Category Archives: Reading

Traverse session: Experiential and Instructional: Promoting Productive Mathematical Struggle #tvrse18

At Traverse Boulder, I facilitated the following session on Tuesday, June 5, 2018.

Experiential and Instructional:
Promoting Productive Mathematical Struggle

How might we implement tasks that promote reasoning and problem solving to deepen conceptual understanding? Let’s identify and implement high quality tasks grounded in real experiences. Advancing the teaching and learning of mathematics cannot be accomplished with decontextualized worksheets. Discuss, sketch, and solve tasks that promote flexibility, creative and critical reasoning, and problem solving. Learning math should be anchored in depth of understanding through context – not pseudo context – and built on conceptual understanding as well as procedural fluency.

Here’s my sketch note of our plan:

Here’s the slide deck:

Just say no to worksheets.

Say YES to productive struggle and grappling.

Embolden your inner storyteller and leverage the art of questioning.

Context is key.

#KSULit2018: Mathematizing Read Alouds

At the 27th Annual KSU Conference on Literature for Children and Young Adults where the theme was Reimagining the Role of Children’s and Young Adult Literature, I presented the following 50-minute session on Tuesday, March 20, 2018.

Mathematizing Read Alouds

How might we deepen our understanding of numeracy using children’s literature? What if we mathematize our read-aloud books to use them in math as well as literacy? We invite you to notice and note, listen and learn, and learn by doing while we share ways to deepen understanding of numeracy and literacy.

Let’s debunk the myth that mathematicians do all work in their heads.  Mathematicians notice, wonder, note, identify patterns, ask questions, revise thinking, and share ideas.  Mathematicians show their thinking with details so that a reader understands without having to ask questions.

What if we pause during read-alouds to give learners a chance to analyze text features, to notice and wonder, to ask and answer questions in context?

How might we inspire and teach learners to make their thinking visible so that a reader understands?

Here’s my sketch note of the plan:

Here are more of the picture books highlighted in this session:

And, a list by approximate grade levels:

Early Learners, Pre-K, and Kindergarten

Kindergarten and 1st Grade

2nd, 3rd, 4th Grade

4th, 5th, 6th Grade

I know something!

A motley band of brothers traveling as a pack ambled in at 7:58 for Pre-Cal. Just in time. From a distance they are handsome and well dressed in coats and ties. Up close, they are a little disheveled, like they stepped out of their clothes last night and into them again this morning.  My favorite part is the peacock-ness of their hair.  They slept hard, and it shows. It helps me remember how young they are when they look so grown up. I wonder how many of them brushed their teeth and decided not to go there.

They live together, play together, and learn together. Boarding school builds family and familiarity and deepens connectedness.  Yesterday’s test results require a preface. I prep them by explaining what I learned about them and what we need to do now.  Learning is our focus, and this moment in time tells us that we need to do more, go deeper, and practice harder. This milestone marker says that we need to back up and try again.

I made a 42!” he exclaimed with genuine jubilation. It’s what he said next that confirmed his glee.  “I know something!

“I know something!”

I am in awe of what happens next.  Every man, child, boy learner, in their coats and ties, stands and high-fives him as if he as won a gold medal, sunk the winning shot, made the field goal in the final 30 seconds.

And then, just as quickly as it started, they were all seated as he said “Bring it, Ms. Gough. What do we do now?”

Group culture is one of the most powerful forces on the planet. We sense its presence inside successful businesses, championship teams, and thriving families, and we sense when it’s absent or toxic. (Coyle, xvii pag.)

Culture is a set of living relationships working toward a shared goal. It’s not something you are. It’s something you do. (Coyle, xx pag.)

Live, learn, work, and serve in a community that highlights what is going well. Focus on learning. Build living relationships. Work toward shared goals.

CULTURE: from the Latin cultus, which means care.


Coyle, Daniel. The Culture Code: The Secrets of Highly Successful Groups. Random House Publishing Group. Kindle Edition.

Available for learning

I feel it coming.

Have you seen surfers catch big waves? They paddle out, wait and watch.  Some waves pass by. Others crash over them. Sometimes the surfer gets up, punches through and rides it out.  Other times they wipe out. It is fascinating that they get back up and go back out. They persevere. I wonder how I can do that.

I feel it coming, but I cannot predict how I’m going to handle it. It is different every time. Sometimes I cry. Sometimes I turn and fight an internal battle to stand my ground to punch through the wave. Sometimes I can ask for help, but not always.

I am afraid it won’t be perfect.

I am afraid I can’t do it.

I am afraid others will laugh at me.

I am afraid I’ll disappoint my parents.

I am afraid I’m not good enough.

I am afraid I won’t be accepted.

I am afraid I don’t belong.

I am afraid I am not enough.

I am afraid.

I am afraid.

Labels make it easy to attribute student disengagement to a lack of ability or motivation, when disengagement often results from a lack of confidence. (Hassan and Lennard, 70 pag.)

The key to creating psychological safety, as Pentland and Edmondson emphasize, is to recognize how deeply obsessed our unconscious brains are with it. A mere hint of belonging is not enough; one or two signals are not enough. We are built to require lots of signaling, over and over. This is why a sense of belonging is easy to destroy and hard to build. (Coyle, 13 pag.)

How might we learn more about our learners? What actions are needed so that learners know they are psychologically safe?

What conditions must be set so that more learners punch through and rides out the wave?

CULTURE: from the Latin cultus, which means care.


Coyle, Daniel. The Culture Code: The Secrets of Highly Successful Groups. Random House Publishing Group. Kindle Edition.

Hasson, Julie, and Missy Lennard. Unmapped Potential: an Educator’s Guide to Lasting Change. Dave Burgess Consulting, Inc., 2017.

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.

I’ll help you recover…

We will never know our reach unless we stretch. (Heath, 131 pag.)

When students don’t make errors, it’s probably because they already know the content and didn’t really need the lesson. (Hattie, 17 pag.)

Whack! One second everything was fine, then, for a fraction of a second, black. Kah-whop! I could see my phone, which used to be in my back pocket, hit the ice and slide about 8 feet in front of me.  Searing, hot pain surfaced in my left knee. It’s like I have a view from the ceiling. I can see myself face down on the ice. Cold. Wet.

I return to my eye’s view. I am really not sure what to do as I watch a nice soul skate over to my phone and bring it to me. While it was only a few seconds, it felt like 5 minutes of slow motion.  I was upright by then; no longer spread eagle face down on the ice.  

A sweet young thing glided up and laughed at me. “Ouch!” I heard myself say, “Don’t laugh! I’m hurt, and I don’t think I know how I’m gonna get up.” I saw her flinch but not leave me. My eyes confirmed that I was in a crowd and no one seemed to know what to do but stare.  #NotGood

The music teacher—“a woman with a beehive-ish hairdo and a seemingly permanent frown on her face”—led the choir in a familiar song, using a pointer to click the rhythm of the song on a music stand. Then, Sloop remembered, “She started walking over toward me. Listening, leaning in closer. Suddenly she stopped the song and addressed me directly: ‘You there. Your voice sounds . . . different . . . and it’s not blending in with the other girls at all. Just pretend to sing.’ ” The comment crushed her: “The rest of the class snickered, and I wished the floor would open and swallow me up.” For the rest of the year, whenever the choir sang, she mouthed the words. (Heath, 141 pag.)

Whatever momentary lapse in concentration caused me to fall – splat – did not feel good.  And the laugh, while meant to make light of an awkward situation, was crushing.  It was a mistake and a painful one at that.  

We hear it at school. We want our learners to be risk takers, to work on the edge of their ability, to fail faster, fail up, fail forward.  Right?

Get out there! Try something different! Turn over a new leaf! Take a risk! In general, this seems like sound advice, especially for people who feel stuck. But one note of caution: The advice often seems to carry a whispered promise of success. Take a risk and you’ll succeed! Take a risk and you’ll like the New You better!  That’s not quite right. A risk is a risk. (Heath, 131 pag.)

Errors help teachers understand students’ thinking and address it. Errors should be celebrated because they provide an opportunity for instruction, and thus learning. (Hattie, 16 pag.)

And just like that, she arrived.  An angel on the ice.  As she stretched out her hands, palms up, she said “Just take my hands.” I could get one foot square on the ice, though I felt like I was buried in a foot of snow, and then the other. Patiently she said “Now look at me and just press down.” I was up; shaken, but not broken.  Her beautiful brown eyes connected with mine and she smiled warmly as she said firmly “you are up and you are fine.” Just as quickly and elegantly as she arrived, she floated away.  

Then, in the summer after her seventh-grade year, she attended a camp for gifted kids in North Carolina called the Cullowhee Experience. She surprised herself by signing up to participate in chorus. During practice, she mouthed the words, but the teacher noticed what she was doing and asked Sloop to stick around after class. The teacher was short and thin, with hair down to her waist—a “lovely flower child,” said Sloop. She invited Sloop to sit next to her on the piano bench, and they began to sing together in the empty room. Sloop was hesitant at first but eventually lowered her guard. She said, “We sang scale after scale, song after song, harmonizing and improvising, until we were hoarse.” Then the teacher took Sloop’s face in her hands and looked her in the eyes and said: “You have a distinctive, expressive, and beautiful voice. You could have been the love child of Bob Dylan and Joan Baez.” As she left the room that day, she felt as if she’d shed a ton of weight. “I was on top of the world,” she said. Then she went to the library to find out who Joan Baez was. “For the rest of that magical summer,” Sloop said, she experienced a metamorphosis, “shedding my cocoon and emerging as a butterfly looking for light.” (Heath, 142 pag.)

My knee still throbbed and most of me was shaking.  I limped over to the edge of the rink until I could steady my nerves.  I’m not sure which hurt worse, my knee or my pride.  In either case, it hurt. But, I was up and I was fine.

The words, tones, facial expression, and body language we use with our learners matters.

Memorizing facts, passing tests, and moving on to the next grade level or course is not the true purpose of school, although sadly, many students think it is. School is a time to apprentice students into the act of becoming their own teachers. We want them to be self-directed, have the dispositions needed to formulate their own questions, and possess the tools to pursue them. (Hattie, 32 pag.)

How might we highlight what is going well for our young learners, accent the positive, and gently guide them to stretch, risk, and reach? What if we craft our feedback so our learners know we believe in their ability and expect great things even when they stumble, fall, and hurt? What if we guide their apprentice work to learn to use needed tools and hone their skills.

Our hopes and dreams for learning don’t include pretending – just stand there and mouth the words. Our learners must emerge as butterflies.

What type of feedback are we practicing? Laughter to make light of a stumble? Calm, “take my hand and push; you are fine?”

The promise of stretching is not success, it’s learning. (Heath, 131 pag.)

What great mentors do is add two more elements: direction and support. I have high expectations for you and I know you can meet them. So try this new challenge and if you fail, I’ll help you recover. (Heath, 123 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.

 

Reader’s Response: Learning to use learning progressions (reflections from 5th grade learners)

What if we design a lesson to orchestrate productive discussion, critique the reasoning of others, grow as readers and writers, and deepen understanding through reflection? How might we engineer effective discussions, tasks, and activities that elicit evidence of learning as we learn to provide feedback that moves learning forward.  Will this help activate students as learning resources for one another?

The 5th grade team invited me to co-labor with them to help our young learners deepen their understanding of reader’s response journals.  Using their readers response learning progressions, our 5th graders offered me feedback to help me grow as a reader-writer and to practice critiquing the reasoning of others.

Knowing how important it is to close the lesson with purpose, we asked our young learners to reflect using the following prompts.

Here are a few samples from their reflections.

  • I learned to pay attention to making sure I explain the book.  I learned to ask myself if I added quotes and page numbers.  An “ah ha” for me was when I learned about the importance of adding page numbers and quotes.
  • I learned to pay attention to the page numbers and the definitions of words. I learned to ask myself where are the mistakes in this and how can I make it better? An “ah ha” for me is to look up definitions of words I don’t understand.
  • I learned to pay attention to focusing a lot on text evidence. I learned to ask myself if I really did my best and met the level 3 requirements. An “ah ha” for me is to be able to link my writing and the book together.
  • I learned to pay attention to specific details and listening closely. I learned to ask myself questions about the text. An “ah ha” for me is critique versus criticism and constructive criticism.
  • I learned to pay attention to feedback I receive, because it will make my writing better.  I learned to ask myself about text evidence, making thinking visible, and formatting.  An “ah ha” for me is including text information in my writing at all times.

How will classroom culture grow as we strive to focus on the five key strategies we studied in Embedding Formative Assessment: Practical Techniques for F-12 Classrooms by Dylan Wiliam and Siobhan Leahy?

  • Clarify, share, and understand learning intentions and success criteria
  • Engineer effective discussions, tasks, and activities that elicit evidence of learning
  • Provide feedback that moves learning forward
  • Activate students as learning resources for one another
  • Activate students as owners of their own learning

Wiliam, Dylan; Leahy, Siobhan. Embedding Formative Assessment: Practical Techniques for F-12 Classrooms. (Kindle Locations 493-494). Learning Sciences International. Kindle Edition.