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 coopted 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, 163164 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 levelup strategy, we multiply the number of motivating milestones we encounter en route to a goal. That’s a forwardlooking 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 K12: 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.
]]>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. Kahwhop! 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 beehiveish 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 seventhgrade 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 selfdirected, 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 K12: 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.
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Arriving at school, ready to learn at 7:15, a small and dedicated cohort of 14 facultylearners gathered every Wednesday morning to deeply study, learn, and implement NCTM’s Mathematics Teaching Practices. These eight teaching practices provide a framework for strengthening the teaching and learning of mathematics.
Sounds a little boring, huh? Was it worth it?
“Yes! This class has helped me deepen my learning in math, and then in turn, deepen the way I teach math for my students. I loved being able to take the math we did and applying it in my classroom through number talks, number strings, children’s literature, and mathematical practices. I always was thinking deeply about math as soon as I entered the class at 7:15 because of engaging tasks and conversation with colleagues.” Caroline Tritschler, Kindergarten Teacher
“I enjoyed the opportunity to work on math that was applicable to my grade level, but we also had the chance to see where our students have been and where they are going. I also felt as if this class pushed us to strengthen our own number sense, perseverance, and use of strategies – all of which are qualities we strive to empower in our own learners.” Casey Leonard, 2nd Grade Teacher
“This course was a huge asset in recognizing the connections throughout grade levels. I loved seeing how our calculus work could be translated into finding patterns and connections the same way we do with our most fundamental skills in PreK.” Katherine Anderson, PreK Teacher
What is worth it? What was learned?
“I learned new ways of solving problems and showing my work, different ways of thinking about a problem, and validation for insisting that students have a full understanding of the “why” behind concepts.” Vicki Eyles, 5th Grade Teacher
“I feel like I really understand the importance of showing your work in more than one way and being able to explain your thinking to others. I better understand the importance of laying a foundation for using manipulatives and drawings that will carry far past an early elementary level.” Mary Catherine Gober, 1st Grade Teacher
“I am more thoughtful about the questions I ask students and I feel like I can give parents more detail about our approach to math instruction. Additionally, I have a deeper understanding of the benefit of talking to others while “doing” math, as well as the importance of showing one’s thinking in more than one way and making connections to others’ work.” Hilary Daigre, 1st Grade Teacher
What was learned? How has it helped Trinity students?
“My students seem surprised that I am in a class, learning more math. I like to share my struggles and successes with them, modeling growth through perseverance and sharing of ideas with other teachers. I have been able to share my experiences with them, using them to encourage their growth as students. Learning with others who have different backgrounds, strengths, and perspective has been powerful.” Vicki Eyles, 5th Grade Teacher
“I have seen tremendous growth in our class as they begin to take a risk in showing their work in multiple ways. Even those that “struggle” are at least willing to take a risk in trying to solve a problem. I believe the work we did in writing learning progressions for a specific topic has really helped the students want to reach for a higher level or at least work towards asking questions to better understand the problem before they go off and try to work through the problem.” Mary Catherine Gober, 1st Grade Teacher
“Our work with multiplication and division was mindblowing! I LOVED learning the various ways to approach multiplication/division, including using manipulatives and drawing models. It made more sense to me than anything I had learned in the past. I have shared stories about this experience with my class, including how I had to make sense of problems and really think about how I could solve them. I may not have had the most efficient method for a particular problem, but by talking with others and connecting to what they did, I was able to persevere and feel successful.” Hilary Daigre, 1st Grade Teacher
“I have a greater appreciation for the number line, the modeling, and the ability to make connections. I think the work we did impacted my students weekly. The activities we did I was able to either take back to my students or reminded me of other activities that I then used with the 6th graders. The visual patterns and connecting representations (work from Fawn Nguyen) was the most recent example. The 6th graders loved it. I also really enjoyed the math in literature as did the students!” Kristi Story, 6th Grade Teacher
But… was it boring? Would you recommend this experience to your colleagues?
“It was so much fun to be able to work with colleagues across EED and UED. I think my favorite part was mathematizing children’s literature.” Caroline Tritschler, Kindergarten Teacher
“It’s not only a great place to learn and grow in your understanding, but it’s also a great place to get to know your colleagues in a smaller setting. I’ve really enjoyed getting to know teachers that I wouldn’t have otherwise gotten to know. I genuinely looked forward to Wednesdays because of this class.” Chandler Balentine, 4th Grade Teacher
“I think it is both valuable and fun to spend time struggling with math problems which help us understand our students’ perspectives.” Jon Frank, 5th Grade Teacher
“I think the whole faculty (those that teach any grade level math) should embolden their inner mathematician. I think it was good to have a broad range of “comfort levels” in these sessions. We all learned from each other.” Kristi Story, 6th Grade Teacher
Without fail, at 9:30 after all was said and done, the time that was spent learning pedagogy and math, in fun, creative ways advanced teaching and learning at Trinity. Each Wednesday was a long day, and it was an important day for learners individually and collectively.
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Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
Principles to Actions: Ensuring Mathematical Success for All
15 min  Homework discussion, Q&A, Problem of the Week 
15 min  Number talk and birthday breakfast 
45 min  Numeracy through Literature – Notice and Note 
35 min

Designing for Learning
Read, select, and design –

10 min  Closure 
End of session 
Possibilities:
Learning Progressions:
Standards for Mathematical Practice
“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.
Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
Previous Embolden Your Inner Mathematician agendas:
Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.
Principles to Actions: Ensuring Mathematical Success for All
15 min  Homework discussion, Q&A, Problem of the Week 
15 min  Deepening: Use and connect representations 
15 min  Construct a viable argument and critique the reasoning of others 
20 min  5 Practices: Anticipate, Monitor, Select, Sequence, Connect 
40 min  Visual Patterns – Routines for Reasoning 
15 min  Closure 
End of session 
Homework:
Standards for Mathematical Practice
“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.
Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
Previous Embolden Your Inner Mathematician agendas:
Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.
Principles to Actions: Ensuring Mathematical Success for All
15 min  Homework discussion, Q&A 
45 min  Apples and Bananas Task 
30 min  Number Talk – Flexibility: Show what you know more than one way. 
10 min  Break 
20 min  Connecting multiple representations 
End of session 
Homework:
Standards for Mathematical Practice
“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.
Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
Previous Embolden Your Inner Mathematician agendas:
Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.
Principles to Actions: Ensuring Mathematical Success for All
15 min  Homework discussion using ConnectExtendChallenge Visible Thinking Routine 
35 min  Which pizza is the better deal? – Robert Kaplinsky (@robertkaplinsky) 
10 min  Break 
30 min  the Whopper Jar 3Act Task – Graham Fletcher (@gfletchy) 
20 min  Number Talks 
10 min  Closure 
End of session 
Homework:
Standards for Mathematical Practice
“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.
Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
Previous Embolden Your Inner Mathematician agendas:
]]>The 5th grade team invited me to colabor 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 readerwriter 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.
How will classroom culture grow as we strive to focus on the five key strategies we studied in Embedding Formative Assessment: Practical Techniques for F12 Classrooms by Dylan Wiliam and Siobhan Leahy?
Wiliam, Dylan; Leahy, Siobhan. Embedding Formative Assessment: Practical Techniques for F12 Classrooms. (Kindle Locations 493494). Learning Sciences International. Kindle Edition.
]]>The 5th grade team invited me to colabor with them to help our young learners deepen their understanding of reader’s response journals. As a team, they are focused on implementing and deepening their understanding of these five strategies from Wilam and Leahy:
Can we engineer learning experiences that orchestrate effective discussion and elicit evidence of learning? Can we empower our young learners to serve as learning resources for one another and deepen their own learning?
The plan called for crisp, quick moments to think, write, and talk. Using the learning intentions below, our young learners read a reader’s response entry from me and offered me critique.
First, they read my entry silently and analyzed it using the given success criteria. Next, with a partner, they discussed what they read, what they thought, and if they agreed on their ratings? Then, we began to develop critique using the starters shown below.
After thinking and writing silently, partners shared their sentences. Then, they chose one sentence each to share aloud in the group. I heard important, informative feedback for every voice in the room. Here are a few samples from their feedback.
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?
Wiliam, Dylan; Leahy, Siobhan. Embedding Formative Assessment: Practical Techniques for F12 Classrooms. (Kindle Locations 493494). Learning Sciences International. Kindle Edition.
]]>On Thursday, they facilitated a lesson on making thinking visible and introduced the following to our young learners.
On Friday, I facilitated a lesson on using the above to improve and strengthen reader’s response journal entries.
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?
Slide deck:
Wiliam, Dylan; Leahy, Siobhan. Embedding Formative Assessment: Practical Techniques for F12 Classrooms. (Kindle Locations 493494). Learning Sciences International. Kindle Edition.
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