Category Archives: Questions

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?

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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.

Read with me? Book study: Positive Discipline in the Classroom

How do we engage with and make meaning and connections from text? How might we notice and note big ideas from a text to capture what speaks to us? How do we show and share what we are thinking? When we cannot find time to meet, how will we connect, learn, and share? What if we try a slow chat book study?

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An invitation sent to members of our learning community:

In preparation for our continuing work with Kelly Gfroerer and Sarah Morgan Bonham, you are invited to learn and share using a “slow chat book study” of Positive Discipline in the Classroom: Developing Mutual Respect, Cooperation, and Responsibility in Your Classroom by Jane Nelsen, Lynn Lott, and H. Stephen Glenn. We will follow the schedule below to read and share ideas from a chapter per week.  

With a slow chat book study you are not required to be online at any set time. Instead, share your ideas and respond to others’ thoughts as you have time. This accommodates different schedules to allow for maximum community participation and for great conversations to unfold at a slower pace. We will use Twitter hashtag #TrinityReads to share and follow  the comments of others.

No need to sign up for the book study – just have a twitter account and search for hashtag #TrinityReads. And, when you post your comments please do include #TrinityReads so others can follow along and find your comments easily.

When you have more to say than 140 characters, we encourage you to link to blog posts, images, or other documents to share more fully.

The Book Study Schedule and Prompts

To help you think about what might be shared as you read we have established the following schedule and prompts to help with sharing and discussion.

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Each week the following prompts will be used to encourage sharing and discussion:

Monday:
Sentence/Phrase – Share a quote that is meaningful to you, that captures the core ideas, that moved, engaged, or provoked you. Say more…

Tuesday:
Connect – How do these ideas connect to what you already know, think, and study?  What text-to-self, text-to-text, text-to-world: connections can we make?

Wednesday:
Extend – What new ideas extend or push your thinking in a new direction?

Thursday:
Challenge – What now is a challenge for you? What will/did you try?

Friday:
I used to think… now I…

 How do we show and share what we are learning? When we cannot find time to meet, how will we connect, learn, and share? What if we try?

Join us.  We value your thinking, learning, and contributions.

Teaming: Deepen Understanding to Strengthen Academic Foundation

How might we learn and grow together? How do we connect ideas and engage in productive, purposeful professional development (aka learning experiences) around common mission, vision, and goals? What if we model what we want to see and experience in our classrooms?

Influenced, inspired, and challenged by our work at Harvard Graduate School of Education’s 2016 session on the Transformative Power of Teacher TeamsMaryellen BerryRhonda MitchellMarsha Harris, and I set common goals for faculty-learners.

We can design and implement a differentiated action plan across our grade to meet all learners where they are.

But, how do we get there?

For a while, we will narrow to a micro-goal.

We can focus on the instructional core, i.e. the relationship between the content, teacher, and learner.

For today’s Pre-Planning session, a specific goal. At the end of this session, every faculty-learner should be able to say

We can engage in purposeful instructional talk concerning reading, writing, and math to focus on the instructional core.

Here’s our learning plan:

8:00 Intro to Purpose
Instructional Core: Relationship between content, teacher, student

Explain Content Groups tasks

8:30 Movement to Content Groups
8:35 Content Groups Develop Mini-Lesson

9:05 Movement back to Grade-Level Teams in the Community Room
9:10 Share Readers’ Workshop Instructional Core ideation
9:20 Q&A and transition
9:25 Share Writers’ Workshop  Instructional Core ideation
9:35 Q&A and transition
9:40 Share Number Talk  Instructional Core ideation
9:50 Q&A and transition
9:55 Closure:  Planning, Reflection, Accountability

We also shared our learning progressions with faculty so they might self-assess and grow together.

Today’s goal:
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Year-long goal:
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When  we focus on the instructional core and make our thinking visible, we open up new opportunities to learn and to impact learning with others.

How might we deepen understanding to strengthen learning?

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?

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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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ASCD 2016: Sketchnotes for learning

Association for Supervision and Curriculum Development IASCD)
April 2-4, 2016
Atlanta, GA

Don Wettrick asked how might we offer time for learners to act on their imaginative ideas to create prototypes, products, and new outcomes.

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Manny Scott challenged us to serve the whole child.  How might we offer hope to every learner?

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Doug Fisher, Nancy Frey, and Stefani Hite shared their latest research and learning around purpose driven instruction and challenged us to collect evidence of impact.

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Carol Ann Tomlinson and Michael Murphy encouraged us to level up in our ability to differentiate.  Do we have both short-term and long-term goals for our learners?

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Carol Dweck asks how might we focus on learning and offer feedback that is observational instead of judgemental.

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Shauna Peeples highlighted the power of positivity.  How might we send message containing love and purpose?

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Nina Culbertson and David Griffith discussed CASEL’s social-emotional competencies and needs for all to thrive.

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Kami Thordarson and Karen Wilson facilitated an interactive session for leaders embracing design thinking in their daily practice.  How might we use the DT iterative process to impact all learners in our care?

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Notice and note: check for comprehension

Is it true that the only time we expect demand that our learners draw a picture to accompany their work is when they are working with trigonometry and related rates?

How do we know – Do we know – that our learners are invested and engaged with the context of the task?

What if we connect to ideas they are using and learning in their literacy blocks?  How might we collaborate to use the same language with our learners?

Good mathematicians and scientists, just like good readers and writers, notice and note.  We seek patterns and wonder about things that occur again and again. We look for and express regularity in repeated reasoning.

How might we show our learners how to notice and note? What if we leverage their creativity and curiosity to show what they know more than one way?

Have you tried Robert Kaplinsky‘s task, How much does a 100×100 In-N-Out cheeseburger cost?

How would you notice and note? What might you and your learners wonder? Do I and my learners just note “the facts?”

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Or, do we take the time to sketch what we see?

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I wonder… I believe that the sketch doodle helps the thinker analyze what they see, notice what is repeated and what is not repeated.

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How might we deepen understanding and engagement by taking the time to notice and note what occurs again and again and to look for and express regularity in repeated reasoning?

 

Focus on learning: build a team – Embedding Formative Assessment VTR SPW

What if we collect evidence of progress to plan for next steps in learning?

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What if we take up a series of 30 Day Challenges: Step outside your comfort zone! as described in Justin Cahill’s linked post? Justin (@justybubpe) writes:

How about professionally? How can I apply the 30-day challenge to my job as a physical education teacher? How can I use this challenge to motivate my students? How can I take advantage of trying something new for 30 days to help bolster my planning and strengthen my curriculum? How will I answer all of these questions in under 30 days?

What if we focus on learning? When we set goals, are we committed to reaching them? What if we set micro-goals and action-steps that move our learning forward regularly?  How might we choose to team to step outside our comfort zone for 30 days to shift our practice to more formative assessment?

What if we choose to build a supportive accountability team to carve out moments for self- and peer-assessment?

Four weeks appears to be a minimum period of time for teachers to plan and carry out a new idea in their classroom. (Wiliam, 22 pag.)

How might we shift to grow from

a knowledge-giving business to a habit-changing business? (Wiliam, 19 pag.)

What if we try for 30 days?

Indeed, the evidence suggests that attention to classroom formative assessment can produce greater gains in achievement than any other change in what teachers do. (Wiliam, 11 pag.)

How might we try for 30 days?

Viewed from this perspective, choice is not a luxury but a necessity. (Wiliam, 15 pag.)


Cahill, Justin. “30 Day Challenges: Step outside Your Comfort Zone!” Keeping Kids in Motion. WordPress, 06 Jan. 2016. Web. 08 Jan. 2016.

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