Rethinking Classroom Design: Collaborative Stations, VNPS & Desmos

Twitter Math Camp ’15 sent me down the vertical classroom path (Click here to read post). Throughout the 2015-2016 school year, I promoted vertical non-permanent surfaces (VNPS) whenever possible.  Lucky for me, Joe, a 7th/8th grade teacher, was interested and additional white (shower) boards were installed in his room.  As I observed his students using VNPS, my support of the vertical classroom grew. By years end, I was convinced that implementing collaborative stations would naturally shift instruction to an inquiry and problem based classroom.

By May, 6th grade teacher, Kim, jumped on board. We planned out her redesign and over the summer white (shower) boards, cut to size, were installed. School’s not in session yet, but here are some pics. (In my original design, the white boards were higher.  They can be raised if needed)


Collaborative Stations in College

Part of my summer was spent attending college tours for my son.  The tour guide at UC Riverside in Riverside, California walked us through their library. In addition to the typical library contents, I noticed collaboration stations!  Stations consisted of a flat surface, monitor to project a computer screen and a white board. This multi-medium approach to learning and collaborating is becoming the norm.


Gearing up for 2016 -2017

Implementing Collaborative Stations

As mentioned earlier, I believe collaborative stations naturally cause a shift in instruction. It’s hard to compete with direct teaching when students have access to computers and a group white board.  Once students experience working in this structure, they’ll ask for more lessons using this format.

Therefore, my coaching team and I began this school year by modeling the collaborative approach. We ran a 7th and 8th grade professional development workshop which focused on solving linear equations using collaborative groups.

The Task:  Discuss

  1. the process of solving,  -8 + 2(x + 5) = -3(x – 1) + 4 

  2. the meaning of the equation’s solution.


Part 1:  Establish ResponsibilitiesCapture

Arrange students in groups of 4. Give each student a number from 1 – 4. Each number represents the individual’s responsibility within the group:

  • 1’s: Desmos component
  • 2’s: Vertical white board: Equation
  • 3’s: Vertical while board: Properties
  • 4’s: Desmos component

Part 2: Establishing Curiosity

 Display the equation and ask

  • 1’s to enter the equation into the Desmos graphing calculator
  • 2’s to write the equation on the board
  • 3’s to grab the property descriptions
  • 4’s to enter the left side & right side expressions into Desmos (on different rows)


              View for the 1’s                                                           View for the 4’sCapture1




At this point, ask the Desmos students to show the group their screens and describe what they see. Someone is bound to click on the intersection point, toggling the coordinate (1, 4).Students are naturally inquisitive. They’ll ask questions and search for meaning. A stage for discovery has been set.

Part 3: Working Through the ProcessCapture5.JPG

Students at the white board are responsible for recording an informal 2-column proof. The teachers to the right, are working on a different problem as described above, but you can see the development of their 2 column-proof.  Left side lists the computation.  Right side lists the respective justification.

The steps written on the board are also entered into Desmos. Since the students already know the answer to the equation, their focus is directed on the process. Desmos provides constant feedback.  As each version of the equation is entered, students immediately know if their current step was correct.  If the value of x doesn’t show the number 1 (for this case), or if a 3rd line pops up then a mistake was made and error analysis kicks in.

The computer views:

Capture    Capture1

Part 4:  The Teacher as a Facilitator

During the task, the teacher circulates the room listening to and facilitating conversations.  Transitioning from the Sage on the Stage to a Teacher Facilitator can be tricky at first.  It takes practice. Here are a few practices to keep in mind:

 1:  Transitioning  To avoid groups separating into 2 subgroups (computer and white board), teachers first need to monitor the transition. Scan the room and observe each group.  First, confirm that all members are executing their individual responsibility and then assure group members are talking to each other.  To refocus students or aid in collaboration, I ask questions.

  • Who’s in charge of writing the justification? Who had the responsibility to enter the equation into Desmos?
    • With these questions, groups begin to self-monitor
  • (To a student who looks confused) Which job were you assigned?  (To the group):  Can one of you help out … 
    • These questions are to place the responsibility back onto the group.
  • Have you coordinated with your group members working on Desmos? On the white board?
    • I ask these, when I notice a lack of communication between group members

2:  Formative Assessment – Ask Direct Questions  As groups progress through their task, visit each group, and ask questions to assure collaboration and to check for understanding. Examples of questions:

  • To the Desmos person:
    • In which row was the distributive property used?
    • Explain what happened from row 2 to row 3.
  • To the white board person
    • What does it mean when the value of x changes in the computer? Is it good or bad? Why?
    • Explain where you used the addition property of equality?

If a student is unable to respond, I’ll prompt the group to step in.

  • Teacher:  Could I have everyone’s attention?  The question I’d like everyone to answer is: Explain all the places where the addition property of equality was used? Please make sure everyone in the group can answer this question.  I’ll be back in a minute.

When I return, I typically call on the original student but not always. If he/she responded appropriately, then I may ask a second member to restate their response.  If the original student could not answer correctly, then I’d say…

  • It seems you need 30 more seconds.  Work together.  I’ll be back.

Usually by the second time, the original student is able to answer the question.

3:  Highlight Different Methods. During the training, the two groups below approached their given problem differently.  The group on the left began by multiplying both sides of the equation by 2, whereas the group on the right combined like terms first.

The same experience is destined to happen with students. When it does, take time to acknowledge and embrace alternate paths to a solution. VNPS allow students to review and critique each other’s work from a distance – providing both planned and unplanned opportunities to absorb multiple strategies.

4:  The Question Bomb:  A question bomb occurs when a teacher asks a question and walks away leaving the group members to rely on each other for the answer.

  • Teacher:  I can tell that you (the group) clearly understand the relationship between the equation’s solution of 1 and the intersection point.  What’s the significance of the 4?  I’ll be back to check in with you.  (Teacher smiles and walks away giving students space to discuss)
  • Once a question is dropped, the teacher circulates the room before heading back to check in. It’s alright if the group doesn’t have a complete answer as long as they provide evidence of a discussion. Based on the evidence, the teacher chooses the next guiding question.  Without teacher follow through, the initial question bomb will not push student thinking. Teachers: Keep moving, ask questions and connect with students.


Getting Back to the Training

The coaching team reworked the content to create more inquiry within the lessonCapture2

Equation 1:  We introduced the collaborative processed described above.

Equation 2:  We switched roles and practiced again.  Those working with the computer now wrote on the white board and vice versa.

Equation 3:  Teachers entered the equation and noticed the twist.  For students, the missing x value and parallel lines create curiosity.  Why are the lines now parallel? Why is the x value not displayed? What about the equation causes parallel lines? Some students may even search the earlier equation for answers.

Capture Capture1

Equation 4:  The last equation involves the final twist – A missing x value matched with a single line. Another mystery. A missing x value but only one line.  Why??

Capture Capture1

Students can organize their information in the template.  To create mathematical intrigue, the first row intentionally left blank. As students record information and make connections, the three categories of solutions will become apparent..



Closing Thoughts

 A summary of main ideas.

  1. Collaborative stations involve desk space, technology (Desmos), manipulatives (etc…) and a VNPS
  2. Present students with a mathematical situation to explore – incorporate mystery 
    1. In this case, students were to discover the 3 types of linear solutions.
  3. Incorporate explorations that require students to use multi-medium approach such as white boards, technology and/or manipulatives simultaneously. 
    1. Students collaborated on creating a 2-column proof on the white board.
    2. They checked their process on Desmos.
    3. They also explored the meaning of the graphical representations on Desmos.
  4. Let students discover connections.  The discovery process creates a more meaningful experience.
  5. Practice facilitation techniques. Work the room
    1. Transitioning
    2. Formative Assessment – Ask Direct Questions
    3. Highlight Different Methods
    4. Drop a Question Bomb
    5. Keep moving, ask questions and connect with students

About jgvadnais

Math Coach. Desmos Fellow. Google Level 1 Certified. SoCal transplant. New Englander at heart. Lover of yoga, dogs, green smoothies and coffee.
This entry was posted in desmos, Math Education, TMC15, Twitter Math Camp and tagged , , , , , , , , . Bookmark the permalink.

One Response to Rethinking Classroom Design: Collaborative Stations, VNPS & Desmos

  1. Pingback: The Vertical Classroom Project Begins | Communicating Mathematically

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s