Tag Archives: Doug Fisher

Focus on Learning: Establish Mathematics Goals to Focus Learning

Worry in her beautiful, tired, sad eyes communicates so much. Strain across her face makes my heart ache. As we sit down for coffee with our children playing nearby, she blurts, “I don’t know how to make myself clearer, Jill. They just don’t, won’t, can’t – I don’t know – get it!” I sigh into my coffee which causes steam to fog up my glasses, and she laughs through her tears.  

Knowing that I am an evidence-interested educator, she pulls out her unit plans for me to see and offer feedback. “You were in our class yesterday. What I can I do better…? How do I help them learn?” Love and concern for her students is evident in her thoughtfulness, craftsmanship, and design.

I was in this class yesterday and had been for many days of the unit. I go again and again, because I am learning from her and with her students. This strong, organized, empathetic teacher is, in fact, a very good teacher.  

“What if we take your teaching up a level to a stronger focus on learning? Let’s look at the output that is causing you this worry and stress. Together, can we look at their work and identify what they, in your words, ‘just don’t, won’t, can’t’ do?’ And then, what if we establish mathematics goals to focus learning for you and your students?”

Sitting there on the bank of the Chattahoochee, occasionally interrupted, joyfully, by a toddler that needed to show us a valuable rock or other important discovery, we combed through student work. Outpouring concern and frustration, she talked about each learner, their strengths, and what surprised her about what they did not understand. I listened in awe of what she knew about her students in granular detail, and what she thought they knew but didn’t really. My notes highlighted every success she saw and the joy and pride she felt with every success.

How might we shift her work to increase the amount of success for her and her students? How might we empower learners to take action, self-assess, and ask questions early and often to improve their understanding and communication? What if we take what we just learned about her class and level it out to make her expectations and her thinking visible?

We found four categories or groupings:

  1. As soon I as finish explaining the task, they are all over me, Jill. They have no idea what to do or are too scared to get started. They want me to hold their hand. They are not empowered or safe enough to try.” They are splashing around in the shallow end, maybe even thrashing.
  2. They started, but cannot think flexibly when their first attempt gets them nowhere. They will not hear feedback or collaborate to think differently. They just shut down.
  3. “They are happily working along and find success.” They are willing to work in the pool, but need support build around them to know this is a safe, brave space to draft and redraft to think and learn. Mistakes are opportunities to learn; they do not define you.
  4. “They are first and fast and successful. They want and need more. I want to deepen and connect their learning, not broaden it.” They are willing to dive into the deep end confidently to explore new connections and representations.

This hard, important work helped us gain clarity about what is essential to learn in her classroom. Articulating frustration points as well as success points during her analysis of learning in her classroom revealed and organized a path for communication of learning intentions.

How might we empower and embolden our learners to ask the questions they need to ask by improving the ways we communicate and assess?

What if we make our thinking visible to our learners? What if we display learning progressions in our learning space to show a pathway for learners?

Great teachers lead us just far enough down a path so we can challenge for ourselves.  They provide just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out 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.)

We want every learner in our care to be able to say

I can make sense of problems and persevere in solving them.  (CCSS.MATH.PRACTICE.MP1)

But, as a learner…What if I think I can’t? What if I’m stuck? What if I feel lost, confused, or discouraged? How might we offer a pathway for success? What if we provide cues to guide learners and inspire interrogative self-talk?

NCTM’s recent publication, Principles to Actions: Ensuring Mathematical Success for All, calls us to support productive struggle in learning mathematics. How do we encourage our students to keep struggling when they encounter a challenging task? They 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?

How might we coach our learners in to asking more questions? Not just any questions – 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 pursue 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.)

Our coffee is cold and our children have lost interest in playing together. As we wrap up our reflection, feedback, and planning session, we agree to experiment the next week with her students. How might the work and learning change if we make a pathway for self-assessment and self-talk visible to the learners?

We plan to post #LL2LU SMP-1:  I can make sense of problems and persevere in solving them in the classroom and on the tables for easy reference.  Our immediate learning goal for the students is to make sense and persevere, to ask clarifying questions and try again, to show thinking for clarity and questioning, and to find multiple ways to solutions and find connections.

Excellent teachers think hard about when they will present the learning intention. They don’t just set the learning intentions early in the lesson and then forget about them. They refer to these intentions throughout instruction, keeping students focused on what it is they’re supposed to learn. (Hattie, 55-56 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.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

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

Pink, Daniel H. (2012-12-31). To Sell Is Human: The Surprising Truth About Moving Others. Penguin Group US. Kindle Edition.

 

I can establish mathematics goals to focus learning #NCTMP2A #LL2LU

We strive to grow in our understanding of the Eight Mathematics Teaching Practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All. This research-informed framework of teaching and learning reflects a core set of high leverage practices and essential teaching skills necessary to promote deep learning of mathematics.

Establish mathematics goals to focus learning.

Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.

In order to support our teaching teams as they stretch to learn more, we drafted the following learning progressions. We choose to provide a couple of pathways to focus teacher effort, understanding, and action.

When working with teacher teams to establish mathematics goals to focus learning, we refer to 5 Practices for Orchestrating Productive Mathematics Discussions by Peg Smith and Mary Kay Stein and Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning by John Hattie, Douglas Fisher, and Nancy Frey along with Principles to Actions: Ensuring Mathematical Success for All by Steve Leinwand.

To deepen our understanding around establishing mathematics goals, we anticipate, connect to prior knowledge, explain the mathematics goals to learners, and teach learners to use these goals to self-assess and level up.

From  NCTM’s 5 Practices for Orchestrating Productive Mathematics Discussions, we know that we should do the math ourselves, predict (anticipate) what students will produce, and brainstorm what will help students most when in productive struggle and when in destructive struggle.

Once prior knowledge is activated, students can make connections between their knowledge and the lesson’s learning intentions. (Hattie, 44 pag.)

To strengthen our understanding of using mathematics goals to focus learning, we make the learning goals visible to learners, ask assessing and advancing questions to empower students, and listen and respond to support learning and leveling up.

Excellent teachers think hard about when they will present the learning intention. They don’t just set the learning intentions early in the lesson and then forget about them. They refer to these intentions throughout instruction, keeping students focused on what it is they’re supposed to learn. (Hattie, 55-56 pag.)

How might we continue to deepen and strengthen our ability to advance learning for every learner?

What if we establish mathematics learning goals to focus learning?

Cross posted on Easing The Hurry Syndrome


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.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

Stein, Mary Kay., and Margaret Smith. 5 Practices for Orchestrating Productive Mathematics Discussions. N.p.: n.p., n.d. Print.

High-purpose environment. Teacher clarity. Touchpoints of praise.

I wait patiently for my turn.

Carrots. Beep. Doritos. Beep. Milk. Beep.

Donned in her green Publix smock, she makes eye contact and small talk with the customer ahead of me as she swipes items across the reader.

Hamburger. Beep. Kale. Beep. Beep. Beep.

She says, “That will be forty-two. twenty-eight” Wincing, she shook her head and said, “No, no wait! It is twenty-eight forty-two.” Smiling sheepishly, she blushes and says “Ugh! I just hate numbers.” The customer, patient and kind, concludes her business at the register and goes on about her way.

I cannot stop myself. Why can’t I stop myself from attempting to put salve on the raw wound that someone else – knowingly or unknowingly – has inflected on this poor young woman? I hear my internal voice say, “You don’t have to fix this. You really can’t fix this. You did not do this.”

I know I should stop myself. I cannot. I softly say, “So I’m a math teacher. It is easy to mix numbers up. Don’t worry.”

And then it happens… again. It breaks my heart a little more every time. Though it is not unexpected, I brace myself for what is coming.

She takes a deep breath. In a painful blurt, she replies, “I did so many posters just so I could pass.  She decided that was never going to ‘do’ math well, so she let me create bulletin boards and cut out letters in order to pass. I just hate it. Math was never my thing. Early, we knew that I could not do it, and we created workarounds so I could pass and graduate.”

So then, as always, I apologize for her terrible experience.

I am so sorry.

I am so sorry that any child is led to believe they cannot be successful at math – the language, art, and communication tool that is my love and passion.

I am so sorry that any child is led to believe they cannot be successful.

I seethe inside that any teacher would “extra credit” a child out of learning.

High-purpose environments are filled with small, vivid signals designed to create a link between the present moment and a future ideal. They provide the two simple locators that every navigation process requires: Here is where we are and Here is where we want to go. The surprising thing, from a scientific point of view, is how responsive we are to this pattern of signaling. (Coyle, 180 pag.)

Teachers need to determine the gap between students’ current level of performance or understanding and the expected level of mastery. (Hattie, 66 pag.)

If someone received just three or more touchpoints, or instances, of praise in a single quarter, their performance score in the next review period significantly increased. If they received four or more touchpoints of praise or recognition in a quarter, the retention rate increased to 96 percent over the next year. (Achor, Kindle Locations 1766-1768.)

How might we create more classrooms that are high-purpose environments where teacher clarity empowers learners to close gaps between what is known and what is needed?  What if we highlight what is going well to create touch points of praise to embolden learners to reach for a next level?

CULTURE: from the Latin cultus, which means care.


Achor, Shawn. Big Potential: How Transforming the Pursuit of Success Raises Our Achievement, Happiness, and Well-Being (Kindle Locations 1766-1768). The Crown Publishing Group. Kindle Edition.

Coyle, Daniel. The Culture Code: The Secrets of Highly Successful Groups (Kindle Locations 2378-2380). Random House Publishing Group. Kindle Edition.

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.

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.

screen-shot-2017-02-10-at-5-12-49-pm

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.