Tag Archives: NCSM

Deep Practice: Building Conceptual Understanding in the Middle Grades

2017 NCSM Annual Conference
Deep Practice: Building Conceptual Understanding
in the Middle Grades
Jill Gough, Jennifer Wilson

How might we attend to comprehension, accuracy, flexibility, and then efficiency? What if we leverage technology to enhance our learners’ visual literacy and make connections between words, pictures, and numbers? We will look at new ways of using technology to help learners visualize, think about, connect and discuss mathematics. Let’s explore how we might help young learners productively struggle instead of thrashing around blindly.

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. 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.)

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 pag.)

Coyle, Daniel. The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. (p. 18-20). Random House, Inc.. Kindle Edition.

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.

#NCSM17 #Sketchnotes Monday Summary

I’m attending the  National Council of Supervisors of Mathematics  2017 conference in San Antonio.  Here are my notes from Monday along with the session descriptions from the presenters.

Knocking Down Barriers with Technology
Eli Luberoff

One-to-one. Accessibility. Personalization. Internationalization. Low oor. High ceiling. What do these all have in common? Each is targeted to making mathematics work for every student. Not just the con dent students with engaged parents, not just the struggling students, every student. We will explore the technology and techniques that can open doors, challenge the bored, empower the disempowered, and turn every student into a mathematics student.

Gut Instincts: Developing ALL Students’ Mathematical Intuitions
Tracy Zager

We’ve long misunderstood mathematical intuition, assuming it’s innate rather than developed through high-quality learning experiences. As a result, students who haven’t yet had opportunities to foster their intuitions are often denied access to meaningful mathematics. Through analysis of powerful classroom teaching and learning, we’ll explore three instructional strategies you can use to empower ALL students to grasp mathematics intuitively.

Problem Strings to Change Teaching Practice
Pam Harris

A problem string is a purposefully designed sequence of related problems that helps students mentally construct mathematical relationships and nudges them toward a major, efficient strategy, model, or big idea. We show how problem strings can be leveraged for changing teachers’ practice. Because it puts students’ ideas at the center, teachers are forced to listen deeply to kids and structure mathematics conversations around their thinking.

Rethinking Expressions and Equations:
Implications for Teacher Leaders
Michelle Rinehart

How are one- and two-variable expressions, one- and two- variable equations, and the standard form of a line connected in a powerful way? How might this progression support student learning of these “tough-to-teach/tough-to-learn” ideas? Explore the underlying theme that uni es these seemingly disparate topics using a technology-leveraged approach. Consider research and the role of teacher leaders in developing real understanding of these topics.

Talk Less and Listen More
Zachary Champagne

It’s a simple, and very complex, idea that great teachers
do and do well. Genuinely listening to students can yield incredible opportunities for teachers to not only know and connect with their students, but also increase the quality of teaching and learning that happens in the classroom. Join us as we explore the power of listening to students and using that information to inform our instruction. We’ll also explore strategies to help provide the supportive conditions and frameworks to help leaders support teachers in doing this work. We’ll do this through examining video clips of students sharing their mathematical ideas and consider what listening affords and what questions could be asked to further their mathematical thinking.

Leading Mathematics Education in the Digital Age

Leading Mathematics Education in the Digital Age
2017 NCSM Annual Conference
Pre-Conference Sessions
Jennifer Wilson
Jill Gough

How can leaders effectively lead mathematics education in the era of the digital age?  

There are many ways to contribute in our community and the global community, but we have to be willing to offer our voices. How might we take advantage of instructional tools to purposefully ensure that all students and teachers have voice: voice to share what we know and what we don’t know yet; voice to wonder what if and why; voice to lead and to question.

Sneak peek: Leading Mathematics Education in the Digital Age

Leading Mathematics Education in the Digital Age
2017 NCSM Annual Conference
Pre-Conference Session
Sunday, April 2, 2017 from 1:00-5:00 p.m.
Jennifer Wilson
Jill Gough

How can leaders effectively lead mathematics education in the era of the digital age? There are many ways to contribute in our community and the global community, but we have to be willing to offer our voices. How might we take advantage of instructional tools to purposefully ensure that all students and teachers have voice: voice to share what we know and what we don’t know yet; voice to wonder what if and why; voice to lead and to question?

Sneak peek for our session includes:

How might we strengthen our flexibility to make sense and persevere? What if we deepen understanding to show what we know more than one way?

Interested? Here’s a sneak peek at a subset of our slides as they exist today. Disclaimer: Since this is a draft, the slides may change before we see you in San Antonio.

I wonder what Jennifer’s sneak peek looks like? Do you?

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”?

Conference Sketch Note - 28

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?

Conference Sketch Note - 29

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?

Conference Sketch Note - 30

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?

Conference Sketch Note - 33

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?

Conference Sketch Note - 34

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.

Conference Sketch Note - 35

JGough observes JWilson – #NCSM14 Developing Conceptual Understanding Through the Progressions

Peer-to-Peer Observations…who learns?


Piloting an Observation of Practice with Jennifer Wilson (@jwilson828), I observed Jennifer during our NCSM presentation, Developing a Conceptual Understanding of Fractions. Below is a record of what I observed and then my reflection.  I am grateful for the opportunity to observe Jennifer and to learn from and with her.

Jill Gough observes Jennifer Wilson
NCSM: Wednesday, April 9, 2014, 10:00 – 11:00, New Orleans, LA
Session:  Developing Conceptual Understanding Through the Progressions:  Fractions, Ratios, and Proportions


Jennifer began her session with Essential Learnings for the hour.  By the end of this session, everyone should be able to say:

  • I can describe a fraction a/b as a copies of 1/b.
  • I can construct questions that push and probe student thinking about questions.
  • I can explain the role that technology plays in deepening student understanding of fractions.

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I like that Jennifer began her session this way, because it offered participants focus and direction. I wonder if the audience appreciated this intentional guiding of thinking.  I like that there was a content essential learning, an assessment essential learning, and a process essential learning.  What if all PD lessons were launched this way? I wonder if we would see more engagement and thought and less nervousness about which button to press.

I appreciated the situation Jennifer experienced with technology as the session began.  The same situation happened to me in Sacramento a couple of weeks ago.  After playing her PowerPoint slide, Jennifer returned to the Navigator software to find all the traditionally black text was now white making is difficult to read.  In addition, when she returned to the slideshow, it was frozen.  (Same for me in Sacramento, but I was using Keynote.)

I like that Jennifer pressed forward, abandoning her slide deck to keep the conversation going with the participants.  I wonder how she would handle this in such a short session if she was presenting alone.

I liked the formative assessment question sent via quick poll to engage the audience right away.  While I was not quick enough to capture the results, they were varied. Each choice had some takers.  I liked the use a warm-up question using the Navigator. I liked that Jennifer took action based on the results.  Good modeling.  I liked that the Navigator was used as a tool and that fractions were the featured event that anchored the discussion.

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I love watching Jennifer facilitate peer-to-peer discourse, because she requires individual thinking time prior to group discussion.  I aspire to use her protocol. I need this when I am learning. What if we established this as a goal or must do for all instructors?

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Jennifer used the following files during her session:

Using appropriate wait time, Jennifer offered hands-on experience and investigation time for participants to explore each of the files.  She prompted participants to shoulder-partner up and brainstorm push and probe questions that might be asked of students.  Jennifer used the Navigator to capture class responses to comment on and visualize quality questions from the audience and the authors.  I like that she modeled push and probe questioning through this discussion.  She honored participant questions and offered advancing questions to help push their thinking.

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I observed participants struggle with what questions to ask and what response to hope for from learners.  One participant said “I don’t know how to explain these true/false questions.  I know which ones are true and which are false, but how do I explain in words?” Evidence of probing for understanding and that thinking was being pushed.  I liked that I had the opportunity to witness and then facilitate peer-to-peer discourse as these teacher-learners grappled with the why of fractions.  I wonder if we should incorporate the 5-whys protocol and theWhat Makes You Say That Visible Thinking Routine to facilitate rich discussion and uncover possible misconceptions.

Using the Navigator class capture, Jennifer complimented the audience on their approaches to Fractions and Unit Squares and that none of their methods were the way she thought.  “My students continually surprise me. You too!” I like that she modeled her way only after showing several correct ways.

Jennifer closed by returning to the Essential Learnings to remind participants of their experience and what the target was for the session.

Jill’s reflection:

 As a result of this observation of practice and feedback loop, which aspects of my teaching do I feel are bright spots?

I like starting sessions with Essential Learnings written as I can… statements.  Observing Jennifer launch and close her session with the I can… statements was the first time I’ve seen someone other than me leverage them in a professional development session.  In my own practice, I send the agenda ahead of the session when possible. I wonder if I should declare them as the beginning of the session. I thought it was a powerful anchor for our work.

I like starting with a warm-up question that turned into formative assessment.  In my own practice, I have intentionally described how I am shifting gears based on a warm-up question to model adjusting (not abandoning) the plan to meet learners where they are.  I wonder how many teacher-learners miss the adjustment when we are not direct about the shift we are making.  At the Social Media PD Saturday, Sam commented on the shifts I made based on the learners’ questions and the fact that I still accomplished everything on the plan.  What if we are more intentional when we shift to make the shift transparent? Based on these results, we are going to shift to X, and we will get to our destination. This connects to Jo Boalers’ I am giving you this feedback because I believe in you. What if we are direct? I/we are shifting the plan because we need to do X to accomplish XX.

I like using the Navigator to highlight multiple pathways to success.  I appreciated Jennifer using the Navigator to intentionally highlight more than one way to accomplish a task.  I wonder if zooming in to show 2 screens from the class capture helps participants sitting in the back to see.  What if we regularly and intentionally honor work by showing multiple correct pathways?

As a result of this observation of practice and feedback loop, what questions do I have about my own teaching?

I wonder how to include more participants when using the Navigator.  At Jennifer’s session, there were 30 handhelds and 40 participants.  I wonder how to engage all participants. Do we need more resources? Should we partner? I want to try more participants connected to Navigator in my work with large groups.  Even though every participant (40-90 participants) had a handheld, we observed those not connected and displayed were less engaged.

What if I am more intentional about Think-Team-Share? I appreciated Jennifer’s direct and intentional let’s take 30-60 seconds to organize our thoughts silently before sharing. What if I add this to my facilitation toolkit? What if I add let’s take a minute to quick-write. Describe your thinking on paper to offer a visual of your idea when sharing with others. How might I model this as a strategy for any learning episode?

As a result of this observation of practice and feedback loop, what new ideas do have?

Well, one is in the paragraph above.  “What if I add this to my facilitation toolkit? What if I add let’s take a minute to quick-write? Describe your thinking on paper to offer a visual of your idea when sharing with others. How might I model this as a strategy for any learning episode?” I hear myself talk about teaching learners visual note taking, but do I model it for teacher-learners? What if I write a blog post that show what is in my head so that it is clearer to me and to others?

I am inspired to work on my closings.  I like how Jennifer cycled back to the Essential Learning for the session to have participants do a quick mental self-assessment.  I believe the way she closed the session improved the chances that the message will stick.

[Cross posted at Easing the Hurry Syndrome]