Power of the Purposeful Task with @GFletchy #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 6, Harnessing the Power of the Purposeful Task, with Graham Fletcher.


Notes from previous sessions:

Putting Student Thinking at the Center with @MathMinds #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 5, Putting Student Thinking at the Center, with Kristin Gray.


Notes from previous sessions:

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?

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:

Leave No Question Unasked: Maximizing Demand & Engagement in Math Tasks with @ddmeyer #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 3, Leave No Question Unasked: Maximizing Demand & Engagement in Math Tasks, with Dan Meyer.


Notes from previous sessions:

Learner choice: using appropriate tools strategically takes time and tools

All students benefit from using tools and learning how to use them for a variety of purposes.  If we don’t make tools readily available and value their use, our students miss out on major learning opportunities. (Flynn, 106 pag.)

I’m taking the #MtHolyokeMath #MTBoS course, Effective Practices for Advancing the Teaching and Learning of Mathematics.  Zachary Champagne facilitated the second session and used The Cycling Shop task from Mike Flynn‘s TMC article.

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You can see the notes I started on paper.

mtholyokemath-2-zakchamp

Jim, Casey and I used a pre-made Google slide deck provided to us to collaborate since we were located in GA, MA, and CA.  We challenged ourselves to consider wheels after working with 8 wheels.

Here’s what our first table looked like.

cyclingshop1

Now, I was having trouble keeping up with the number of wheels and the number of cycles.  So I did this:

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This made it both better and worse for me (and for my group).

Here’s an interesting thing.  I’ve been studying, practicing, and teaching the Standards for Mathematical Practices. Jennifer Wilson and I have written a learning progression to help learners learn to say I can use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. (Sage, 6 pag.)

Clearly, I was not even at Level 1 during class.  Not once – not once – during class did it occur to me how much a spreadsheet would help me, strategically.

8wheelsspreadsheet

The spreadsheet would calculate the number of wheels automatically for each row so that I could confirm correct combinations.  (You can view this spreadsheet and make a copy to play with if you are interested.)

When making mathematical models, [mathematically proficient students] know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. (Sage, 6 pag.)

With a quick copy and paste, I could tackle any number of wheels using my spreadsheet.  I can look for and make use of structure emerged quickly when using the spreadsheet strategically.  (I want to also highlight color as a strategic tool.) Play with it; you’ll see.

9_wheelsspreadsheet

[Mathematically proficient students] are able to use technological tools to explore and deepen their understanding of concepts. (Sage, 6 pag.)

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There is no possible way I would have the stamina to seek all the combinations for 25 or 35 wheels by hand, right?

Students have access to a wide assortment of tools that they must learn to use for their mathematical work. The sheer volume of possibilities can seem overwhelming, but with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal. (Flynn, 106 pag.)

Important to repeat, “with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal.

For this to happen, we need to have a solid understanding of the kinds of tools available, the purpose of each tool, and how students can learn to use them flexibly and strategically in any given situation. This also means that we have to make these tools readily available to students, encourage their use, and provide them with options so they can decide which tool to use and how to use it. If we make all the decisions for them, we remove that critical component of MP5 where students make decisions based on their knowledge and understanding of the tools and the task at hand. (Flynn, 106 pag.)

To be clear, a spreadsheet was available to me during class, but I didn’t see it.  How might we make tools readily available and visible for learners to choose?

When we commit to empower students to deepen their understanding, we make tools available and encourage exploration and use, so that each learner makes decisions for themselves. In other words, how do we help learners to level up in both content and practice?

What if we make I can look for and make use of structure; I can use appropriate tools strategically; and I can make sense of tasks and persevere in solving them essential to learn for every learner?

How might we offer tools and time?

It’s about learning by doing, right?


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

Flynn, Mike. “The Cycling Shop.” Nctm.org. Teaching Children Mathematics, Aug. 2016. Web. 03 Feb. 2017.

Common Core State Standards.” The SAGE Encyclopedia of Contemporary Early Childhood Education (n.d.): n. pag. Web.

Talk Less and Listen More with @ZakChamp #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 2, Talk Less and Listen More,  with Zak Champagne.

Notice the piece of art at the top of my sketch and compare it to what I found the next day at Spotlight on Art.


Notes from previous sessions:

 

 

 

 

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.