Tag Archives: Leading Learners to Level Up

#T3IC Leading Learners to Level Up: Deepening Understanding of Mathematical Practices

At the 2018 International T³ Conference in San Antonio, Jennifer Wilson (@jwilson828) and I presented the following 90-minute session. 

Leading Learners to Level Up:
Deepening Understanding of Mathematical Practices

We say: Persevere! Express regularity in repeated reasoning! Be precise! Show your work!… But what if I can’t yet? How might we make our thinking visible to empower our young learners to become self-correcting, self-reliant and independent? How do we coach – what strategies do we use – to help learners to embrace the Common Core State Standards for Mathematical Practice? At the end of this session, participants should be able to say I can provide my learners leveled support on the Standards for Mathematical Practice on their journey towards mathematical proficiency. I can make my thinking visible to motivate learners to ask high quality questions. I can focus on the art of questioning and formative assessment tools to lead learners to level up.

Here’s the plan:

  1. Opening remarks
  2. Council (30 seconds each): Share your name, school and grade level(s) or course(s) with your table; How are you feeling this morning?
8:40 Make Sense of Tasks and Persevere Solving Them (SMP 1)

9:05 Look for & Make Use of Structure (SMP 7)

9:35 Look for & Express Regularity in Repeated Reasoning (SMP 8)

9:55 Goal setting: Back with my learners … Next steps

Here’s my sketch note of the plan for our session.

Dave Johnston (@Johnston_MSMath) recorded his thinking and learning and shared it with us via Twitter.

Notice success, celebrate multiple milestones, level up

Learning intentions are more than just statements to convey to students what the learning is composed of; they are a means for building positive relationships with students. (Hattie, 48 pag.)

It is what I didn’t notice.  The bell rang. As always, I heard a chorus of “Thank you, Ms. Gough. Bye, Ms. Gough.” It was normal practice – and a much appreciated practice – for my students to say thank you and goodbye as they left for their next class.

I thought to myself “what a great class, everything went well, and they are so nice.” I busied myself straightening my desk, organizing paper, and mentally listing off the things I needed to do before my next class rolled in.  Eat lunch was at the top of the list.

Then, I sensed it. I was not alone.  It is what I didn’t notice.  There she sat, so still, except for the river of tears falling out of her beautiful, sad, green eyes. The river ran off the desk and pooled on the floor. “What is wrong?” I asked as I sat down beside her.

As I gently placed my hand on her arm, her shoulders began to shake as she said “I f..f..f..failed!” Whoosh, another flood of tears.

Now, she had not failed from my point of view. Her test score, damp as her test was now, showed a grade of 92 – an A.  And yet, she deeply felt a sense of failure.  As we sat together and looked at her work, we discovered that there was one key essential learning – in fact, a prerequisite skill – that caused her to stubble.

Tears, still streaming down her face, she said “I don’t know where I’m going wrong. I don’t miss this in class, but on the test, I fall apart.”

The point is to get learners ready to learn the new content by giving their brains something to which to connect their new skill or understanding. (Hattie, 44 pag.)

So, of course, the stumbling block for this sweet child is a known pain point for learners who master procedures without conceptual understanding.  Consistently, she expanded a squared binomial by “distributing” the exponent – a known pitfall. #petpeeve

When our learners do not know what to do, how do we respond? What actions can we take – will we take – to deepen learning, empower learners, and to make learning personal?

Kamb’s insight was that, in our lives, we tend to declare goals without intervening levels. We declare that we’re going to “learn to play the guitar.” We take a lesson or two, buy a cheap guitar, futz around with simple chords for a few weeks. Then life gets busy, and seven years later, we find the guitar in the attic and think, I should take up the guitar again. There are no levels. Kamb had always loved Irish music and had fantasized about learning to play the fiddle. So he co-opted gaming strategy and figured out a way to “level up” toward his goal:

Level 1: Commit to one violin lesson per week, and practice 15 minutes per day for six months.

Level 2: Relearn how to read sheet music and complete Celtic Fiddle Tunes by Craig Duncan.

Level 3: Learn to play “Concerning Hobbits” from The Fellowship of the Ring on the violin.

Level 4: Sit and play the fiddle for 30 minutes with other musicians.

Level 5: Learn to play “Promontory” from The Last of the Mohicans on the violin.

BOSS BATTLE: Sit and play the fiddle for 30 minutes in a pub in Ireland.

Isn’t that ingenious? He’s taken an ambiguous goal—learning to play the fiddle—and defined an appealing destination: playing in an Irish pub. Better yet, he invented five milestones en route to the destination, each worthy of celebration. Note that, as with a game, if he stopped the quest after Level 3, he’d still have several moments of pride to remember. (Heath, 163-164 pgs.)

What if I’d made my thinking visible?

What if I’d connected this learning to how 3rd graders are taught multiplication of two digit numbers by decomposing into tens and ones.  What if I’d connected this learning to how 3rd graders are also taught to draw area models to visualize the distributive property?

What if I’d shared my thinking and intentionally connected prior learning in levels?

By using Kamb’s level-up strategy, we multiply the number of motivating milestones we encounter en route to a goal. That’s a forward-looking strategy: We’re anticipating moments of pride ahead. But the opposite is also possible: to surface those milestones you’ve already met but might not have noticed. (Heath, 165 pag.)

How might we help our learners level up, experience success at several motivating milestones, and notice successes that might otherwise go unnoticed?

By multiplying milestones, we transform a long, amorphous race into one with many intermediate “finish lines.” As we push through each one, we experience a burst of pride as well as a jolt of energy to charge toward the next one. (Heath, 176 pag.)

Taken together, these practices make learning visible to students who understand they are under the guidance of a caring and knowledgeable teacher who is invested in their success. (Hattie, 48 pag.)

Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L.. Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series). SAGE Publications. Kindle Edition.

Heath, Chip. The Power of Moments: Why Certain Experiences Have Extraordinary Impact. Simon & Schuster. Kindle Edition.

PD in Action: #LL2LU Math Formative Assessment #TrinityLearns with #MVPSchool

This really says it all:

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Isn’t this what we want from professional development? I learned something yesterday that I can (and do) put into practice today. How often does that happen? Well, it happened twice today.  Stephanie, #MVPSchool’s @TeachingSteph, and Vicki Eyles, #TrinityLearns @EylesMath, joined forces yesterday to design a learning progression and a leveled assessment to lead learners to level up.  The tweet above gives evidence that Stephanie put her learning into action today.  Vicki met me at the door at 7:15 this morning on her way to the office to print the leveled assessment for our 5th graders.  Awesome!

Here’s some of the feedback from the day:

I believe in the process and had time to actually complete an assessment that I can use in my classroom tomorrow. It was so helpful to collaborate with others on the project.

I need to be able to assess my students as they are learning. I always find that students are telling me that they don’t know or understand, and I would love for them to focus on what they know and work from there.

It was very beneficial to learn about the difference between “I can” and “I can’t” statements and learn how to refocus our students. To learn how to word statements that will allow students to focus on the target and to create an assessment that will help communicate with both students and teachers about where students are and where they are going.

So…here’s the story:

What if we build common formative assessments that communicate how to level up, ask targeted questions, and motivate learning? Teachers of 3rd – 6th graders from Trinity and Mount Vernon met yesterday to learn more about Leading Learners to Level Up. Shelley Paul (@lottascales) joined us to co-facilitate and offer perspective from a beginner’s mindset.

We started with the 4-minute overview and “sat in the seat of a learner” as we took the leveled assessment on adding fractions.  With such a small group, we used the fishbowl time to hear multiple perspectives on the learning progression of the adding fractions formative assessment.

The mashup of growth mindset with learning progressions and standards-based feedback was clear to these teacher-learners.  We should write learning progressions to empower our learners to identify their strengths and ask questions to grow.  Using “I can…” statements offers learners the opportunity and the language to identify what they can do and advocate for what they want/need to do next.

Working in grade-level teams, we drafted learning progressions with “I can…” statements for a learning outcome.


Once we drafted a learning progression, we stopped to collaborate and offer feedback.  It was awesome!  We used Post-it Notes and the protocol I like…, I wish…, I wonder/What if… to offer each other positive, constructive, and directed feedback.

LL2LU Feedback

Illustrating the power of social media and connected learning, John Burk (@occam98) immediately added to our learning by replying to the tweet of the above image.

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Feedback on our feedback with, I might add, a new resource for our teachers. Wow!

Once we adjusted our learning progressions based on the feedback, we worked to write  leveled assessments that would offer learners the opportunity to show what they know.  You can see artifacts of the work in the learning plan at the bottom of this post.

Embracing a do the work in the workshop philosophy, we took time to complete these leveled assessments.  Then, the magic happened.  Yes, another round of feedback.  Each teacher-learner took every leveled assessment and worked through it as a learner.  It was a spectacular way to calibrate expectations vertically.  Every assessment was vetted through teachers and admin-learners. Everyone received written feedback as well as face-to-face feedback.  Candid feedback…questioning feedback…growth-oriented feedback.

Intentionally, we paired these teacher-learners by the grade they teach.  Our hope was that our teacher-learners would share best practice, strategies, and bright spots that work in their schools.  We were not disappointed.  Our learning plan called for a session where we would regroup and work as a vertical school team to review, discuss, and calibrate levels in each assessment.  While we did not formally separate into two school teams, there was lots of discussion to calibrate expectations? Finding plateaus and steep jumps in curriculum always happens when vertically aligning these learning progressions and leveled assessments.

As a team of 20, we agreed to meet again in a couple of weeks to discuss how the impact of these learning progressions and leveled assessments.  We also plan to accept the challenge of writing a learning progression and a leveled assessment of one topic to learn more about vertical alignment of curriculum and expectations.  I’ll keep you posted.

Even in the briefest of communications, people develop and share common models that allow them to communicate effectively.  If you don’t share the model, you can’t communicate. If you can’t communicate, you can’t teach, learn, lead, or follow.  (Lichtman, 32 pag.)


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

Formative Assessment – Leading Learners to Level Up (#LL2LU) – A Definition of Derivative

We want more students to experience the burst of energy that comes from asking questions that lead to making new connections, feel a greater sense of urgency to seek answers to questions on their own, and reap the satisfaction of actually understanding more deeply the subject matter as a result of the questions they asked.  (Rothstein and Santana, 151 pag.)

Do we offer learners a way to decode their understanding and ask targeted questions to improve their work? Have we, as a team, identified what is essential to learn and at least one path to success? How do we communicate and collaborate with our learners and our colleagues to build paths to success for all learners?

What if we offered non-graded self-assessment that helped everyone calibrate what they know with what is essential to learn?

What does it take for a calculus learner to show they understand how to use a definition of the derivative? What might the essential learning look like?

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What must one be able to do to show understanding of this topic in calculus? Can the teaching team break it down into components that are necessary to use this definition of a derivative?

In our brainstorming session, Sam and I decided that the following was needed when finding a derivative analytically using this definition:

You have to understand function notation. You have to be able to use function notation when x is a constant and when x is a variable. You have to be able to simplify polynomial and rational expressions.

Do our young learners understand what the words in the previous paragraph mean? Do they need to see it too?  Are we communicating clearly? Is there a difference between saying I understand it and actually understanding?

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What if we asked our learners to show what they know by working through a document to “level” where they are based on our expectations?

Would young learners of calculus be empowered and emboldened to ask specific questions about their understanding? In other words, will learners begin to differentiate for themselves? I assure you it is much more rewarding and fun to be asked specific questions instead of fielding “I don’t know nothing” statements.

Would this type of ungraded self-assessment build confidence and relationship? From experience, I know the answer is yes IF the message is that it does not matter where you are as long as you are working to get to Level 3.  As a community, we must all get to Level 3, the essential learning.

How might we change the conversation in our classes?  How might we use assessment for learning? How might we provide enough insight to compel learners down a path?

The excitement of learning, the compelling personal drive to take one more step on the path towards wisdom, comes when we try to solve a problem we want to solve, when we want to solve, when we see a challenge and say yes, I can meet it.  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.)


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

Rothstein, Dan, and Luz Santana. Make Just One Change: Teach Students to Ask Their Own Questions. Cambridge, MA: Harvard Education, 2011. Print.