PD in Action: 4th Grade Math fluency and communication

More results from PD that causes action…It makes me wonder about learning design.  Are we designing PD experiences for teacher-learners and lessons for student-learners that cause action and gain traction? Do we see products of our PD learning being translated into classrooms? Do we see products of our classroom learning being translated into action?

Last week I wrote about mathematical communication at an early age after co-teaching 4th grade math. In the comments, Kato helped me refine a learning progression for showing work so that it was more student-friendly for 4th graders. Kato commented:

I would love to experiment with these levels in Fourth Grade. I like the levels about showing your work, and that they never say “show your work.” I find that that phrase overwhelms Fourth Graders (of all abilities) because they don’t really know what it means. Level 3 and 4 are good. I wonder if they are too wordy or have too many action steps to follow.

I’ve revised the learning progression as follows.

Level 4
I can show more than one way to find a solution to the problem.
Level 3
I can describe or illustrate how I arrived at a solution in a way that the reader understands without talking to me.
Level 2
I can find a correct solution to the problem.
Level 1
I can ask questions to help me work toward a solution to the problem.

Arleen invited me back to 4th grade math this week. As I arrived, the children were working on a Math Message. On the page with today’s Math Message, Arleen included the learning progression that she designed with Kato during the #LL2LU Faculty Forum PD session last week.

I was thinking about Kato’s comment I find that [the] phrase [show your work] overwhelms Fourth Graders (of all abilities) because they don’t really know what it means. How do we communicate how to show your work when the phrase show your work is confusing or unclear?

Arleen’s outcome for the children was about computational fluency.  My target for the children was about mathematical communication.  As we worked – Arleen presented questions and I modeled math communication – we observed the written work and coached.

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Look at the children’s work.  Do we know that we are clearly communicating both learning targets? Can we see evidence of learning in the work? I know I said (over and over) how to organize work and show what you know? Did they receive the coaching? Did our work cause action and learning?

Are the targets clear? Do we do enough in-the-moment formative assessment and coaching? Do we offer feedback that causes action and learning? What if we collect evidence and analyze the products of our work? What if we use artifacts of learners’ work to formatively self-assess?


  1. Hi Jill,
    I’m still a regular “stalker” here, although I haven’t commented much. I really like the phrasing you are using to define the 4 levels of the learning progression above. I’m sure those levels will be useful to students and teachers at all grade levels. I will be sharing this with others.

    Take care.



    • Thank you, Gloria! Sam and Jeff have both made the same comment to me about the levels being useful in high school too. I’d love to know if this helps teachers in your area.


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