Tag Archives: Nancy Frey

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.

 

Productive struggle with deep practice – what do experts say

NCTM’s publication, Principles to Action, in the Mathematics Teaching Practices, calls us to support productive struggle in learning mathematics. How do we encourage our students to keep struggling when they encounter a challenging task? How many learners are accustomed to giving up when they can’t solve a problem immediately and quickly. How do we change the practice of how our students learn mathematics?

Effective teaching not only acknowledges the importance of both conceptual understanding and procedural fluency but also ensures that the learning of procedures is developed over time, on a strong foundation of understanding and the use of student-generated strategies in solving problems. (Leinwand, 46 pag.)

Low floor, high ceiling tasks allow all students to access ideas and take them to very high levels. Fortunately, [they] are also the most engaging and interesting math tasks, with value beyond the fact that they work for students of different prior achievement levels. (Boaler, 115 pag.)

Deep learning focuses on recognizing relationships among ideas.  During deep learning, students engage more actively and deliberately with information in order to discover and understand the underlying mathematical structure. (Hattie, 136 pag.)

Deep practice is built on a paradox: struggling in certain targeted ways — operating at the edges of your ability, where you make mistakes — makes you smarter.  (Coyle, 18 pag.)

Or to put it a slightly different way, experiences where you’re forced to slow down, make errors, and correct them —as you would if you were walking up an ice-covered hill, slipping and stumbling as you go— end up making you swift and graceful without your realizing it. (Coyle, 18 pag.)

The second reason deep practice is a strange concept is that it takes events that we normally strive to avoid —namely, mistakes— and turns them into skills. (Coyle, 20 pag.)

We need to give students the opportunity to develop their own rich and deep understanding of our number system.  With that understanding, they will be able to develop and use a wide array of strategies in ways that make sense for the problem at hand. (Flynn, 8 pag.)

…help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems. (Flynn, 8 pag.)

This term productive struggle captures both elements we’re after:   we want students challenged and learning. As long as learners are engaged in productive struggle, even if they are headed toward a dead end, we need to bite our tongues and let students figure it out. Otherwise, we rob them of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere. (Zager, 128-129 ppg.)

Encourage students to keep struggling when they encounter a challenging task.  Change the practice of how our students learn mathematics.

Let’s not rob learners of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere.


Boaler, Jo. Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (p. 115). Wiley. Kindle Edition.

Coyle, Daniel. The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. (p. 20). Random House, Inc.. Kindle Edition.

Flynn, Michael, and Deborah Schifter. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, ME: Stenhouse, 2017. (p. 8) Print.

Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy, Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series) (p. 136). SAGE Publications. Kindle Edition.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Zager, Tracy. Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Portland, ME.: Stenhouse Publishers, 2017. (pp. 128-129) Print.

PD planning: #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 reading and writing workshop?

Have you read Love Monster and the last Chocolate from Rachel Bright?

Becky Holden and I planned the following professional learning session to build common understanding and language as we expand our knowledge of teaching numeracy through literature.  Each Early Learners, Pre-K, and Kindergarten math teacher participated in 2.5-hours of professional learning over the course of the day.

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To set the purpose and intentions for our work together we shared the following:

screen-shot-2017-01-15-at-8-35-21-am screen-shot-2017-01-15-at-8-35-31-am

Becky’s lesson plan for Love Monster and the last Chocolate is shown below:

lovemonsterlessonplan

After reading the story, we asked teacher-learners what they wondered and what they wanted to know more about.  After settling on a wondering, we asked our teacher-learners to use pages from the book to anticipate how their young learners might answer their questions.

After participating in a gallery walk to see each other’s methods, strategies, and representations, we summarized the ways children might tackle this task. We decided we were looking for

  • counts each one
  • counts to tell how many
  • counts out a particular quantity
  • keeps track of an unorganized pile
  • one-to-one correspondence
  • subitizing
  • comparing

When we are intentional about anticipating how learners may answer, we are more prepared to ask advancing and assessing questions as well as pushing and probing questions to deepen a child’s understanding.

If a ship without a rudder is, by definition, rudderless, then formative assessment without a learning progression often becomes plan-less. (Popham,  Kindle Locations 355-356)

Here’s the Kindergarten learning progression for I can compare groups to 10.

Level 4:
I can compare two numbers between 1 and 10 presented as written numerals.

Level 3:
I can identify whether the number of objects (1-10) in one group is greater than, less than, or equal to the number of objects in another group by using matching and counting strategies.

Level 2:
I can use matching strategies to make an equivalent set.

Level 1:
I can visually compare and use the use the comparing words greater than/less than, more than/fewer than, or equal to (or the same as).

Here’s the Pre-K  learning progression for I can keep track of an unorganized pile.

Level 4:
I can keep track of more than 12 objects.

Level 3:
I can easily keep track of objects I’m counting up to 12.

Level 2:
I can easily keep track of objects I’m counting up to 8.

Level 1:
I can begin to keep track of objects in a pile but may need to recount.

How might we team to increase our own understanding, flexibility, visualization, and assessment skills?

Teachers were then asked to move into vertical teams to mathematize one of the following books by reading, wondering, planning, anticipating, and connecting to their learning progressions and trajectories.

During the final part of our time together, they returned to their base-classroom teams to share their books and plans.

After the session, I received this note:

Hi Jill – I /we really loved today. Would you want to come and read the Chocolate Monster book to our kids and then we could all do the math activities we did as teachers? We have math most days at 11:00, but we could really do it when you have time. We usually read the actual book, but I loved today having the book read from the Kindle (and you had awesome expression!).

Thanks again for today – LOVED it.

How might we continue to plan PD that is purposeful, actionable, and implementable?


Cross posted on Connecting Understanding.


Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L. (2016-09-16). Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series). SAGE Publications. Kindle Edition.

Norris, Kit; Schuhl, Sarah (2016-02-16). Engage in the Mathematical Practices: Strategies to Build Numeracy and Literacy With K-5 Learners (Kindle Locations 4113-4115). Solution Tree Press. Kindle Edition.

Popham, W. James. Transformative Assessment in Action: An Inside Look at Applying the Process (Kindle Locations 355-356). Association for Supervision & Curriculum Development. Kindle Edition.

Deep understanding: visualize, connect, comprehend

We need to give students the opportunity to develop their own rich and deep understanding of our number system.  With that understanding, they will be able to develop and use a wide array of strategies in ways that make sense for the problem at hand.  (Flynn, 8 pag.)

Let’s say that the essential-to-learn is I can subtract within 100.  In our community we hold essential I can show what I know more than one way. 

Using our anchor text, we find the following strategies:

  • I can subtract tens and one on a hundred chart.
  • I can count back to subtract on an open number line.
  • I can add up to subtract on an open number line.
  • I can break apart numbers to subtract.
  • I can subtract using compensation.

What if we engage, as a team, to deepen our understanding of subtraction?

Deep learning focuses on recognizing relationships among ideas. During deep learning, students engage more actively and deliberately with information in order to discover and understand the underlying mathematical structure. (Hattie, 136 pag.)

In his Effective Practices for Advancing the Teaching and Learning of Mathematics class last week, Mike Flynn highlighted three advantages  of using representations to deepen understanding.

  • Representations build conceptual understanding and help assess comprehension.
  • Representations serve as a tool to make sense of the task and the mathematics.
  • Representations help develop proof of generalizations.

What if we, as a team, prepare to facilitate experiences so that learners can say I can subtract within 100 by deepening our understanding with words, pictures, numbers, and symbols?

Context: Annie had some money in her “mad money” jar.  Today, she added $39 to the jar and discovered that she now has $65. How much money was in the “mad money” jar before today?

2ndgrade65-39

Can we connect the context to each of the above strategies? Can we connect one strategy to another strategy?

If we challenge ourselves to “do the math” using words, pictures, numbers, and symbols, we deepen our understanding and increase our ability to ask more questions to advance thinking.

How might we use Van de Walle’s ideas for developing conceptual understanding through multiple representations to assess comprehension and understanding?


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

Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L. (2016-09-16). Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series). SAGE Publications. Kindle Edition.

Van de Walle, John. Teaching Student-centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K-2. Boston: Pearson, 2014. Print.

PD Planning: Number Talks and Number Strings

As we begin the second part of our school year and as the calendar changes from 2016 to 2017, we review our goals.

The leaders of our math committee set the following goals for this school year.

Goals:

  • Continue our work on vertical alignment.
  • Expand our knowledge of best practices and their role in our current program.
  • Share work with grade level teams to grow our whole community as teachers of math.
  • Raise the level of teacher confidence in math.
  • Deepen, differentiate, and extend learning for the students in our classrooms.

Our latest action step works on scaling these goals in our community. The following shows our plan to build common understanding and language as we expand our knowledge of numeracy.  Over the course of two days, each math teacher (1st-6th grade) participated in 3-hours of professional learning.

Jan10-13Agenda.png
Sample timestamp from PD sessions.

Our intentions and purpose:

Screen Shot 2017-01-15 at 8.35.21 AM.png

Screen Shot 2017-01-15 at 8.35.31 AM.png

We started with a number talk and a number string from Kristin Gray‘s NCTM Philadelphia presentation. We challenged ourselves to anticipate the ways our learners answer the following.

kristingraynumbertalk

We also referred to Making Number Talks Matter to find Humphreys and Parker’s four strategies for multiplication.  We pressed ourselves to anticipate more than one way for each multiplication strategy to align with Smith and Stein’s 5 Practices for Orchestrating Productive Mathematics Discussions.

Screen Shot 2017-01-15 at 7.23.12 PM.pngFrom our earlier work with Lisa Eickholdt, we know that our ability to talk about a strategy directly impacts our ability to teach the strategy.  What can be learned if we show what we know more than one way? How might we learn from each other if we make our thinking visible?

Screen Shot 2017-01-15 at 8.46.22 PM.pngAfter working through Humphreys and Parker’s strategies (and learning new strategies), we transitioned to the number string from Kristin‘s presentation.

Screen Shot 2017-01-15 at 7.41.14 PM.pngThe goal for the next part of the learning session offered teaching teams the opportunity to select a number string from one of the Minilessons books shown below.  Each team selected a number string and worked to anticipate according to Smith and Stein’s 5 Practices for Orchestrating Productive Mathematics Discussions.

To practice, each team practiced their number string and the other grade-level teams served as learners.  When we share and learn together, we strengthen our understanding of how to differentiate and learn deeply.

Deep learning focuses on recognizing relationships among ideas. During deep learning, students engage more actively and deliberately with information in order to discover and understand the underlying mathematical structure.
—John Hattie, Doug Fisher, Nancy Frey

As we begin the second part of our school year and as the calendar changes from 2016 to 2017, what action steps are needed to reach our goals?


Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L. (2016-09-16). Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series) (p. 136). SAGE Publications. Kindle Edition.

Humphreys, Cathy; Parker, Ruth (2015-04-21). Making Number Talks Matter (Kindle Locations 1265-1266). Stenhouse Publishers. Kindle Edition.

Norris, Kit; Schuhl, Sarah (2016-02-16). Engage in the Mathematical Practices: Strategies to Build Numeracy and Literacy With K-5 Learners (Kindle Locations 4113-4115). Solution Tree Press. Kindle Edition.

Smith, Margaret Schwan., and Mary Kay. Stein. 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teachers of Mathematics, 2011. Print.