Category Archives: #LL2LU

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.

Learner choice: using appropriate tools strategically takes time and tools

All students benefit from using tools and learning how to use them for a variety of purposes.  If we don’t make tools readily available and value their use, our students miss out on major learning opportunities. (Flynn, 106 pag.)

I’m taking the #MtHolyokeMath #MTBoS course, Effective Practices for Advancing the Teaching and Learning of Mathematics.  Zachary Champagne facilitated the second session and used The Cycling Shop task from Mike Flynn‘s TMC article.

screen-shot-2017-02-03-at-2-50-42-pm

You can see the notes I started on paper.

mtholyokemath-2-zakchamp

Jim, Casey and I used a pre-made Google slide deck provided to us to collaborate since we were located in GA, MA, and CA.  We challenged ourselves to consider wheels after working with 8 wheels.

Here’s what our first table looked like.

cyclingshop1

Now, I was having trouble keeping up with the number of wheels and the number of cycles.  So I did this:

screen-shot-2017-02-03-at-3-08-56-pm

This made it both better and worse for me (and for my group).

Here’s an interesting thing.  I’ve been studying, practicing, and teaching the Standards for Mathematical Practices. Jennifer Wilson and I have written a learning progression to help learners learn to say I can use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. (Sage, 6 pag.)

Clearly, I was not even at Level 1 during class.  Not once – not once – during class did it occur to me how much a spreadsheet would help me, strategically.

8wheelsspreadsheet

The spreadsheet would calculate the number of wheels automatically for each row so that I could confirm correct combinations.  (You can view this spreadsheet and make a copy to play with if you are interested.)

When making mathematical models, [mathematically proficient students] know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. (Sage, 6 pag.)

With a quick copy and paste, I could tackle any number of wheels using my spreadsheet.  I can look for and make use of structure emerged quickly when using the spreadsheet strategically.  (I want to also highlight color as a strategic tool.) Play with it; you’ll see.

9_wheelsspreadsheet

[Mathematically proficient students] are able to use technological tools to explore and deepen their understanding of concepts. (Sage, 6 pag.)

screen-shot-2017-02-03-at-4-03-03-pm

There is no possible way I would have the stamina to seek all the combinations for 25 or 35 wheels by hand, right?

Students have access to a wide assortment of tools that they must learn to use for their mathematical work. The sheer volume of possibilities can seem overwhelming, but with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal. (Flynn, 106 pag.)

Important to repeat, “with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal.

For this to happen, we need to have a solid understanding of the kinds of tools available, the purpose of each tool, and how students can learn to use them flexibly and strategically in any given situation. This also means that we have to make these tools readily available to students, encourage their use, and provide them with options so they can decide which tool to use and how to use it. If we make all the decisions for them, we remove that critical component of MP5 where students make decisions based on their knowledge and understanding of the tools and the task at hand. (Flynn, 106 pag.)

To be clear, a spreadsheet was available to me during class, but I didn’t see it.  How might we make tools readily available and visible for learners to choose?

When we commit to empower students to deepen their understanding, we make tools available and encourage exploration and use, so that each learner makes decisions for themselves. In other words, how do we help learners to level up in both content and practice?

What if we make I can look for and make use of structure; I can use appropriate tools strategically; and I can make sense of tasks and persevere in solving them essential to learn for every learner?

How might we offer tools and time?

It’s about learning by doing, right?


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

Flynn, Mike. “The Cycling Shop.” Nctm.org. Teaching Children Mathematics, Aug. 2016. Web. 03 Feb. 2017.

Common Core State Standards.” The SAGE Encyclopedia of Contemporary Early Childhood Education (n.d.): n. pag. Web.

Teaming: Deepen Understanding to Strengthen Academic Foundation

How might we learn and grow together? How do we connect ideas and engage in productive, purposeful professional development (aka learning experiences) around common mission, vision, and goals? What if we model what we want to see and experience in our classrooms?

Influenced, inspired, and challenged by our work at Harvard Graduate School of Education’s 2016 session on the Transformative Power of Teacher TeamsMaryellen BerryRhonda MitchellMarsha Harris, and I set common goals for faculty-learners.

We can design and implement a differentiated action plan across our grade to meet all learners where they are.

But, how do we get there?

For a while, we will narrow to a micro-goal.

We can focus on the instructional core, i.e. the relationship between the content, teacher, and learner.

For today’s Pre-Planning session, a specific goal. At the end of this session, every faculty-learner should be able to say

We can engage in purposeful instructional talk concerning reading, writing, and math to focus on the instructional core.

Here’s our learning plan:

8:00 Intro to Purpose
Instructional Core: Relationship between content, teacher, student

Explain Content Groups tasks

8:30 Movement to Content Groups
8:35 Content Groups Develop Mini-Lesson

9:05 Movement back to Grade-Level Teams in the Community Room
9:10 Share Readers’ Workshop Instructional Core ideation
9:20 Q&A and transition
9:25 Share Writers’ Workshop  Instructional Core ideation
9:35 Q&A and transition
9:40 Share Number Talk  Instructional Core ideation
9:50 Q&A and transition
9:55 Closure:  Planning, Reflection, Accountability

We also shared our learning progressions with faculty so they might self-assess and grow together.

Today’s goal:
screen-shot-2016-09-10-at-10-09-44-am
Year-long goal:
Screen Shot 2016-08-13 at 8.04.56 PM
When  we focus on the instructional core and make our thinking visible, we open up new opportunities to learn and to impact learning with others.

How might we deepen understanding to strengthen learning?

Agents of formative assessment – Embedding Formative Assessment VTR SPW

Anyone – teacher, learner, or peer – can be the agent of formative assessment. (Wiliam, 8 pag.)

I wonder if we have a common understanding of formative assessment.  I like the following from Dylan Wiliam and Paul Black (2009).

image

…evidence elicited, interpreted, and used…to make decisions…

How might we empower every learner in our community to act as an agent of formative assessment?  What if we all use evidence of student learning to make decisions about next steps?

What if we team to clarify and share learning intentions and success criteria? How might we diagnose where learners are and start from there? While we already offer some feedback, what if we are intentional about the messaging in our feedback? Do learners know where they are now and where we want them to go next?

The third strategy emphasizes the teacher’s role in providing feedback to the students that tells them not only where they are but also what steps they need to take to move their learning forward. (Wiliam, 11 pag.)

How might we increase the frequency of feedback loops to offer feedback in the moment rather than the next day?

But the biggest impact happens with “short-cycle” formative assessment, which takes place not every six to ten weeks but every six to ten minutes, or even every six to ten seconds. (Wiliam, 9 pag.)

image

If we want the biggest impact, we need help.  Are our learning intentions and success criteria clear and visible to learners? Do we offer moments for self- and peer-assessment? How might we grow in our ability to give high quality feedback that enables learners to move forward?

If anyone can be an agent of formative assessment, how might we team to offer big impact?


Wiliam, Dylan, and Siobhán Leahy. Embedding Formative Assessment: Practical Techniques for F-12 Classrooms. West Palm Beach, FL: Learning Sciences, 2015. Print.

 

#ShowYourWork: words, pictures, numbers

In her Colorful Learning post, Learning: Do our students know we care about that?, Kato shared the following learning progression for showing your work.

What if we guide our learners to

I can describe or illustrate ow I arrived at a solution so that the reader understands without talking to me?

Isn’t this really about making thinking visible and clear communication?  Anyone who has taught learners who take an AP exam can attest to the importance of organized, clear pathways of thinking. It is not about watching the teacher show work, it is about practicing, getting feedback, and revising.

Compare the following:

What if a learner submits the following work?

Screen Shot 2015-11-09 at 8.43.46 AM

Can the reader understand how the writer arrived at this solution without asking any questions?

What if the learner shared more thinking? Would it be clearer to the reader? What do you think?

IMG_1330

How often do we tell learners that they need to show their work? What if they need to show more work? What if they don’t know how?

How might we communicate and collaborate creatively to show and tell how to level up in showing work and making thinking visible?

How might we grow in the areas of comprehension, accuracy, flexibility, and deeper understanding if we learn to communicate clearly using words, pictures, and numbers?

#SlowMath: look for meaning before the procedure

In her #CMCS15 session, Jennifer Wilson (@jwilson828) asks:

How might we leverage technology to build procedural fluency from conceptual understanding?  What if we encourage sketching to show connections?

What if we explore right triangle trigonometry and  equations of circles through the lens of the Slow Math Movement?  Will we learn more deeply, identify patterns, and make connections?

How might we promote and facilitate deep practice?

This is not ordinary practice. This is something else: a highly targeted, error-focused process. Something is growing, being built. (Coyle, 4 pag.)

What if we S…L…O…W… down?

How might we leverage technology to take deliberate, individualized dynamic actions? What will we notice and observe? Can we Will we What happens when we will take time to note what we are noticing and track our thinking?

CTP_mVLVEAA8DEY

What is lost by the time we save being efficient, by telling? How might we ask rather than tell?

#SlowMath Movement = #DeepPractice + #AskDontTell

What if we offer more opportunities to deepen understanding by investigation, inquiry, and deep practice?


Coyle, Daniel (2009-04-16). The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. Random House, Inc.. Kindle Edition.

Fluency: comprehension, accuracy, flexibility, and efficiency

No strategy is efficient for a student who does not yet understand it. (Humphreys & Parker, 27 pag.)

If both sense and meaning are present, the likelihood of the new information getting encoded into longterm memory is very high. (Sousa, 28 pag.)

When we teach for understanding we want comprehension, accuracy, fluency, and efficiency. If we are efficient but have no firm understanding or foundation, is learning – encoding into longterm memory – happening?

We don’t mean to imply that efficiency is not important. Together with accuracy and flexibility, efficiency is a hallmark of numerical fluency. (Humphreys & Parker, 28 pag.)

What if we make I can make sense of problems and persevere in solving them and I can demonstrate flexibility essential to learn?

SMP-1-MakeSensePersevere

Flexibility #LL2LU

If we go straight for efficiency in multiplication, how will our learners overcome following commonly known misconception?

common misconception: (a+b)²=a² +b²

multiplication_flexibility

correct understanding: (a+b)²=a² +2ab+b²

The strategies we teach, the numeracy that we are building, impacts future understanding.  We teach for understanding. We want comprehension, accuracy, fluency, and efficiency.

How might we learn to show what we know more than one way? What if we learn to understand using words, pictures, and numbers?

What if we design learning episodes for sense making and flexibility?


Humphreys, Cathy, and Ruth E. Parker. Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4-10. Portland, ME: Steinhouse Publishers, 2015. Print.

Sousa, David A. Brain-Friendly Assessments: What They Are and How to Use Them. West Palm Beach, FL: Learning Sciences, 2014. Print.