Tag Archives: Transformative Assessment in Action

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.


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

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


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.

Differentiation and mathematical flexibility – #LL2LU

How is flexibility encouraged and practiced? Is it expected? Is it anticipated?  What if we collect evidence of mastery of flexibility along side mastery of skill?

From Jo Boaler’s How to Learn Math: for Students:

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.

This past week Rhonda Mitchell (@rgmteach), Early Elementary Division Head, and I collaborated to reword the learning progression for mathematical flexibility so that it is appropriate for Kindergarten and 1st Grade learners.

How might we differentiate to deepen learning?

If we want to support students in learning, and we believe that learning is a product of thinking, then we need to be clear about what we are trying to support. (Ritchhart, Church, and Morrison, 5 pag.)

How might we collect evidence to inform and guide next steps?

Monitoring students’ mastery of a learning progression leads to evidence collection for each building block in a progression. (Popham, Kindle location 2673)

How might we prepare for mid-course corrections to intervene, enrich, and personalize learning for every learner?

By learning to insert feedback loops into our thought, questioning, and decision-making process, we increase the chance of staying on our desired path. Or, if the path needs to be modified, our midcourse corrections become less dramatic and disruptive. (Lichtman, 49 pag.)

What if we consider pairing a skill learning progression with a process learning progression? How might we differentiate to deepen learning?

Students love to give their different strategies and are usually completely engaged and fascinated by the different methods that emerge. Students learn mental math, they have opportunities to memorize math facts and they also develop conceptual understanding of numbers and of the arithmetic properties that are critical to success in algebra and beyond. (Boaler and Williams)

Boaler, Jo, and Cathy Williams. “Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts.” Youcubed at Stanford University. Stanford University, 14 Jan. 2015. Web. 22 Feb. 2015.

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

Popham, W. James (2011-03-07). Transformative Assessment in Action: An Inside Look at Applying the Process. Association for Supervision & Curriculum Development. Kindle Edition.

Ritchhart, Ron, Mark Church, and Karin Morrison. Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. San Francisco, CA: Jossey-Bass, 2011. Print.