Category Archives: Questions

Fear of imperfection; deep practice; just make a mark

Do you know any learner’s that are stuck?  Are they convinced that they can’t?

“Fear of imperfection keeps us perched on the edge, afraid to dive in and start writing. If we sit and wait for the perfect words, they don’t come. Inertia sets in. Our mind halts. The clock slows. Much like hesitating at the edge of the ocean, afraid of the shock of cold, we wait. And in waiting, our anxiety spins.” (Anderson, 9 pag.)

Hesitating at the edge, afraid, we wait. How might we develop brave, bold learners who wonder – on paper – what they are thinking so that they might see it? What do we do to overcome the fear of the blank page? This fear, as real as it seems, is just a doodle away from getting your feet wet, right? The editor in my head – no, not the editor; the critic in my head convinces me to wait: wait until I know, wait for someone else, wait. What force is needed to overcome inertia? Is it just as simple as a doodle?

Are math and writing this closely related? Wow! Far too many students will not write the first step in math because they are not sure if they are going to be right? If they are going to be right, are they learning anything?

In Daniel Coyle’s “The Talent Code,” he writes about deep practice, working at the edge of your ability so that you make mistakes, learn, and repeat.

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.)

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.)

In SMP-1, “I can make sense of tasks and persevere in solving them,” the first level asks for a visible attempt to think and reason into the task.

Are our young mathematicians and writers stuck due to inertia? Is it blank page fright? Is there space in class to draft and redraft, making revisions as you go? Are missteps celebrated and seen as opportunities to learn?

How can we help students dive – or tiptoe – in to get their feet wet? What if encourage learners to just make a mark and see where it takes them?

It doesn’t have to be perfect the first time… or does it?


Anderson, Jeff. 10 Things Every Writer Needs to Know. Stenhouse Publishers, 2011.

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

Reynolds, Peter H. The Dot. Library Ideas, LLC, 2019.

Embolden Your Inner Writer: Session 1 plans

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Course Goals:

At the end of the course, participants should be able to say:

  • I can write more frequently and confidently.
  • I can heighten my awareness of the craft and conventions of writing.

Session Goals:

At the end of this session, participants should be able to say:

  • I can maintain momentum by reading, writing, and seeking feedback.
  • I can strengthen my craft, word choice, and mechanics by applying techniques from models and mentor texts.

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Resources:

Mentor Sentences

  • The goal is always the same: to break a skill into its component pieces (circuits), memorize those pieces individually, then link them together in progressively larger groupings (new, interconnected circuits) [The Talent Code]
  • Salva’s younger brother, Kuol, was taking care of just one cow; like his brothers before him, he would be in charge of more cows every year. [A Long Walk to Water]

Next steps and challenges:

  • Read 10 Things Every Writer Needs to Know: Energy and Words, Chapters 8 and 9, starting page 171
  • Share at least two Quick Write posts in Seesaw
  • Read the posts of others and “like” when read and comment if appropriate
  • Collect and share mentor sentences from your independent reading (at least one)

Session One Learning Progressions (Drafts):


Anderson, Jeff. 10 Things Every Writer Needs to Know. Stenhouse Publishers, 2011.

Coyle, Daniel. The Talent Code: Greatness Isn’t Born. It’s Grown. Bantam Books, 2009.

Park, Linda Sue. A Long Walk to Water: Based on a True Story. Rock the Boat, 2018.

Embolden Your Inner Writer – plans and resources

How can we strengthen and deepen understanding, confidence, and efficacy in the art and practice of writing? Joe Marshall, Marsha Harris, and I are facilitating a series for interested Trinity School faculty and staff.

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In this course, we will discuss, sketch, and write to deepen our flexibility, critical reasoning, and problem-solving. Writing should be anchored in reading rich literature and developed through a cycle of reading, writing, and feedback.

Goals:
At the end of the course, participants should be able to say:

  • I can write more frequently and confidently.
  • I can heighten my awareness of the craft and conventions of writing.

Session structure:

  1. Motion and Models (01/17/2020)
  2. Energy and Words (01/31/2020)
  3. Focus and Form (02/14/2020)
  4. Cohesion and Frames (02/28/2020)
  5. Details and Clutter (03/13/2020)
  6. Celebration (03/27/2020)

Resources:

Preparing for Session 1: Motion and Models:

Challenges to take up:

  • Read and write daily with the goal of building stamina
  • Read and write daily with the goal of strengthening this habit
  • Notice and note sentences that inspire or challenge and share in your journal so that others may learn alongside you

Joe, Marsha, and I have been planning this course for several months.  In one of my early journal entries I wrote:

I seem to have fallen into writing reports of PD and plans and posting them on my blog. I seem to fail to tell exciting stories associated with adult learning.

And now, I have done just that… again. For the next six sessions, I will share the agenda, learning goals, and tasks. AND, I will share my take on each session, my outcomes, learnings, ah-ha’s, and struggles.

Advance Your Inner Mathematician #TrinityLearns Session 5: Sequence and Connect

This semester we are piloting a new course, Advance Your Inner Mathematician, for teachers to continue learning after Embolden Your Inner Mathematician. This work is anchored in Smith and Sherin’s The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussion in Your Middle School Classroom.

In session 5, a dilemma presented itself, and I have yet to resolve what I should have done.

The goal is to present a formidable task and monitor learner work and thinking so that the learners in the room participate in productive mathematical discourse to learn from and with each other.

Before session 5, I selected learning goals and a task, and I anticipated learner thinking.

  • Learning goals for session 5:
    • I can use ratio reasoning to solve tasks.
    • I can look for and express regularity in repeated reasoning.
    • I can show my work so a reader understands without asking me questions.
  • The task for session 5: Jim and Jessie’s Money from Illustrative Mathematics 
  • Anticipated *ways learners might think and work:

Paper.Productive_Struggle.18

*Note: I had not anticipated using a number line, but it was used well in the session, so I added it to my notes after the fact to capture it for future classes.

During the session:

  • I established the first goal:  I can look for and express regularity in repeated reasoning.
  • I launched the task using the Three Reads Routine to support learners entering and thinking in the task.
  • I monitored student thinking and collaboration. I noticed and took notes on strategies and tools being used.
  • I facilitated the whole group discussion by sequencing learner’s work to build understanding and flexibility, and to help learners persevere in making sense of other’s thinking.
  • I did not have to connect the mathematics because the learners did it for themselves. #Awesome.

Here are notes about the sequence during the class discussion and a bit of the narrative:

The pair of teachers, Group 1, using the number line shared first leading with an initial guess of Jim and Jessie each having $150 at first. The next to share, Group 2, was the pair that used a table where the guesses were anchored in how much money Jim and Jessie had at first; their initial guess was $100.  Group 2’s comment to Group 1 was that the number line made it so much easier to understand the numbers in their table, and Group 2’s replay was that the table was so helpful to see the pattern.  #Nice

The next pair, Group 3, shared that they found a difference of $21 in how much money Jim and Jessie had after their expenses, and they were still grappling with how that would help them. They asked for a little more time to think.

The final pair, Group 4, to share started with how difficult it was to find a second pathway after using algebra.  The struggle, they said, is real when trying to think of how to start over with a different tool or strategy.

This is what makes anticipating as a team magical.
We expand each other’s thinking and flexibility
just by showing up and bravely sharing our thinking.

As Group 4 finished their algebraic solution, I noticed that a member of Group 3 was standing… well, bouncing… with an urgent need to share.  “The connections,” she said, “has been here all along. It is with the number line reasoning.” This excited learner connected all of the shared thinking and learning together.  #Awesome

Now, here is my burning question. I have not resolved this dilemma.

My way – the way I thought first – was not shared.

Learning happened and was articulated. Connections were made in a rich discussion.

Do I care that there is another way to think about this task and that it was not taught? No one’s idea, other than mine, was left out of the discussion.  I like my way, and I think it is easier. (Isn’t that the way it is with teachers?) Am I being selfish wanting to share my way too? Or, do you think it might continue the learning to see yet another way?

I’d really love to know what you think.

Number Talks: developing fluency, flexibility, and conceptual understanding #AuthorAndIllustrate

How might we work on fluency (accuracy, flexibility, efficiency, and understanding) as we continue to teach and learn with students? What if our young learners are supposed to be fluent with their multiplication facts, but… they. ..just…aren’t!?

It really isn’t a surprise, right? Children learn and grow at different rates. We know that because we work with young learners every day.  The question isn’t “Why aren’t they fluent right now?” It isn’t. It just isn’t. The question should be and is:

“What are we going to do, right now, to make this better
for every and each learner in our care?”

In Making Number Talks Matter, Cathy Humphreys and Ruth Parker write:

Multiplication Number Talks are brimming with potential to help students learn the properties of real numbers (although they don’t know it yet), and over time, the properties come to life in students’ own strategies. (Humphreys, 62 p.)

Humphreys and Parker continue:

Students who have experienced Number Talks come to algebra understanding the arithmetic properties because they have used them repeatedly as they reasoned with numbers in ways that made sense to them. This doesn’t happen automatically, though. As students use these properties, one of our jobs as teachers is to help students connect the strategies that make sense to them to the names of properties that are the foundation of our number system. (Humphreys, 77 p.)

So, that is what we will do. We commit to deeper and stronger mathematical understanding. And, we take action.

This week our Wednesday workshop focused on Literacy, Mathematics, and STEAM in grade level bands.  Teachers of our 4th, 5th, and 6th graders gathered to work together, as a teaching team, to take direct action to strengthen and deepen our young students’ mathematical fluency.

We began with the routine How Do You Know? routine from NCTM’s High-Yield Routines for Grades K-8 using this sentence:

81-25=14×4
How do you know?

Here’s how I anticipated the ways learners might think.

Paper.Productive Struggle.195

From The 5 Practices in Practice: Successfully Orchestrating Mathematical Discussion in your Middle School Classroom:

Anticipating students’ responses takes place before instruction, during the planning stage of your lesson. This practice involves taking a close look at the task to identify the different strategies you expect students to use and to think about how you want to respond to those strategies during instruction. Anticipating helps prepare you to recognize and make sense of students’ strategies during the lesson and to be able to respond effectively. In other words, by carefully anticipating students’ responses prior to a lesson, you will be better prepared to respond to students during instruction. (Smith, 37 p.)

How many strategies and tools do we use when modeling multiplication in our classroom? It is a matter of inclusion.

It is a matter of inclusion.

Every learner wants and needs to find their own thinking in their community. This belonging, sharing, and learning matters. We make sense of mathematics and persevere. We make sense of others thinking as they learn to construct arguments and show their thinking so that others understand.

Humphreys and Parker note:

They are learning that they have mathematical ideas worth listening to—and so do their classmates. They are learning not to give up when they can’t get an answer right away because they are realizing that speed isn’t important. They are learning about relationships between quantities and what multiplication really means. They are using the properties of the real numbers that will support their understanding of algebra. (Humphreys, 62 p.)

As teachers, we must anticipate the myriad of ways students think and learn. And, as Christine Tondevold (@BuildMathMinds) tells us:

The strategies are already in the room.

Our job is to connect mathematicians and mathematical thinking.

From NCTM’s Principles to Actions:

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.

And:

Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

What if we take up the challenge to author and illustrate mathematical understanding with and for our students and teammates?

Let’s work together to use and connect mathematical representations as we build procedural fluency from conceptual understanding.


Humphreys, Cathy. Making Number Talks Matter. Stenhouse Publishers. Kindle Edition.

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

Smith, Margaret (Peg) S.. The Five Practices in Practice [Middle School] (Corwin Mathematics Series). SAGE Publications. Kindle Edition.

Multiplication Fact Fluency prototype – feedback requested

I am concerned that we are conflating automaticity with fluency.  How might we get clear on the difference?

From Assessing Basic Fact Fluency by Gina Kling and Jennifer M. Bay-Williams:

Think about how you assess reading fluency. Does your assessment plan involve listening and observing as children read as well as asking reading comprehension questions? Now imagine what you might learn about students’ reading fluency if you used only timed quizzes. How would your confidence in your assessment change?

When I use Google to search for sample “multiplication fluency assessments, worksheets from TPT show up.If you haven’t yet, it is important to stop and read three articles:

From Fluency: Simply Fast and Accurate? I Think Not! by Linda Gojak:

Building fluency should involve more than speed and accuracy. It must reach beyond procedures and computation.

From Fluency without Fear by Jo Boaler:

The best way to develop fluency with numbers is to develop number sense and to work with numbers in different ways, not to blindly memorize without number sense.

Ok, so how do we assess fluency? Do we have common language for mathematical fluency?

From  Principles to Actions: Ensuring Mathematical Success for All

Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

Let’s focus this 3rd grade standard:

Multiply and divide within 100.

CCSS.MATH.CONTENT.3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

 

Do any of the fluency assessments from the above Google search help us assess fluency?

What if we try a different type of assessment? An assessment that involves listening and observing as children compute, reason, and respond.

What if we confer with learners individually, just like we do with reading assessments, to listen, record, and encourage learners as they think, reason, and compute?

I need, want, and invite your feedback on the following prototype.  I hope that I have constructed a viable argument and I seek your constructive critique.

Multiplication Fluency (within 100)
Conferring with Mathematicians

Section 1 asks students if they know their multiplication facts. We intentionally ask these questions because of John Hattie’s work on student expectations of self – effect size of 1.44.

Section 2 checks for accuracy and efficiency.  The teacher will code the student’s response as recall, uses a strategy, or skip counts.  The first 8 facts are common for all students. The next 8 facts can be customized for each student based on their responses to easiest and hardest.

 Section 3 checks for accuracy and flexibility.  In the previous section, the teacher gave the multiplication expression and the student responded with the product.  Now it is reversed. The teacher gives the answer and student states an expression and are asked if they know another way.

Section 3 also checks for accuracy and flexibility using images from #UnitChat.  Students are asked how many they see and how do they see them.  If they skip count, their answer is confirmed, and they are asked if they can say or write it again using multiplication.

If you open this Multiplication Fluency (within 100) pdf, you will find each image on its own page so students can touch to count when needed.

Will you take time to offer actionable, growth-oriented feedback using I like…, I wonder…, and What if… to help clarify or improve the assessment?

Thank you in advance.

#TrinityLearns Leading Learners to Level Up as a TEAM (#LL2LU) Part 2

Continuing our work from last month, Trinity School’s Assessment Committee continues to grapple with the following questions.

As a team, how are we united (aligned) in our understanding and assessment of learning?  How might we grow our assessment literacy, understanding, and actions to focus on learning, assign competence, and empower learners to become agents of learning?

Under the leadership of Thomas Benefield (@yerlifeguard) and Becky Holden (@BHolden86), Trinity School’s Assessment Committee we continue our commitment to read and take action on Developing Assessment-Capable Visible Learners, Grades K-12: Maximizing Skill, Will, and Thrill by Nancy Frey, John Hattie, Douglas Fisher.  

Below is our agenda for the April meeting where we have begun to grapple with growing our understanding together.

As a team of teachers representing all grade-levels at our school, we chose to analyze student work together and hold a norming meeting to explore and learn one way to help our grade-level teams calibrate and clarify expectations around collaboration and citizenship.

To ensure that all voices were heard, we started with quiet reading time to preview the draft of the learning progressions.  As we did last month,  we used a Google form (shown below) to record everyone’s initial thinking around the level of work based on the drafted learning progressions for Working Cooperatively and Displays Respect.

The artifact, in this case, was a two minute video that offers a glimpse of partner work. (The video is not shared in this post, but a screen shot of one second is shown below.)

Using the Google form continues to be critically important. Everyone’s initial thinking was made visible to the team. Look at the results from our initial thinking.

As you can see, we were all over the place in our interpretation of the meaning and expectations described in our learning progressions.

As a team of assessment leaders, we had anticipated this result. You can see how this might be problematic for students in different sections with different teachers, right?

High-functioning teams that focus on learning must calibrate their understanding of what is essential to learn so that all students are assessed fairly and equitably.

What happened next was nothing short of magical.

First, we discussed our leveling with one partner to explain our reasoning and understanding. It was quiet, calm, and intense.  As partners listened to each other, different interpretations and points of view were represented.  When enough time passed, we returned to the whole group setting and discussed. Again, magical! Everyone confidently shared their initial level assessment and then spoke of how their understanding was shifted by discussing it with someone else.

Then, we took time for individual reflection and leveled the same artifact again, based on our developing common assessment. Just look at the results.

Closer, so much closer to common understanding.

To hone our skills and understanding, we used the same two learning progressions for Works Cooperatively and Displays Respect using video from a different grade level. (The video is not shared in this post, but a screen shot of one second is shown below.)

Again, more closely aligned understanding.

What can be gained when all ideas are made visible to the entire team? How might we learn and grow together by sharing our thinking, seeking feedback, and calibrating with our team?

How do your school’s teams calibrate expectations, shared values, and common understanding?

What actions will we take to become stronger and clearer as a team?


Frey, Nancy, et al. Developing Assessment-Capable Visible Learners, Grades K-12: Maximizing Skill, Will, and Thrill. Corwin Literacy, 2018.