#LL2LU Fractions – we are smarter than me & modeling C’s – #MPVschool & #TrinityLearns

A new definition of strength: Can we learn together? What if we collaborate, ask for feedback, and lean in to leverage expertise and perspective of others?

If we truly believe in communication, collaboration, and the other C’s, how are we – as lead learners – modeling and taking action?

<Note the timestamps in the following communication, collaboration, critical thinking, and problem-solving.>

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“Hear” snippets of Nicole’s thoughts as she is developing the assessment shown above:

    •  I’m  writing a mathematics unit for a grade level that I have never taught to learn, to  help my team, to help our young learners.
    • This is hard.
    • I’m trying to model backwards design unit planning (Grant Wiggins hung the moon, most recently evidenced by his math blog post today). Stage 2 (How will I know when they have learned it?) must come before Stage 3 (the learning plan). Teachers should have access to the assessments (formative and summative) at the beginning of the unit.
    • Our learning outcomes are all I have to work with.  Reading these standards in depth helps me some, but I need feedback.
    • I heart Google.
    • The “I can…” statements need to be student-friendly. They will be directly related to the standards-based rubric we will need to create.
    • I’ve worked through several leveled assessments as collaborations with classroom teachers, but I have yet to write one independently.
    • Wait, why am I writing this independently? It’s nearly midnight. I’m sending this to Jill.

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“Hear” snippets of Jill’s thoughts as she gave feedback and edited the assessment shown above:

      • Wow…Such good work.
      • Level 1 “I can decompose a figure into equal parts. I can name each part.”  
        • I wonder if decompose is a 3rd grade word. (I do not know.)  I also wonder about “partition” as a 3rd grade word.
        • I wonder if you are having a resolution problem with the shapes in Level 1. The image shown is a rectangle, not a square.
        • I wonder how successful a child can be partitioning the circle without having the center marked and using a compass.
      • Level 2 “I can represent a fraction on the number line when some fractions are given to me.“  
        • Can we eliminate the word “some” and/or simplify?
        • What if we say I can represent fractions on a number line?
        • What if we add number lines to identify fractions before asking students to take action on number lines? Just this month, Jennifer Wilson and I presented on conceptual understanding of fractions and the new way to convey a consistent story using number lines. 
        • My TI-Nspire software and the fraction lessons will give me number lines. I’m not sure about mixed numbers and partitions past 1, but Nicole will know.  At least adding a visual might help.

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Nicole thinking:

How on earth did Jill create this fancy number line in a Google doc? I like her train of thought here but think the visual at it stands now will be too hard for grade 3 students.

Jill’s thinking:

Right. Number lines too hard. Would it be easier if we think together now that we are both awake?

Below is a copy of the next iteration of this assessment after a Google hangout discussion and co-learning conversation.

How might we collaborate, ask for feedback, and lean in to leverage expertise and perspective of others?

A new definition of strength: We are stronger than me. Learn and share!

[Cross posted on Curriculum Reflections] 

JGough observes JWilson – #NCSM14 Developing Conceptual Understanding Through the Progressions

Peer-to-Peer Observations…who learns?


Piloting an Observation of Practice with Jennifer Wilson (@jwilson828), I observed Jennifer during our NCSM presentation, Developing a Conceptual Understanding of Fractions. Below is a record of what I observed and then my reflection.  I am grateful for the opportunity to observe Jennifer and to learn from and with her.

Jill Gough observes Jennifer Wilson
NCSM: Wednesday, April 9, 2014, 10:00 – 11:00, New Orleans, LA
Session:  Developing Conceptual Understanding Through the Progressions:  Fractions, Ratios, and Proportions


Jennifer began her session with Essential Learnings for the hour.  By the end of this session, everyone should be able to say:

  • I can describe a fraction a/b as a copies of 1/b.
  • I can construct questions that push and probe student thinking about questions.
  • I can explain the role that technology plays in deepening student understanding of fractions.

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I like that Jennifer began her session this way, because it offered participants focus and direction. I wonder if the audience appreciated this intentional guiding of thinking.  I like that there was a content essential learning, an assessment essential learning, and a process essential learning.  What if all PD lessons were launched this way? I wonder if we would see more engagement and thought and less nervousness about which button to press.

I appreciated the situation Jennifer experienced with technology as the session began.  The same situation happened to me in Sacramento a couple of weeks ago.  After playing her PowerPoint slide, Jennifer returned to the Navigator software to find all the traditionally black text was now white making is difficult to read.  In addition, when she returned to the slideshow, it was frozen.  (Same for me in Sacramento, but I was using Keynote.)

I like that Jennifer pressed forward, abandoning her slide deck to keep the conversation going with the participants.  I wonder how she would handle this in such a short session if she was presenting alone.

I liked the formative assessment question sent via quick poll to engage the audience right away.  While I was not quick enough to capture the results, they were varied. Each choice had some takers.  I liked the use a warm-up question using the Navigator. I liked that Jennifer took action based on the results.  Good modeling.  I liked that the Navigator was used as a tool and that fractions were the featured event that anchored the discussion.

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I love watching Jennifer facilitate peer-to-peer discourse, because she requires individual thinking time prior to group discussion.  I aspire to use her protocol. I need this when I am learning. What if we established this as a goal or must do for all instructors?

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Jennifer used the following files during her session:

Using appropriate wait time, Jennifer offered hands-on experience and investigation time for participants to explore each of the files.  She prompted participants to shoulder-partner up and brainstorm push and probe questions that might be asked of students.  Jennifer used the Navigator to capture class responses to comment on and visualize quality questions from the audience and the authors.  I like that she modeled push and probe questioning through this discussion.  She honored participant questions and offered advancing questions to help push their thinking.

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I observed participants struggle with what questions to ask and what response to hope for from learners.  One participant said “I don’t know how to explain these true/false questions.  I know which ones are true and which are false, but how do I explain in words?” Evidence of probing for understanding and that thinking was being pushed.  I liked that I had the opportunity to witness and then facilitate peer-to-peer discourse as these teacher-learners grappled with the why of fractions.  I wonder if we should incorporate the 5-whys protocol and theWhat Makes You Say That Visible Thinking Routine to facilitate rich discussion and uncover possible misconceptions.

Using the Navigator class capture, Jennifer complimented the audience on their approaches to Fractions and Unit Squares and that none of their methods were the way she thought.  “My students continually surprise me. You too!” I like that she modeled her way only after showing several correct ways.

Jennifer closed by returning to the Essential Learnings to remind participants of their experience and what the target was for the session.

Jill’s reflection:

 As a result of this observation of practice and feedback loop, which aspects of my teaching do I feel are bright spots?

I like starting sessions with Essential Learnings written as I can… statements.  Observing Jennifer launch and close her session with the I can… statements was the first time I’ve seen someone other than me leverage them in a professional development session.  In my own practice, I send the agenda ahead of the session when possible. I wonder if I should declare them as the beginning of the session. I thought it was a powerful anchor for our work.

I like starting with a warm-up question that turned into formative assessment.  In my own practice, I have intentionally described how I am shifting gears based on a warm-up question to model adjusting (not abandoning) the plan to meet learners where they are.  I wonder how many teacher-learners miss the adjustment when we are not direct about the shift we are making.  At the Social Media PD Saturday, Sam commented on the shifts I made based on the learners’ questions and the fact that I still accomplished everything on the plan.  What if we are more intentional when we shift to make the shift transparent? Based on these results, we are going to shift to X, and we will get to our destination. This connects to Jo Boalers’ I am giving you this feedback because I believe in you. What if we are direct? I/we are shifting the plan because we need to do X to accomplish XX.

I like using the Navigator to highlight multiple pathways to success.  I appreciated Jennifer using the Navigator to intentionally highlight more than one way to accomplish a task.  I wonder if zooming in to show 2 screens from the class capture helps participants sitting in the back to see.  What if we regularly and intentionally honor work by showing multiple correct pathways?

As a result of this observation of practice and feedback loop, what questions do I have about my own teaching?

I wonder how to include more participants when using the Navigator.  At Jennifer’s session, there were 30 handhelds and 40 participants.  I wonder how to engage all participants. Do we need more resources? Should we partner? I want to try more participants connected to Navigator in my work with large groups.  Even though every participant (40-90 participants) had a handheld, we observed those not connected and displayed were less engaged.

What if I am more intentional about Think-Team-Share? I appreciated Jennifer’s direct and intentional let’s take 30-60 seconds to organize our thoughts silently before sharing. What if I add this to my facilitation toolkit? What if I add let’s take a minute to quick-write. Describe your thinking on paper to offer a visual of your idea when sharing with others. How might I model this as a strategy for any learning episode?

As a result of this observation of practice and feedback loop, what new ideas do have?

Well, one is in the paragraph above.  “What if I add this to my facilitation toolkit? What if I add let’s take a minute to quick-write? Describe your thinking on paper to offer a visual of your idea when sharing with others. How might I model this as a strategy for any learning episode?” I hear myself talk about teaching learners visual note taking, but do I model it for teacher-learners? What if I write a blog post that show what is in my head so that it is clearer to me and to others?

I am inspired to work on my closings.  I like how Jennifer cycled back to the Essential Learning for the session to have participants do a quick mental self-assessment.  I believe the way she closed the session improved the chances that the message will stick.

[Cross posted at Easing the Hurry Syndrome]

Summer Reading 2014 – Themes and Choices

As a team of 150 learners charged with a responsibility of developing and maintaining a learning community for ourselves and the 640 children that we love and care for, 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.  How do we model learner choice? We know student-learners need and deserve differentiated learning opportunities.  Don’t all learners?

There is so much to learn, practice, prototype, and consider.  How do we learn and share? What if we divide, conquer, and share to learn?

From: Jill Gough
Date: Friday, April 11, 2014 12:13 PM
To: All Trinity
Subject: Summer Reading 2014

Summer reading for our community offers choices again this year.  We offer three themes from which to choose.  You may want to continue with the Art of Questioning, or you may want to explore Creativity or Social-Emotional as an interest.  Each theme offers three choices, and if available, you may choose to read using a traditional book, a Kindle book, or an audio book.
A quick note and thank you: Last year Laurel Martin asked me why the books weren’t hyperlinked to Amazon so that we could quickly read reviews.  Great idea! (Hmm…I didn’t know how to hyperlink an image using Pages…but I do now. Thank you Laurel for pushing me to learn!) So, thanks to Laurel, if you want to read reviews, just click on a book in the flyer.
We will use the 4As protocol to debrief during Pre-Planning.  We are also going to schedule a Wednesday afternoon so that our community can hear and share the big ideas from every book.
Please see the attached flyer for information and links to additional information and a form to request your book.  Would you please select a book by Friday, April 25 so that we can have it for you before we leave in May?
Thank you,

Here’s our flyer:

And, our version of the 4 As protocol worksheet:

#NCSM14 Art of Questioning: Leading Learners to Level Up #LL2LU

What if we empower and embolden our learners to ask the questions they need to ask by improving the way we communicate and assess?

Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level.  Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)

On Monday, April 7, 2014, Jennifer Wilson (@jwilson828) and Jill Gough (@jgough) presented at the National Council of Supervisors of Mathematics Conference in New Orleans.

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Jill started with a personal story (you’re letting her shoot…) about actionable feedback and then gave the quick 4-minute Ignite talk on the foundational ideas supporting the Leading Learners to Level Up  philosophy.

Our hope was that many of our 130 participants would help us ideate to craft leveled learning progressions for implementing the Common Core State Standards Mathematical Practices.  Jennifer prompted participants to consider how we might building understanding and confidence with I can make sense of problems and persevere in solving them. After giving time for each participant to think, she prompted them to collaborate to describe how to coach learners to reach this target.  Jennifer shared our idea of how we might help learners grow in this practice.

Level 4:
I can find a second or third solution and describe how the pathways to these solutions relate.

Level 3:
I can make sense of problems and persevere in solving them.

Level 2:
I can ask questions to clarify the problem, and I can keep working when things aren’t going well and try again.

Level 1:
I can show at least one attempt to investigate or solve the task.

 Participants then went right to work writing an essential learning – Level 3 – I can… statement and the learning progression around this essential learning. Artifacts of this work are captured on the #LL2LU Flickr page.

Here are the additional resources we shared:

How might we coach our learners into asking more questions? Not just any question – targeted questions.  What if we coach and develop the skill of questioning self-talk?

Interrogative self-talk, the researchers say, “may inspire thoughts about autonomous or intrinsically motivated reasons to purse a goal.”  As ample research has demonstrated, people are more likely to act, and to perform well, when the motivations come from intrinsic choices rather than from extrinsic pressures.  Declarative self-talk risks bypassing one’s motivations.  Questioning self-talk elicits the reasons for doing something and reminds people that many of those reasons come from within. (Pink, 103 pag.)

[Cross-posted on Easing the Hurry Syndrome]


Lichtman, Grant, and Sunzi. The Falconer: What We Wish We Had Learned in School. New York: IUniverse, 2008. Print.

Pink, Daniel H. To Sell Is Human: The Surprising Truth about Moving Others. New York: Riverhead, 2012. Print.

@HughHerr’s TED talk on new bionics celebrates humanity and shows need for mashup of STEM and Design Thinking

Hugh Herr: The new bionics that let us run, climb and dance is a must watch for all.

How are we intentionally creating opportunities for learners to engage in human-centered problem-solving, integrating studies, and teaming with others?