Tag Archives: Mike Flynn

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

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.

Summer PD: Day 1 Make Sense; Persevere

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:

Productive struggle with deep practice – what do experts say

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.

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:

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:

Goal work: learn more math, study the Practices

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.