Transform Your Classroom for Collaborative Learning

What is it?

Setting up your classroom so that collaborative groups can stand to solve problems on vertical surfaces around the room has been shown to be an effective strategy to increase student thinking, engagement, and math discourse. I first tried this innovative strategy in my 4th grade classroom after hearing about 360 Degree Math. They explain it as, “all students work through the math on the four walls of the classroom while the teacher stands in the middle of room and sees the learning as it happens. The teacher can see student misconceptions immediately and provide feedback to the students in real-time. Students organically form into social networks of learning...helping one another grow as learners with the teacher's support.” Similar to the Japanese lesson structure called Bansho, or board writing, students represent and solve a rich problem-solving task. The teacher sequences the work in a visual display designed to develop mathematical understanding and help students make connections. Then the class engages in mathematical discourse to analyze the varied solution paths.(For more information, see “Bansho: Visually Sequencing Mathematical Ideas” https://pubs.nctm.org/view/journals/tcm/24/6/article-p362.xml)

Why should we do it?

Peter Liljedahl, in his book, “Building Thinking Classrooms in Mathematics”, asserts “students sitting at their desks …. turned out to be the workspace least conducive to thinking. What emerged as optimal was to have the students standing and working on vertical non-permanent surfaces (VNPSs) such as whiteboards, blackboards, or windows… having students work, in their random groups, on VNPSs had a massive impact on transforming previously passive learning spaces into active thinking spaces…” This practice in conjunction with 13 other researched based practices in his book including “thinking tasks” and effective questioning, insures we are not just teaching mathematics but developing mathematicians.

In my own lessons, I have found having this instructional strategy promotes:

• more visibility into student thinking
• more student discussions (about MATH!)
• more cross pollination of student thinking
• more student engagement and ownership

I recently demonstrated a lesson where students collaboratively solved a word problem using self-selected strategies on chart paper hung around the room. After a vigorous class discussion where they debated the solution, argued for the most efficient strategy, and unpacked a common computation error, a 4th grader announced, "This was the BEST math class ever!” The observing teachers noted sustained deep thinking about the lesson’s mathematical objective.

How do I start?

1. Prior to the lesson, set up stations around the room where student groups can work on walls: chart paper, chalkboards, whiteboards, Dry Erase Sticky Notes, Dry Erase or Chalkboard Paint, portable doc cameras, etc. Have writing utensils available at each station. I prefer to have each student choose their own color; this way they are ALL accountable to make their thinking visible.
2. Prepare a math problem or task that is engaging, mathematically rigorous, and has more than one solution path. Consider the various ways your students may solve the problem and anticipate what barriers they may encounter.
3. Provide a selection of math tools that students may choose to solve the problem (in addition to pictorial and symbolic representations). These may be concrete math manipulatives such as cubes, number lines, ten frames, etc. However, there are many magnetic math manipulatives ideal for use on classroom vertical whiteboards, such as:
   • PLACE VALUE
   • FRACTIONS
   • GEOMETRY
   • DECIMALS
4. Invite random groups of 3-4 students to work together to solve the problem. Students may use any representation (numbers, pictures, and/or words) to solve and show their thinking. Making student thinking visible is CRITICAL to this classroom routine. If needed, prior to sending students to stations, consider discussing ways to ensure all the group members have a voice and a role in the process.
5. Monitor student groups, ask open-ended questions, and take notes about varied strategies. Select student work to be shared and sequence them in a fashion that guides students to the mathematical objective.
6. Invite students do a gallery walk or guide students to view select work. Then facilitate student-student discourse by inviting them to share their thinking, ask questions, agree/disagree, and offer other solutions or strategies. Ask questions that help students make connections between the various solution pathways. Note – often conversations about mistakes or abandoned strategies are the most fruitful, especially when such conversation is student-led.

Using vertical surfaces not only adds visibility but also encourages active participation, visual models, math discourse, and a deeper understanding of mathematical concepts. Comment on how you use vertical surfaces in math! Better yet – send us an email or a photo. Reach out to sales@didax.com or info@didax.com for custom kits that support active learning in math, even when working on walls.