Category Archives: Learning

Learner choice: using appropriate tools strategically takes time and tools

All students benefit from using tools and learning how to use them for a variety of purposes.  If we don’t make tools readily available and value their use, our students miss out on major learning opportunities. (Flynn, 106 pag.)

I’m taking the #MtHolyokeMath #MTBoS course, Effective Practices for Advancing the Teaching and Learning of Mathematics.  Zachary Champagne facilitated the second session and used The Cycling Shop task from Mike Flynn‘s TMC article.

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You can see the notes I started on paper.

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Jim, Casey and I used a pre-made Google slide deck provided to us to collaborate since we were located in GA, MA, and CA.  We challenged ourselves to consider wheels after working with 8 wheels.

Here’s what our first table looked like.

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Now, I was having trouble keeping up with the number of wheels and the number of cycles.  So I did this:

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This made it both better and worse for me (and for my group).

Here’s an interesting thing.  I’ve been studying, practicing, and teaching the Standards for Mathematical Practices. Jennifer Wilson and I have written a learning progression to help learners learn to say I can use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. (Sage, 6 pag.)

Clearly, I was not even at Level 1 during class.  Not once – not once – during class did it occur to me how much a spreadsheet would help me, strategically.

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The spreadsheet would calculate the number of wheels automatically for each row so that I could confirm correct combinations.  (You can view this spreadsheet and make a copy to play with if you are interested.)

When making mathematical models, [mathematically proficient students] know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. (Sage, 6 pag.)

With a quick copy and paste, I could tackle any number of wheels using my spreadsheet.  I can look for and make use of structure emerged quickly when using the spreadsheet strategically.  (I want to also highlight color as a strategic tool.) Play with it; you’ll see.

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[Mathematically proficient students] are able to use technological tools to explore and deepen their understanding of concepts. (Sage, 6 pag.)

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There is no possible way I would have the stamina to seek all the combinations for 25 or 35 wheels by hand, right?

Students have access to a wide assortment of tools that they must learn to use for their mathematical work. The sheer volume of possibilities can seem overwhelming, but with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal. (Flynn, 106 pag.)

Important to repeat, “with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal.

For this to happen, we need to have a solid understanding of the kinds of tools available, the purpose of each tool, and how students can learn to use them flexibly and strategically in any given situation. This also means that we have to make these tools readily available to students, encourage their use, and provide them with options so they can decide which tool to use and how to use it. If we make all the decisions for them, we remove that critical component of MP5 where students make decisions based on their knowledge and understanding of the tools and the task at hand. (Flynn, 106 pag.)

To be clear, a spreadsheet was available to me during class, but I didn’t see it.  How might we make tools readily available and visible for learners to choose?

When we commit to empower students to deepen their understanding, we make tools available and encourage exploration and use, so that each learner makes decisions for themselves. In other words, how do we help learners to level up in both content and practice?

What if we make I can look for and make use of structure; I can use appropriate tools strategically; and I can make sense of tasks and persevere in solving them essential to learn for every learner?

How might we offer tools and time?

It’s about learning by doing, right?


Flynn, Michael. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, Maine.: Stenhouse, 2017. Print.

Flynn, Mike. “The Cycling Shop.” Nctm.org. Teaching Children Mathematics, Aug. 2016. Web. 03 Feb. 2017.

Common Core State Standards.” The SAGE Encyclopedia of Contemporary Early Childhood Education (n.d.): n. pag. Web.

Review, revisit, recommit to norms – our hopes and dreams

Strong teams regularly self-assess how well they function within their norms – the hopes and dreams for how they are when together. As we learn and grow together, we pause to reflect, revise, and recommit to strengthen our teams by reviewing our community norms.

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  • We commit to collaboratively design the agenda for each team meeting and that the agendas are shared ahead of the meetings. (ALT)
  • We commit to fostering a growth mindset with our learners and ourselves. We embrace the power of yet. (Carol Dweck)
  • We commit to use technology as a tool for learning and not as a barrier between us. (ALT)
  • We commit to speaking about our learners as if they are in the room with us. (Katherine Boles, Harvard)
  • We learn, i.e., we have permission to change our minds. (Elizabeth Stratmore)
  • We agree to ask for and offer the umbrella of mercy. (Tim Kanold)
  • We serve all learners. Teams committee to take responsibility, together, to differentiate to help all learners learn and grow.
  • We resist labeling students – all learners.  We agree to design for the edges to dramatically expand our talent pool. (Todd Rose)

How might we strengthen our team? What if we review, reflect, and recommit to our hopes and dreams of how we are?

#ObserveMe – the other side – invitation and purpose

Observation by invitation and with purpose.

For context, stop and read Robert Kaplinsky’s
(@robertkaplinsky) #ObserveMe challenge if you haven’t.

How might we serve one another? What if we have questions about our practice? In a community of confident, competent risk-takers, it is safe to declare what we’d like to learn, our goals, and hoped for feedback.

Today, I served as observer-learner for two such teacher-learners.

Julia Kuipers (@J_kuipers3) 6th Grade Spanish:

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Since Julia was seeking feedback on how much time they spoke in the target language, I tried to incorporate a timestamp in my sketch.

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I could share my sketch in real-time prior to leaving the classroom for immediate feedback.  Later in the day, I could reflect on Julia’s class and use my sketch, I could offer additional feedback in her feedback collection form.

Her feedback form:

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I liked that I could write about what I noticed and what I wonder.  I made sure that I commented on what I saw that could be used as evidence of time in the target language, students empowered to level up and stretch themselves, and students serving as resources for each other.  I wondered about extending formative assessment to include performance as well as efficacy.


Megan Hayes-Golding (@mgolding) Physics:

First, it is important to note that we are not at the same school, though this is still observation by invitation and with purpose.

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While my sketch chronicled my observation, I noticed and noted when Megan provided levels of challenge within an activity and when students were set up for success when working independently.

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Since it was at the end of the day, I had the opportunity to debrief and offer direct feedback in conversation with Megan.


I am thankful for the learning experiences today.  I am grateful for the invitations. I appreciate knowing what to observe so that I can learn and serve.

Observation by invitation and with purpose.

Everyone learns.

Wow!


Addendum: Megan’s reflection of this #ObserveMe experience

Mashup: #5Practices and #WODB

What if we engage in purposeful instructional talk as a team to focus on the instructional core? How might we design and implement a differentiated action plan across our grade to meet all learners where they are? What if we learn to integrate Smith and Stein’s 5 Practices for Orchestrating Productive Mathematics Discussions?

Becky Holden (@bholden86), our EED math specialist, and I are working on formative assessment using anticipate and monitor, the first two of Smith and Stein’s 5 Practices.  While we don’t want a template, we keep using this sketch to plan, think, and share.

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It’s still a work in progress.  We’d love to know what you think.

Brian Toth (@btoth4thgrade) shared his learners and time with me so that I could play and work with our students on SMP-6, attend to precision.

The following three sketches are the notes and jots of what we anticipate our learners will think and say prior to the start of class.

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Our purposeful instructional talk set learning goals of I can attend to precision, and I can demonstrate flexibility to show what I know more than one way.  From our students, we are looking for complete sentences with strong vocabulary and word choice.  We want to see internal motivation to think deeply and a willingness to go past a surface initial answer. We know that we are growing toward constructing viable arguments. From our team, we are collaborating to learn more about our learners, to become more flexible ourselves, and to notice and note details of student answers so that we can design and implement a differentiated action plan across our grade to meet all learners where they are.

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What if we learn and practice together? How might we grow in confidence, competence, precision, and flexibility?

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.

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

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August 9: Early Elementary Division meeting

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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.

Summer Learning 2016 – 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.  This year, we take a slightly broader approach to our Summer Reading Learning menu by adding two streams of TED talks, Voices of Diversity and SAIS.

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

We will 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.)

We have the opportunity to model how to incorporate reading strategies into all classrooms.  Think about teaching young learners to read a section of their book and jot down a sentence, phrase, and word that has meaning to them.  Great formative assessment as the lesson begins!

When we share what resonates with us, we offer others our perspective.  What if we engage in conversation to learn and share from multiple points of view?


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. Prin