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.

Agenda: Embolden Your Inner Mathematician (11.07.18) Week 8

Week Eight of Embolden Your Inner Mathematician

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

Course Goals:
At the end of the semester, teacher-learners should be able to say:

  • I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
  • I can exercise mathematical flexibility to show what I know in more than one way.
  • I can make sense of tasks and persevere in solving them.

Today’s Goals

At the end of this session, teacher-learners should be able to say:

  • I can use and connect mathematical representations. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them. (#SMP-1)

From Principles to Actions: Ensuring Mathematical Success for All

Use and connect mathematical representations.  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.

Learning Progressions for today’s goals:

  • I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them.

Tasks:

What the research says:

From Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5

Too often students see mathematics as isolated facts and rules to be memorized. … students are expected to develop deep and connected knowledge of mathematics and are engaged in learning environments rich in use of multiple representations.

Mathematics learning is not a one size fits all approach …, meaning not every child is expected to engage in the mathematics in the same way at the same time. … the diversity of their sense-making approaches is reflected in the diversity of their representations. [p. 140]

[Cross posted at Sum it up and  Multiply it out]


Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.

Agenda: Embolden Your Inner Mathematician (10.24.18) Week 7

Week Seven of Embolden Your Inner Mathematician

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

Course Goals:
At the end of the semester, teacher-learners should be able to say:

  • I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
  • I can exercise mathematical flexibility to show what I know in more than one way.
  • I can make sense of tasks and persevere in solving them.

Today’s Goals

At the end of this session, teacher-learners should be able to say:

  • I can implement tasks that promote reasoning and problem solving. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them. (#SMP-1)

From Principles to Actions: Ensuring Mathematical Success for All

Implement tasks that promote reasoning and problem-solving: Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Learning Progressions for today’s goals:

  • I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them.

Tasks:

  • Poetry and watercolor (a.k.a., the beauty of mathematics)
  • Phases of the moon (See slide deck)

What the research says:

From Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5

In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners.  The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy.(Smith, 4 pag.)

Equitable teaching of mathematics focuses on going deep with mathematics, including developing a deep understanding of computational procedures and other mathematical rules, formulas, and facts. When students learn procedures with understanding, they are then able to use and apply those procedures in solving problems. When students learn procedures as steps to be memorized without strong links to conceptual understanding, they are limited in their ability to use the procedure. (Smith, 93 pag.)

Evidence of work and thinking:

Slide deck:

[Cross posted at Sum it up and  Multiply it out]


Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.

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.

Agenda: Embolden Your Inner Mathematician (10.17.18) Week 6

Week Six of Embolden Your Inner Mathematician

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

Course Goals:
At the end of the semester, teacher-learners should be able to say:

  • I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
  • I can exercise mathematical flexibility to show what I know in more than one way.
  • I can make sense of tasks and persevere in solving them.

Today’s Goals

At the end of this session, teacher-learners should be able to say:

  • I can use and connect mathematical representations. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them. (#SMP-1)
  • I can show my work so that a reader understands without have to ask me questions.

From Principles to Actions: Ensuring Mathematical Success for All

Use and connect mathematical representations: 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.

From Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5

In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners.  The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy.(Smith, 4 pag.)

Learning Progressions for today’s goals:

  • I can use and connect mathematical representations. (#NCTMP2A)

  • I can show my work so that a reader understands without have to ask me questions.

Tasks:

  • Visual representation of multiplication, exponents, subtraction. (Connect 2nd-5th grade with Algebra I and II.)
  • Apples and Bananas task (see slide deck)

What the research says:

Not only should students be able to understand and translate between modes of representations but they should also translate within a specific type of representation. [Smith, pag. 139] 

Equitable teaching of mathematics includes a focus on multiple representations. This includes giving students choice in selecting representations and allocating substantial instructional time and space for students to explore, construct, and discuss external representations of mathematical ideas. [Smith, pag. 141]

Too often students see mathematics as isolated facts and rules to be memorized. [Smith, pag. 141]

\Anticipated work and thinking:

Slide deck:

[Cross posted at Sum it up and Multiply it out]


Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doingor Easing the Hurry Syndrome.WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.

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.

Agenda: Embolden Your Inner Mathematician (10.10.18) Week 5

Week Five of Embolden Your Inner Mathematician

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

Course Goals:
At the end of the semester, teacher-learners should be able to say:

  • I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
  • I can exercise mathematical flexibility to show what I know in more than one way.
  • I can make sense of tasks and persevere in solving them.

Today’s Goals

At the end of this session, teacher-learners should be able to say:

  • I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can show my work so that a reader understands without have to ask me questions.

From Principles to Actions: Ensuring Mathematical Success for All

Implement tasks that promote reasoning and problem-solving:Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Learning Progressions for today’s goals:

  • I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can show my work so that a reader understands without have to ask me questions.

Tasks:

  • Read and “do the math” from Each Orange Had 8 Slices by Paul Giganti Jr. (Author), Donald Crews (Illustrator).
  • Select, read, and mathematize a book of your choice. Plan a lesson for your students.

[Cross posted at Sum it up and Multiply it out]


Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doingor Easing the Hurry Syndrome.WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

Seeking brightspots and dollups of feedback about learning and growth.

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