Category Archives: Learning

Regularity in Repeated Reasoning through Choral Counting: Start at 6; count up by 5

Choral Counting gets to the heart of what we want for our mathematical communities. This activity creates space for all students to notice, to wonder, and to pursue interesting ideas. Students and teachers alike wonder together about patterns, and why and how numbers change or stay the same. [Franke, Kindle Locations1526-1528}

I wonder what can be learned from using a number line or ten-frames to shed more light on the patterns naturally found from members of the chorus.

Beginning with 6 and counting by 5s, we counted. Learners began adding “because…” to what they noticed. #Awesome

Choral Counting is an invitation; it provides an opportunity for each student to generate important mathematical ideas and for teachers to be curious about their students’ thinking. [Franke, Kindle Location 2057]

One learner said, “To move from one row to the next row, you add 30 because 6×5 is 30.” It is a regularity that repeats. Using the number line shows that to move from 6 to 36 there are 6 hops of 5 or a distance of 30.

The next comment was, “Each term on the diagonal going from the top left to the bottom right increases by 35 because 7×5 is 35.” Another regularity that repeats. Again, the number line shows 7 hops of 5 from 6 to 41, 11 to 46, 41 to 76, and so on.

Awesome that one “I notice…” that includes “because” inspires additional ones. Facilitating meaningful mathematical discourse invites students to develop and share important mathematical ideas.

What tools are within reach of learners as they deepen their numeracy and understanding? What is to be gained when we both author and illustrate mathematical understanding?

[Cross-posted at Author and Illustrate Understanding]


Franke, Megan L. Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom. Stenhouse. Kindle Edition

Learn, not memorize (within playing with sentences)

Playing with sentences begins with witnessing writing as performance. It’s a concrete way to reach out and engage our audience’s eyes and ears. (Anderson, 180 pag.)

Intent on learning more about sentence variation, my feedback partner helped me notice that I begin many of my sentences with nouns. Challenged to play more with my writing, I assigned myself the task of writing an 11 sentence paragraph using each of Anderson’s 11 Sentence Pattern Options from Chapter 8, Energy.

As a young learner, I was a memorizer. Doing what was expected of me, I learned the rules required for “the test”. Relieved and exhausted, I promptly forgot them. As concepts became more complex, my workload and anxiety increased. My favorite professor, Allen Smithers, noticed my lack of understanding. Dr. Smithers, patient and determined, challenged me to develop conceptual understanding. He challenged me to learn – not memorize. He expected me to confirm my understanding using drawings, graphs, tables, and equations. I grew as a mathematician, confident and capable. I learned, deeply. I am grateful.

Here’s the breakdown:

I know that I ended my sentence with an adverb instead of an adjective, but I choose to leave it as is.

Playing with sentences and ideas, I tried again.

As a young learner, I was a memorizer. Doing what was expected of me, I learned the rules required for “the test”. Relieved and exhausted, I promptly forgot them. As concepts became more complex, my workload and anxiety increased. Jill Lovorn, mathematician, was lost yet lucky. Success, assumed and shown, was shallow at best. Rote memorization – pages and pages of hidden work – masked missing conceptual understanding. I could use procedures, theorems, techniques, and algorithms. I got the right answers, mysteriously and remarkably.  No one knew, sadly. I survived.

Still ending that sentence with an adverb, I enjoyed playing with ideas and with sentences. Here’s the structure with a sentence checkup.

What do you think?


Anderson, Jeff. 10 Things Every Writer Needs to Know. Stenhouse Publishers, 2011.

Sentence Checkup: Mathematical Play with Sentence Patterns and Length

We know young writers will do what feels comfortable. They don’t play with their writing. They don’t try a sentence three different ways when it’s not working. They don’t explore what a varied sentence pattern or length can do for their writing’s rhythm and fluency. (Anderson, 178 pag.)

Blending a little math into writer’s workshop, what if we analyze and visualize our sentence patterns and lengths? Will learners play with their sentences after collecting and graphing a little data as described in 10 Things Every Writer Needs to Know?

Knowing how important visuals are to my learning, I used Google Sheets to “see” the variation in sentence length and to analyze the pattern of my sentence beginning.

Sentence checkup 1: Advance Your Inner Mathematician #TrinityLearns Session 5: Sequence and Connect

Wow! I am not worried about my sentence length. (Are they long? Is there an average number of words in great sentences, or is it about variety and rhythm?) However, I am appalled at the lack of interesting first words. It would have been so easy to write:

“Advance Your Inner Mathematician is a new course we are piloting this semester.”

And, the second sentence could have easily been,

“Anchored in Smith and Sherin’s ‘The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussion in Your Middle School Classroom’, this course supports continued teacher learning after Embolden Your Inner Mathematician.”

Or the two sentences could have been combined into one sentence.

“Advance Your Inner Mathematician, a new course we are piloting this semester is anchored in Smith and Sherin’s ‘The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussion in Your Middle School Classroom’, to support continued teacher learning after Embolden Your Inner Mathematician.”

Sentence Checkup 2: Fear of Imperfection; Deep Practice; Just Make A Mark 

I notice that this post is chock-full of questions (16 of 18 sentences) – a known trait of my writing.  I find the visual of sentence length interesting.

While I chose Google sheets as my tool, students can quickly graph this data by hand (please encourage the use of graph paper so that they attend to precision), and drop it in their writer’s notebook.

Will writers play more with their words and sentences if they see the patterns and frequency?


Anderson, Jeff. 10 Things Every Writer Needs to Know. Stenhouse Publishers, 2011.

Summer Learning 2019 – Choices and VTR

How do we learn and grow when we are apart? We workshop, plan, play, rest, and read to name just a few of our actions and strategies.

We make a commitment to read and learn every summer.

Below is the 2019 Summer Learning flyer announcing the choices for this summer.

In case you are interested, links to reviews of each book are shared below as well as the set of TED Talks for Voices from Diversity. #SoGood

Big Potential and The Power of Moments are repeats from last summer’s list because of faculty/staff engagement and enthusiasm. Blindspot and Developing Assessment-Capable Visible Learners are being used in book study groups during the current school year.  We hope to harness the power of the re-read and spread this ideas.

We will continue to use the Visible Thinking Routine Sentence-Phrase-Word to notice and note important, thought-provoking ideas. This routine aims to illuminate what the reader finds important and worthwhile.

Sentence-Phrase-Word helps learners to engage with and make meaning from text with a particular focus on capturing the essence of the text or “what speaks to you.” It fosters enhanced discussion while drawing attention to the power of language. (Ritchhart, 207 pag.)

However, the power and promise of this routine lies in the discussion of why a particular word, a single phrase, and a sentence stood out for each individual in the group as the catalyst for rich discussion . It is in these discussions that learners must justify their choices and explain what it was that spoke to them in each of their choices. (Ritchhart, 208 pag.)

What are you reading/watching/doing to grow as a learner over the summer? Please feel invited and encouraged to watch us (or join us) learn by following #TrinityLearns and #TrinityReads in June and July.


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

Book study: #ChoralCounting and #CountingCollections – session 1 #TrinityLearns

In Making a Case for ‘Timely, Purposeful, Progressive’ PD, Brian Curtin writes

Want to maximize professional-development opportunities? Provide specific content that suits teachers’ most pressing needs—when they need it most. In order to ensure relevancy, teachers must be able to use the new insights they’ve gained right away.

As a community, we are focused on high-quality instruction that leads to deep understanding.  The teachers of our youngest learners take action to develop young, strong mathematicians.  Together, we are studying Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom to deepen and strengthen our understanding of learning and teaching early numeracy.

Prior to our first meeting on February 4, 2019, 16 teachers and administrators committed to learning together by studying the first chapter of Choral Counting and Counting Collections.  The plan for the Feb. 4 meeting is shown at the end of this post and included time to discuss what we read as well as practice together.

We started with this collection.

And ended up with this:

How might we anticipate ways students will show their thinking and record their work?

Were teachers able to use the new insights they’ve gained right away?

The authors of Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom tell us:

These activities help us enact our commitments to equity. We know that a sense of belonging and investment, of being seen, known, and heard by teachers and classmates, is fundamental to creating schools where children and families feel welcome and where they flourish. Because these activities foreground student sense making and cultivate a joy for doing mathematics, they can be powerful tools for teachers to counter narrow views that only a few can identify with mathematics or that mathematics is disconnected from students’ home lives, their communities, and their own interests.

We are motivated and driven to learn more so that we continue to serve our young learners in the spirit of our mission and vision:

Trinity School creates a community of learners in a diverse and distinctly elementary-only environment, in which each child develops the knowledge, skills, and character to achieve his or her unique potential as a responsible, productive, and compassionate member of the School and greater community.

Celebrating the present and preparing our students for the future within a nurturing and caring educational environment, we:

  • Cherish Childhood
  • Deepen Students’ Educational Experience
  • Empower Students in Their Learning

So that our students:

  • Build Academic Foundation
  • Develop Character Foundation
  • Exhibit Continued Curiosity, Creativity, and Confidence


Curtin, Brian. “Making a Case for ‘Timely, Purposeful, Progressive’ PD.” Education Week Teacher, Education Week, 19 Feb. 2019, www.edweek.org/tm/articles/2017/12/06/making-a-case-for-timely-purposeful-progressive.html.

Franke, Meghan L., et al. Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom. Stenhouse Publishers, 2018.

Collaboration – How might we level up again?

Last week, we drafted a learning progression for a team around collaboration and asked for feedback..   ICYMI: I wrote:

I’m curious to know what you think about the draft below. If we put this out in our classroom, will learners have a stronger opportunity to self-assess and level up?

I am grateful for all of the feedback we received.  Thank you.

The teaching team that I am coaching asked an important question.  “This works, Jill, for collaboration in our daily classroom learning. If we launch a team project, the Level 4 should really be the Level 3. How might we emphasize collaboration is co-creating something new together?

If we establish I can collaborate to co-create evidence of shared learning, work, and understanding as a goal, how can we level up to focus learning?

We want all learners in this community to be able to say

I can collaborate to co-create evidence of
shared learning, work, and understanding

At Level 1, learners are working side-by-side and periodically check-in with each other. While closer to collaboration, this is really parallel play. We are in the same place doing the same thing, and we at least acknowledge that other learners exist in our space.

At Level 2, learners exchange thinking and ideas as they discuss questions and actions to take together. At this level, learners add to each other’s thinking and make sense of new, different ideas and pathways.

At Level 3, learners listen and share deeply to riff and improvise, co-creating ideas, thinking, and learning.

At Level 4, learners reflect on what they knew and what they know now. They can articulate what is now possible because of shared thinking, learning, and working together.

Again, I’m curious to know what you think about the draft above. If we put this out in our classroom, will learners have a stronger opportunity to self-assess and level up?

I love what we learn when we make our thinking visible. Our students and colleagues help us learn, refine, and deepen our work.  Tell a colleague what you want next for and with your students. And don’t stop there. Teach. Help them learn even when you are learning too.

Brainstorm with colleagues.  Talk about you hopes and dreams for students and  level out what you see and want to see. Make your thinking visible to the learners in your care.

Teach.

Empower learners.

Lead learners to level up.

Collaboration – How might we level up?

About 20 years ago, I worked with a wonderful, brilliant teacher who would tease me about collaborative learning. It was not his style. But, he tried. He would say to his class, “Pull your desks up close and uhh…collaborate. I’ll be back in a minute.”  Now, there were good outcomes from this opportunity. Students had a moment to breathe, catch up if behind (or confused) in their notes, and talk with classmates.

What is our definition of collaboration? In our teaching team or teams, have we established common language about collaboration? Have we shared it with the learners in our care?

What if the learners in your care are not meeting your expectations around collaboration?

  • Do we complain to colleagues or the learners that they are not collaborating?
  • Do we tell the learners that they need to collaborate without telling them how?
  • Do we assume that they <should> already know how? And, if they do not, are we frustrated and disappointed? Do we use our blame-thrower to put responsibility on someone else?
  • Do we take time to establish norms and common language around collaboration?

Teaching, telling, or complaining? Which one or ones are we stuck in? Problem-solving dissolves into complaining and venting when we fail to seek solutions and take action.  So, let’s brainstorm what it looks like and try something different.

Excerpts from a coaching session:

Teacher: I have no idea, Jill. They won’t collaborate. Do they not know how? They work in isolation, purposefully.  

Coach: Why is that important? Why should they work collaboratively? 

Teacher: Gosh, I think everyone knows that we collaborate to learn more, deeply. I think it is about perspective and listening to the ideas of others – even when you don’t agree. And, in math, it is about flexibility.

Coach: Tell me more about what you see and what you want to see.

Teacher: I see students sitting in groups, because that is how the furniture is arranged. But, they are not speaking to each other. Well, maybe…<sigh>…occasionally they check an answer. I want an exchange of ideas; I want them to learn from each other, together.  I hope that they will be curious about each other’s thinking and try to make sense of it instead of simply saying, “Oh, that’s not how I did it.” 

I’m curious to know what you think about the draft below. If we put this out in our classroom, will learners have a stronger opportunity to self-assess and level up?

If we establish I can collaborate to learn with and from others as a goal, can we use the above to focus learning?

We want all learners in this community to be able to say

I can collaborate to learn with and from others.

At Level 1, learners are working in isolation, perhaps racing to finish first.. Maybe learners plan to confer with others only after completing the task. Some might be trying to hide what they do not know; others are lapsing into teacher dependence.

At Level 2, learners are working side-by-side and periodically check-in with each other. While closer to collaboration, this is really parallel play. We are in the same place doing the same thing, and we at least acknowledge that other learners exist in our space.

At Level 3, learners exchange thinking and ideas as they discuss questions and actions to take together. At this level, learners add to each other’s thinking and make sense of new, different ideas and pathways.

At Level 4: learners listen and share deeply to riff and improvise, co-creating ideas, thinking, and learning.

All learners need independent think time to organize thinking, process the task, and gather resources.  AND, all learners need to learn from and with others in community because it promotes understanding, perspective taking, flexibility, listening, and critical reasoning.

So, when you are frustrated with how things are going, complain. Tell a colleague what your students are not doing. But don’t stop there. Teach. Help them learn even if they should already know it.

Brainstorm with your team. Ask hard questions. Describe what is going well and what is not.  Use this data to reframe and level out what you see and want to see. Make your thinking visible to the learners in your care.

Teach.

Empower learners.

Lead learners to level up.