Tag Archives: Mike Flynn

#LL2LU, Learning, Learning Progressions, Presentations, Professional Development Plans, Questions, Reading, Sketch Notes

Traverse session: Experiential and Instructional: Promoting Productive Mathematical Struggle #tvrse18

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At Traverse Boulder, I facilitated the following session on Tuesday, June 5, 2018.

Experiential and Instructional:
Promoting Productive Mathematical Struggle

How might we implement tasks that promote reasoning and problem solving to deepen conceptual understanding? Let’s identify and implement high quality tasks grounded in real experiences. Advancing the teaching and learning of mathematics cannot be accomplished with decontextualized worksheets. Discuss, sketch, and solve tasks that promote flexibility, creative and critical reasoning, and problem solving. Learning math should be anchored in depth of understanding through context – not pseudo context – and built on conceptual understanding as well as procedural fluency.

Here’s my sketch note of our plan:

Here’s the slide deck:

Just say no to worksheets.

Say YES to productive struggle and grappling.

Embolden your inner storyteller and leverage the art of questioning.

Context is key.

#LL2LU, Connecting Ideas, Learning, Learning Progressions, Presentations, Professional Development Plans, Questions

Summer PD: Day 1 Make Sense; Persevere

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Summer Literacy and Mathematics Professional Learning
June 5-9, 2017
Day 1 – Make Sense and Persevere
Jill Gough and Becky Holden

Today’s focus and essential learning:

We want all mathematicians to be able to say:

I can make sense of tasks
 and persevere in solving them.

(but… what if I can’t?)

Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level.  Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)

… designed to help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems.  (Flynn, 19 pag.)

Screen Shot 2017-06-06 at 7.53.02 AM.png

Agenda and Tasks:

Slide deck:

Resources:

Connecting Ideas, Questions, Reading, Reflection

Productive struggle with deep practice – what do experts say

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NCTM’s publication, Principles to Action, in the Mathematics Teaching Practices, calls us to support productive struggle in learning mathematics. How do we encourage our students to keep struggling when they encounter a challenging task? How many learners are accustomed to giving up when they can’t solve a problem immediately and quickly. How do we change the practice of how our students learn mathematics?

Effective teaching not only acknowledges the importance of both conceptual understanding and procedural fluency but also ensures that the learning of procedures is developed over time, on a strong foundation of understanding and the use of student-generated strategies in solving problems. (Leinwand, 46 pag.)

Low floor, high ceiling tasks allow all students to access ideas and take them to very high levels. Fortunately, [they] are also the most engaging and interesting math tasks, with value beyond the fact that they work for students of different prior achievement levels. (Boaler, 115 pag.)

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.)

Deep practice is built on a paradox: struggling in certain targeted ways — operating at the edges of your ability, where you make mistakes — makes you smarter.  (Coyle, 18 pag.)

Or to put it a slightly different way, experiences where you’re forced to slow down, make errors, and correct them —as you would if you were walking up an ice-covered hill, slipping and stumbling as you go— end up making you swift and graceful without your realizing it. (Coyle, 18 pag.)

The second reason deep practice is a strange concept is that it takes events that we normally strive to avoid —namely, mistakes— and turns them into skills. (Coyle, 20 pag.)

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.)

…help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems. (Flynn, 8 pag.)

This term productive struggle captures both elements we’re after:   we want students challenged and learning. As long as learners are engaged in productive struggle, even if they are headed toward a dead end, we need to bite our tongues and let students figure it out. Otherwise, we rob them of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere. (Zager, 128-129 ppg.)

Encourage students to keep struggling when they encounter a challenging task.  Change the practice of how our students learn mathematics.

Let’s not rob learners of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere.

Boaler, Jo. Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (p. 115). Wiley. Kindle Edition.

Coyle, Daniel. The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. (p. 20). Random House, Inc.. Kindle Edition.

Flynn, Michael, and Deborah Schifter. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, ME: Stenhouse, 2017. (p. 8) Print.

Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy, Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series) (p. 136). SAGE Publications. Kindle Edition.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Zager, Tracy. Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Portland, ME.: Stenhouse Publishers, 2017. (pp. 128-129) Print.

Connecting Ideas, Learning, Sketch Notes, Social Media

Harnessing the Power of the Purposeful Task with @GFletchy #MtHolyokeMath

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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:

Connecting Ideas, Learning, Sketch Notes

Putting Student Thinking at the Center with @MathMinds #MtHolyokeMath

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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:

Connecting Ideas, Creativity, Sketch Notes

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

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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:

Connecting Ideas, Learning, Professional Development Plans, Reading, Sketch Notes, Summer Reading

Goal work: learn more math, study the Practices

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The math committee met this week to work on our goals. We agreed that, for the rest of this school year, we would spend half of our time on learning more math and the other half studying to learn more about the Standards For Mathematical Practice.

We met this week to learn more math and to discuss Chapter 1, Mathematical 1: Make Sense of Problems and Persevere in Solving Them in Beyond Answers: Exploring Mathematical Practices with Young Children by Mike Flynn.

Yearlong Goals:

  • We can learn more math.
  • We can share work with grade level teams to grow our whole community as teachers of math.
  • We can deepen our understanding of the Standards For Mathematical Practice.

Today’s Goals:

  • I can make sense of tasks and persevere in solving them.
  • I can reason abstractly and quantitatively.
  • I can look for and make use of structure.

Resources:

Learning Plan

3:05 5 min Quick scan of Jo’s YouCubed article (pp. 2, 11)
3:05 20 min Solving equations visually to make sense of the algebra
(Learn more math)

productive-struggle-4 productive-struggle-3
3:25 5 min Book Club warm-up
3:30 20 min Use Visible Thinking Routines to guide discussion of Chapter One: Make Sense and Persevere
(deepen our understanding of the SMPs.)
3:55 5 min Feedback – “I learned…, “I liked…,”I felt…”

Read Chapter 2: Reason Abstractly and Quantitatively

Update on PD (Goal: Scale our work to our teams.)

When we set purposeful team goals, we help each other make progress, and we use our time intentionally.

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

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

#LL2LU, Connecting Ideas, Learning, Learning Progressions, Questions, Reading, Reflection, Sketch Notes

Learner choice: using appropriate tools strategically takes time and tools

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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 n 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:

screen-shot-2017-02-03-at-3-08-56-pm

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.)

screen-shot-2017-02-03-at-4-03-03-pm

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.

Connecting Ideas, Sketch Notes

Talk Less and Listen More with @ZakChamp #MtHolyokeMath

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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:

 

 

 

 

Ask Don't Tell, Connecting Ideas, Creativity, Questions, Reflection, Sketch Notes

Deep understanding: visualize, connect, comprehend

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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.