Tag Archives: Jennifer Wilson

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.


You can see the notes I started on paper.


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.


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


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.


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.


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


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.

NCSM 2016: Sketch notes for learning

NCSM 2016 National Conference – BUILDING BRIDGES BETWEEN LEADERSHIP AND LEARNING MATHEMATICS:  Leveraging Education Innovation and Research to Inspire and Engage

Below are my notes from each session that I attended and a few of the lasting takeaways.

Day One

Keith Devlin‘s keynote was around gaming for learning. He highlighted the difference in doing math and learning math.  I continue to ponder worthy work to unlock potential.  How often do we expect learners to be able to write as soon as they learn? If we connect this to music, reading, and writing, we know that symbolic representations comes after thinking and understanding.  Hmm…Apr_11_NCSM-Devlin

The Illustrative Mathematics team challenged us to learn together: learn more about our students, learn more about our content, learn more about essentials for our grade and the grades around us.  How might we learn a lot together?

Conference Sketch Note - 25

Graham Fletcher teamed with Arjan Khalsa. While the title was Digital Tools and Three-Act Tasks: Marriage Made in the Cloud, the elegant pedagogy and intentional teacher moves modeled to connect 3-act tasks to Smith/Stein’s 5 Practices was masterful.
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Jennifer Wilson‘s #SlowMath movement calls for all to S..L..O..W d..o..w..n and savor the mathematics. Notice and note what changes and what stays the same; look for and express regularity in repeated reasoning; deepen understanding through and around productive struggle. Time is a variable; learning is the constant.  Embrace flexibility and design for learning.

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Bill McCallum challenges us to mix memory AND understanding.  He used John Masefield’s Sea Fever to highlight the need for both. Memorization is temporary; learners must make sense and understand to transfer to long-term memory.  How might we connect imagery and poetry of words to our discipline? What if we teach multiple representations as “same story, different verse”?

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Uri Treisman connects Carol Dweck’s mindsets work to nurturing students’ mathematical competence.  Learners persist more often when they have a positive view of their struggle. How might we bright spot learners’ work and help them deepen their sense of belonging in our classrooms and as mathematicians?

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Day Two

Jennifer Wilson shared James Popham’s stages of formative assessment in a school community. How might we learn and plan together? What if our team meetings focus on the instructional core, the relationships between learners, teachers, and the content?

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Michelle Rinehart asks about our intentional leadership moves.  How are we serving our learners and our colleagues as a growth advocate? Do we bright spot the work of others as we learn from them? What if we team together to target struggle, to promote productive struggle, and to persevere? Do we reflect on our leadership moves?

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Karim Ani asked how often we offered tasks that facilitate learning where math is used to understand the world.  How might we reflect on how often we use the world to learn about math and how often we use math to understand the world in which we live? Offer learners relevance.

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Day Three

Zac Champagne started off the final day of #NCSM16 with 10 lessons for teacher-learners informed from practice through research. How might we listen to learn what our learners already know? What if we blur assessment and instruction together to learn more about our learners and what they already know?

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Eli Luberoff and Kim Sadler created social chatter that matters using Desmos activities that offered learners the opportunities to ask and answer questions in pairs.  How might we leverage both synchronous and asynchronous communication to give learners voice and “hear” them?

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Fred Dillon and Melissa Boston facilitated a task to highlight NCTM’s Principles to Actions ToolKit to promote productive struggle.  This connecting, for me, to the instructional core.  How might we design intentional learning episodes that connect content, process and teacher moves? How might we persevere to promote productive struggle? We take away productive struggle opportunities for learners when we shorten our wait time and tell.

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Read with me? book study: Embedding Formative Assessment

What if we study and practice, together, to embed formative assessment into our daily practice and learning?

Jennifer Wilson (@jwilson828), Kim Thomas (@Kim_math) and I are hosting a virtual book club around Dylan Wiliam’s Embedding Formative Assessment: Practical Techniques for K-12 Classrooms in January and February.

I am intrigued and inspired by the chapter titles. I want to learn more about learning intentions and success criteria, eliciting evidence of learning, feedback that moves learners forward, students serving as resources for each other, and students as owners of their own learning.

If you don’t have the book yet, you can check it out by reading the first chapter from Learning Science’s website.

Here’s our reading plan:


We want you to join us! We commit to reading one chapter per week and sharing our thinking using #T3Learns. To add a little structure to our reflective practice, we are going to share using the following Visible Thinking Routines.  Of course, we will share other things too.

We choose this reading pace in order to prepare for Dylan Wiliam’s keynote and sessions at the 2016 International T3 Conference in Orlando. We want to be able to ask questions and make connections based on our actions, experiences, successes, and struggles.

Join us! Let’s experiment and learn by doing.

How might we impact learning if we work on intentionally embedding formative assessment into our daily practice and learning?

Cross posted on Easing the Hurry Syndrome.

Ritchhart, Ron, Mark Church, and Karin Morrison. Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. San Francisco, CA: Jossey-Bass, 2011. Print.

Wiliam, Dylan, and Siobhán Leahy. Embedding Formative Assessment: Practical Techniques for F-12 Classrooms. West Palm Beach, FL: Learning Sciences, 2015. Print.


#SlowMath: look for meaning before the procedure

In her #CMCS15 session, Jennifer Wilson (@jwilson828) asks:

How might we leverage technology to build procedural fluency from conceptual understanding?  What if we encourage sketching to show connections?

What if we explore right triangle trigonometry and  equations of circles through the lens of the Slow Math Movement?  Will we learn more deeply, identify patterns, and make connections?

How might we promote and facilitate deep practice?

This is not ordinary practice. This is something else: a highly targeted, error-focused process. Something is growing, being built. (Coyle, 4 pag.)

What if we S…L…O…W… down?

How might we leverage technology to take deliberate, individualized dynamic actions? What will we notice and observe? Can we Will we What happens when we will take time to note what we are noticing and track our thinking?


What is lost by the time we save being efficient, by telling? How might we ask rather than tell?

#SlowMath Movement = #DeepPractice + #AskDontTell

What if we offer more opportunities to deepen understanding by investigation, inquiry, and deep practice?

Coyle, Daniel (2009-04-16). The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. Random House, Inc.. Kindle Edition.

Fluency: comprehension, accuracy, flexibility, and efficiency

No strategy is efficient for a student who does not yet understand it. (Humphreys & Parker, 27 pag.)

If both sense and meaning are present, the likelihood of the new information getting encoded into longterm memory is very high. (Sousa, 28 pag.)

When we teach for understanding we want comprehension, accuracy, fluency, and efficiency. If we are efficient but have no firm understanding or foundation, is learning – encoding into longterm memory – happening?

We don’t mean to imply that efficiency is not important. Together with accuracy and flexibility, efficiency is a hallmark of numerical fluency. (Humphreys & Parker, 28 pag.)

What if we make I can make sense of problems and persevere in solving them and I can demonstrate flexibility essential to learn?


Flexibility #LL2LU

If we go straight for efficiency in multiplication, how will our learners overcome following commonly known misconception?

common misconception: (a+b)²=a² +b²


correct understanding: (a+b)²=a² +2ab+b²

The strategies we teach, the numeracy that we are building, impacts future understanding.  We teach for understanding. We want comprehension, accuracy, fluency, and efficiency.

How might we learn to show what we know more than one way? What if we learn to understand using words, pictures, and numbers?

What if we design learning episodes for sense making and flexibility?

Humphreys, Cathy, and Ruth E. Parker. Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4-10. Portland, ME: Steinhouse Publishers, 2015. Print.

Sousa, David A. Brain-Friendly Assessments: What They Are and How to Use Them. West Palm Beach, FL: Learning Sciences, 2014. Print.

Struggle: pay attention; keep moving forward – The Talent Code VTR SPW

What if we reframe mistakes to be billed as opportunities to learn? If we truly believe in fail up, fail forward, fail faster, how do we leverage the quick bursts of failure mistakes struggle to propel learning in a new direction?

Struggle is not optional—it’s neurologically required: in order to get your skill circuit to fire optimally, you must by definition fire the circuit suboptimally; you must make mistakes and pay attention to those mistakes; you must slowly teach your circuit. You must also keep firing that circuit—i.e., practicing—in order to keep myelin functioning properly. After all, myelin is living tissue. (Coyle, 43 pag.)

How might we position each learner to work at the edge of their ability, reaching to a new goal,  capture failure and turn it into skill?

Because the best way to build a good circuit is to fire it, attend to mistakes, then fire it again, over and over. Struggle is not an option: it’s a biological requirement. (Coyle, 34 pag.)

How might we establish a community norm that calls for a trail of mistakes to show struggle and evidence of learning? What if paying attention to mistakes is an essential to learn? How might we celebrate the trail that leads to success, to keep moving forward?


Summer Reading using VTR: Sentence-Phrase-Word:
The Talent Code
Chapter 2: The Deep Practice Cell

How might we target struggle so that it is productive? For what should we reach? What if expand our master coach toolkit to include a pathway to sense making and perseverance?

SMP-1: Make Sense of Problems and Persevere #LL2LU

What if we target productive struggle through process? How might we lead learners to level up by helping them reach? When learners are thrashing around blindly, how might we serve as refuge for support, encouragement, and a push in a new direction?

Coyle, Daniel (2009-04-16). The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. Random House, Inc.. Kindle Edition.

Patient development of conceptual understanding

<true confession>

Sometimes I teach at my pace instead of the pace of the learners in my care.


To where am I racing?

Rule Three from The Talent Code by Daniel Coyle is SLOW IT DOWN.

“Why does slowing down work so well? The myelin model offers two reasons.  First, going slow allows you to attend more closely to errors, creating a higher degree of precision with each firing – and when it comes to growing myelin, precision is everything.  As football coach Tom Martinez likes to say ‘It’s not how fast you can do it. It’s how slowly you can do it correctly.’ Second, going slow helps the practitioner to develop something even more important: a working perception of the skill’s internal blueprint – the shape and rhythm of the interlocking skill circuits.”  (p. 85)

In her Shortest Path post, Jennifer Wilson (@jwilson828) asks:

How many of our students would choose a beautiful path over the shortest path to learn a new topic? Which of our students would always choose the shortest path over a happier path to learn a new topic?

I wonder how many learners would choose a beautiful path over the shortest path.  Listen to Daniele Quercia.

I have a confession to make. As a scientist and engineer, I’ve focused on efficiency for many years. But efficiency can be a cult, and today I’d like to tell you about a journey that moved me out of the cult and back to a far richer reality.

What is lost by the time we save being efficient?

How might we take up the challenge of teaching and learning procedural fluency through patient development of conceptual understanding? What if I can show what I know in more than one way is deemed essential to learn?

What if we guide our learners on a journey that offers beauty, understanding, quiet, more time, and then efficiency?

Let’s avoid the dangers of a single path. Choose patient development of beautiful paths to conceptual understanding.

It is not an impossible dream.

Be patient.


Coyle, Daniel. The Talent Code: Greatness Isn’t Born : It’s Grown, Here’s How. New York: Bantam, 2009. 217.  Print.