Tag Archives: #TrinityLearns

Number Talks: developing fluency, flexibility, and conceptual understanding #AuthorAndIllustrate

How might we work on fluency (accuracy, flexibility, efficiency, and understanding) as we continue to teach and learn with students? What if our young learners are supposed to be fluent with their multiplication facts, but… they. ..just…aren’t!?

It really isn’t a surprise, right? Children learn and grow at different rates. We know that because we work with young learners every day.  The question isn’t “Why aren’t they fluent right now?” It isn’t. It just isn’t. The question should be and is:

“What are we going to do, right now, to make this better
for every and each learner in our care?”

In Making Number Talks Matter, Cathy Humphreys and Ruth Parker write:

Multiplication Number Talks are brimming with potential to help students learn the properties of real numbers (although they don’t know it yet), and over time, the properties come to life in students’ own strategies. (Humphreys, 62 p.)

Humphreys and Parker continue:

Students who have experienced Number Talks come to algebra understanding the arithmetic properties because they have used them repeatedly as they reasoned with numbers in ways that made sense to them. This doesn’t happen automatically, though. As students use these properties, one of our jobs as teachers is to help students connect the strategies that make sense to them to the names of properties that are the foundation of our number system. (Humphreys, 77 p.)

So, that is what we will do. We commit to deeper and stronger mathematical understanding. And, we take action.

This week our Wednesday workshop focused on Literacy, Mathematics, and STEAM in grade level bands.  Teachers of our 4th, 5th, and 6th graders gathered to work together, as a teaching team, to take direct action to strengthen and deepen our young students’ mathematical fluency.

We began with the routine How Do You Know? routine from NCTM’s High-Yield Routines for Grades K-8 using this sentence:

How do you know?

Here’s how I anticipated the ways learners might think.

Paper.Productive Struggle.195

From The 5 Practices in Practice: Successfully Orchestrating Mathematical Discussion in your Middle School Classroom:

Anticipating students’ responses takes place before instruction, during the planning stage of your lesson. This practice involves taking a close look at the task to identify the different strategies you expect students to use and to think about how you want to respond to those strategies during instruction. Anticipating helps prepare you to recognize and make sense of students’ strategies during the lesson and to be able to respond effectively. In other words, by carefully anticipating students’ responses prior to a lesson, you will be better prepared to respond to students during instruction. (Smith, 37 p.)

How many strategies and tools do we use when modeling multiplication in our classroom? It is a matter of inclusion.

It is a matter of inclusion.

Every learner wants and needs to find their own thinking in their community. This belonging, sharing, and learning matters. We make sense of mathematics and persevere. We make sense of others thinking as they learn to construct arguments and show their thinking so that others understand.

Humphreys and Parker note:

They are learning that they have mathematical ideas worth listening to—and so do their classmates. They are learning not to give up when they can’t get an answer right away because they are realizing that speed isn’t important. They are learning about relationships between quantities and what multiplication really means. They are using the properties of the real numbers that will support their understanding of algebra. (Humphreys, 62 p.)

As teachers, we must anticipate the myriad of ways students think and learn. And, as Christine Tondevold (@BuildMathMinds) tells us:

The strategies are already in the room.

Our job is to connect mathematicians and mathematical thinking.

From NCTM’s Principles to Actions:

Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.


Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

What if we take up the challenge to author and illustrate mathematical understanding with and for our students and teammates?

Let’s work together to use and connect mathematical representations as we build procedural fluency from conceptual understanding.

Humphreys, Cathy. Making Number Talks Matter. Stenhouse Publishers. Kindle Edition.

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

Smith, Margaret (Peg) S.. The Five Practices in Practice [Middle School] (Corwin Mathematics Series). SAGE Publications. Kindle Edition.

Committed to learning #EmboldenYourInnerMathematician

The alarm clock goes off. It is only 15 minutes earlier than usual, but still.  Could there be enough coffee to get going this early? From my warm, quiet bed, I wonder if it was a good decision to enroll in a math class that runs from 7:15 to 9:30 am every Wednesday. After wrangling all members of my family through breakfast and our morning routine – because 15 minutes early for me means 15 minutes for everyone at my house – I enjoy the drive to Trinity with slightly less traffic.

Arriving at school, ready to learn at 7:15, a small and dedicated cohort of 14 faculty-learners gathered every Wednesday morning to deeply study, learn, and implement NCTM’s Mathematics Teaching Practices. These eight teaching practices provide a framework for strengthening the teaching and learning of mathematics.

Sounds a little boring, huh? Was it worth it?

“Yes! This class has helped me deepen my learning in math, and then in turn, deepen the way I teach math for my students. I loved being able to take the math we did and applying it in my classroom through number talks, number strings, children’s literature, and mathematical practices. I always was thinking deeply about math as soon as I entered the class at 7:15 because of engaging tasks and conversation with colleagues.” Caroline Tritschler, Kindergarten Teacher

“I enjoyed the opportunity to work on math that was applicable to my grade level, but we also had the chance to see where our students have been and where they are going. I also felt as if this class pushed us to strengthen our own number sense, perseverance, and use of strategies – all of which are qualities we strive to empower in our own learners.” Casey Leonard, 2nd Grade Teacher

“This course was a huge asset in recognizing the connections throughout grade levels. I loved seeing how our calculus work could be translated into finding patterns and connections the same way we do with our most fundamental skills in Pre-K.” Katherine Anderson, Pre-K Teacher

What is worth it? What was learned?

“I learned new ways of solving problems and showing my work, different ways of thinking about a problem, and validation for insisting that students have a full understanding of the “why” behind concepts.” Vicki Eyles, 5th Grade Teacher

“I feel like I really understand the importance of showing your work in more than one way and being able to explain your thinking to others. I better understand the importance of laying a foundation for using manipulatives and drawings that will carry far past an early elementary level.” Mary Catherine Gober, 1st Grade Teacher

“I am more thoughtful about the questions I ask students and I feel like I can give parents more detail about our approach to math instruction. Additionally, I have a deeper understanding of the benefit of talking to others while “doing” math, as well as the importance of showing one’s thinking in more than one way and making connections to others’ work.” Hilary Daigre, 1st Grade Teacher

What was learned? How has it helped Trinity students?

“My students seem surprised that I am in a class, learning more math. I like to share my struggles and successes with them, modeling growth through perseverance and sharing of ideas with other teachers. I have been able to share my experiences with them, using them to encourage their growth as students. Learning with others who have different backgrounds, strengths, and perspective has been powerful.” Vicki Eyles, 5th Grade Teacher

“I have seen tremendous growth in our class as they begin to take a risk in showing their work in multiple ways. Even those that “struggle” are at least willing to take a risk in trying to solve a problem. I believe the work we did in writing learning progressions for a specific topic has really helped the students want to reach for a higher level or at least work towards asking questions to better understand the problem before they go off and try to work through the problem.” Mary Catherine Gober, 1st Grade Teacher

“Our work with multiplication and division was mind-blowing! I LOVED learning the various ways to approach multiplication/division, including using manipulatives and drawing models. It made more sense to me than anything I had learned in the past. I have shared stories about this experience with my class, including how I had to make sense of problems and really think about how I could solve them. I may not have had the most efficient method for a particular problem, but by talking with others and connecting to what they did, I was able to persevere and feel successful.” Hilary Daigre, 1st Grade Teacher

“I have a greater appreciation for the number line, the modeling, and the ability to make connections. I think the work we did impacted my students weekly. The activities we did I was able to either take back to my students or reminded me of other activities that I then used with the 6th graders. The visual patterns and connecting representations (work from Fawn Nguyen) was the most recent example. The 6th graders loved it. I also really enjoyed the math in literature as did the students!” Kristi Story, 6th Grade Teacher

But… was it boring? Would you recommend this experience to your colleagues?

“It was so much fun to be able to work with colleagues across EED and UED. I think my favorite part was mathematizing children’s literature.” Caroline Tritschler, Kindergarten Teacher

“It’s not only a great place to learn and grow in your understanding, but it’s also a great place to get to know your colleagues in a smaller setting. I’ve really enjoyed getting to know teachers that I wouldn’t have otherwise gotten to know. I genuinely looked forward to Wednesdays because of this class.” Chandler Balentine, 4th Grade Teacher

“I think it is both valuable and fun to spend time struggling with math problems which help us understand our students’ perspectives.” Jon Frank, 5th Grade Teacher

“I think the whole faculty (those that teach any grade level math) should embolden their inner mathematician. I think it was good to have a broad range of “comfort levels” in these sessions. We all learned from each other.” Kristi Story, 6th Grade Teacher

Without fail, at 9:30 after all was said and done, the time that was spent learning pedagogy and math, in fun, creative ways advanced teaching and learning at Trinity. Each Wednesday was a long day, and it was an important day for learners individually and collectively.  


Instructional Core practice #WordsMatter How will we show we CARE?

As part of our school’s Pre-Planning, I facilitated a faculty-teams workshop to continue our work and learning in the Instructional Core.

Here are my notes from the session.

The agenda, shared ahead of the meeting, looked like this:

The slide deck that accompanies this plan looks like this:

We watched 4:05 minutes of Practice is Everything to renew and review our norms around teaming.

How we practice, how we team, makes a difference. The words we choose and use when offering feedback contribute to how our learners author their identity.  As we work to calibrate our expectations, we can also hone and enhance our ability to offer high-quality, positive, actionable feedback that empower learners to reach for their next independent level.

As seen in the slides, I used video timers to pace the teamwork time. What I learned is that the timers held me accountable for the work time promised to teachers.  I was forced to wait, to be patient, and to not rush. So helpful to hold the time for our teachers.

When we focus on learning,
we hold time for learners.

And, just as we carefully plan and hold time for learning, we carefully choose what we notice and note. Words matter; the story you tell impacts how a learner is thought of and seen.

Amanda Thomas (@TrinityMrsT) found and shared the video below. I used it in our session to illustrate the power of story.

As we begin a new school year with new learners, how will we seek a balanced story, describe what we want to see next, and balance our feedback to highlight success?

What story will we notice and note?
What feedback will we offer?
What will we contribute to how  learners author their identity?

How will we show we C.A.R.E.?



Common mission and vision: Be together, not the same

What if we share common mission and vision?  During the 2015-16 school year, we worked together as a team on our SAIS accreditation.  We brainstormed, struggled, and learned together.

As a team, we have completed our professional learning during Pre-Planning.  I had the privilege of attending and participating in all meetings.  (I did not sketch the sessions I helped facilitate.)

Can you see our connectedness, themes, and common language?

August 9: All School Meeting


August 9: Early Elementary Division meeting


August 9: Upper Elementary Division meeting03-Berry-PrePlanning1

August 10: Deepen Understanding to Strengthen Academic Foundation

August 10: Goals, Structures, and Processes

August 11: Diversity, Equity, and Inclusion04-Diversity-PrePlanning

August 11: Positive Discipline (a la Dr. Jane Nelsen)05-PositiveDiscipline1 06-PositiveDiscipline2

August 12: Strategic Teaming: Leadership, Voice, Hopes and Dreams

August 15:  Upper Elementary Division Meeting07-Berry-PrePlanning2

August 15: Early Elementary Division meeting08-Mitchell-PrePlanning2

Again… share common mission and vision.

Be together, not the same.

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:
Year-long goal:
Screen Shot 2016-08-13 at 8.04.56 PM
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?

#TEDTalkTuesday: community problem solving

How are we engaging learners in community-issues problem solving? This week’s TED talk celebrates our own.

Andrew Hennessy – Turning “Lost” Into “Found”

My school faced a problem: An unruly Lost and Found space filled with multiple examples of the same clothing, namely blue fleece cover-ups. My goal was to reinvent the process for labeling, sorting, storing and returning items that get left behind at my school. The solution involved applying a wear-proof QR code that contains critical information used to help reunite the lost item with the owner.  Teachers use a phone based QR app complete with automated parental notification to make the magic happen.

How might we continue to teach community problem solving? What if we teach and learn more about perseverance?

How might we help our learners choose and collaborate projects that they care about?  What if we join a team of learners to discover how the content of our discipline can be used in the process of finding, working on, and solving problems?

#TrinityLearns integrated studies (week 3)

When we have the opportunity to see what happens in other parts of our community, we begin to connect ideas and experiences.

Alpin Hong and Jun-Ching Lin surprised our 6th graders with visit and a brilliant lesson on harmony, color theory, and superhero theme music.

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It was Fitness Friday in First Grade. How great is it to combine math and fitness? Don’t you just love that two of our PE team lifted the work and learning of both the student-learners and the teacher-learners in 1st Grade?

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If you read #TrinityLearns Community (week 2), you know that we are teaching each other new ways to communicate learning.  Last week many of us learned about the app Pic Stitch which quickly combines multiple images into a collage.  (I asked Amanda Thomas, and Joe asked Jedd Austin.)  Notice how Kathy bright spots Brian’s work with our 2nd Graders.

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This week, Melissa Walker embedded her class’s twitter feed on her Haiku page.  This seems to be spreading through the 5th and 6th grade Haiku pages so that our families have another view of what happens at school. Amanda bright spots Melissa’s work.

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We’ve also seen our young learners making connections between math and science.

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Perhaps two of my favorite tweets – because they helped me connect in person – were from our 3s and Pre-K classrooms.  I could sit down with these young learners at carpool and ask them good questions.  They could describe details about their day, their interests, and their learning. I now know we need a rocket ship to rescue the balloons that got away.  I learn more and more each day about the interests of our learners.

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What will we learn about, for, and with each other as we continue to learn and share?

There were many more beautiful, rich learning experiences for all learners in our community.  A digest of our Tweets from the 3rd week of school is shown below.

#TrinityLearns Community (week 2)

What did you do at school today? Or, better yet, what happened at school today?

There are many days that I know what I did, but I wonder what else happened.  What if we leveraged technology to learn and share, to have a broader and deeper view into the learning episodes in our community?

There are many more voices contributing to the #TrinityLearns stream of information about the learning and celebrations happening daily.  At the end of this post, I’ve archived some of the tweets of the week, but I want to reflect on several that caught my attention.

I know that our 5th graders take the responsibility to raise the flag each morning, but I don’t see it happen.  Can you imagine a better way to learn about Social Studies and our country?Screen Shot 2013-09-02 at 6.40.12 PM

We know that our young learners are incredibly curious about technology and learning, but what does that look like?

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How did we celebrate the 50th anniversary of Martin Luther King’s “I Have a Dream” speech?

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How do we learn and share? How are we connected? How do we tell  stories of learning? How do we see the entire journey of a child when we experience only a short time with them?

I love my school community.

#TrinityLearns Community (week 1)

It was a busy first week of school getting acquainted with each other, making new friends, and learning together.  We believe in having a strong sense of community, balancing tradition with a forward-thinking philosophy, having a child-centered focus, and personalizing learning where process is equally as important as product.  We have dedicated faculty and staff who love, support, and nurture our young learners.

We learn and share together in many ways.  I learned so much about my school today by reviewing this week’s #TrinityLearns tweets.  The sample below offers a glimpse into our first week of school.

I am always struck by the thoughtfulness of children.  “Keep confidence” was a rule offered by a 1st grader for the class constitution. Wow! I am not sure if I ever had a class where I was offered the opportunity to help set the rules or norms of how we would work together.  If you read through the tweets above, it was a common theme this week at Trinity.

The search for the missing Gingerbread Man became a school-wide event.  Think of the chemistry, collaboration, reading, writing, and community understanding that was explored while creating, searching for, and finding him.  It was a true community celebration.

There is so much to know, observe, and learn.  I see a strong balance of technology and no technology.  I see dedicated adults working with engaged children. I see student choice and student voice. I see personalized learning in many different spaces and environments. I see relationship-building activities for our entire community.

I wonder…what do you see?