# Knowledge Mobility as a Lesson Design Principle

## "It was inspirational to see students begin the school year and jump right into collaborative thinking tasks on the VNPS stations."

During the summer of 2021 I began preparing to implement the routines from Peter Liljedahl’s Building Thinking Classrooms. I had a classroom with whiteboard space to accommodate up to seven groups and needed stations for 13 groups. This was the moment I became a huge fan of Wipebook Flipcharts.

The six VNPS (vertical non-permanent surfaces) stations featuring the reusable Flipcharts are coveted by students. Each station has both a grid and a blank surface supporting student thinking in a variety of tasks. It was inspirational to see students begin the school year and jump right into collaborative thinking tasks on the VNPS stations.

## Visual Patterns Round Robin with Wipebook Workbooks

I recently won a Wipebook Workbook Giveaway and my latest adventure was to find a way to use the Workbooks in a way that continued to foster the spirit of collaboration, but offered an experience that was special with this new product.

That’s when it came to me…

My students have spent a lot of time working through Fawn Nguyen’s amazing visual patterns. Their focus has been on comparing different representations of the same mathematical situation. Fans of VNPS know that one of the benefits of these routines is that it promotes knowledge mobility between groups. As students were ready to consolidate their understanding, I wanted an activity that principally built around students passing knowledge between their groups. From this the Round Robin activity using Workbooks was born.

Students were paired with one Wipebook Workbook and one marker. I also arranged so that each of the four groups interacting within a single workbook had a unique color. Each group was given the following set up task:

As a group, go to visualpatterns.org and select two patterns:

• One should be linear; one should be non-linear.
• Choose patterns you haven’t previously picked.
• Choose patterns you think no one else will pick.

In each of the rounds that followed, groups were instructed to write only on the corresponding page of the workbook. They would complete a task in the workbook, referencing any previous work done by other groups. Then they would pass the workbook to the next group in the sequence I specified. The instructions for each round were projected on the screen.

Round 1

• Work only on page 1 of the workbook.
• Write your names on page 1.
• Name your patterns “Pattern A” and “Pattern B” (you choose which is which).
• Draw Pattern A and Pattern B on page 1.

Round 2

• Write your names on page 2.
• On page 2, create a table for Pattern A and another for Pattern B from page 1.
• Identify which pattern is linear and which is non-linear.

Round 3

• Write your names on page 3.
• Graph both patterns on page 3. Label which is A and which is B.
• Identify which pattern is linear and which is non-linear.

Round 4

• Write your names and do this work on page 4.
• Look over pages 1, 2, and 3. Assess whether the information agrees.
• For the linear pattern, determine the slope, y-intercept, and equation.
• For the non-linear pattern, can you determine what type of function this is? Can you find its equation?

After these four rounds, the Workbooks would move in the reverse order, pausing for a few minutes at each group. Students practiced a routine called Comment/Edit/Affirm, where they would look over the work that had been added to the workbooks since leaving their group. If they had any edits to make, students add as a comment, rather than deleting or changing any other group’s work. The intention was to honor the rough draft process of drawing connections between representations.

## Beyond the Activity

The work of elevating the process of doing mathematics collectively—understanding the perspectives of others, revising thinking with new information, and adopting new strategies—is a major goal this year. A lot of this work has been supported with the use of portfolios based on prompts rooted in reflection and metacognition. Following this activity students are prompted to reflect on the process of synthesizing the mathematics begun by other students as well as looking back at how the mathematics they initiated was developed by others. Screenshots, like the one above, are rich with the story of mathematical thinking and provide a wonderful opportunity for students to synthesize this process goal.

## Nolan Fossum, Teacher, Trabuco Hills High School

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