Comstock Park — The three students huddled around the whiteboard looking at a math problem freshman Alexis LaVallee had just written on the board.
“Does it matter which one we do?” asked Alexis.
“No, you should get the same answer no matter how you start,” replied teacher Maggie Scott.
With that, Alexis handed the dry erase marker to her partner, ninth-grader Addie Schab, who had the task of determining what “x” equaled. The group talked through the equation and Addie determined the answer was -1. She then took a peek at the group next to them to see if they had gotten the same answer.
“How many of you got x equals -1?” Scott asked her class, and most indicated they had. “OK, the next person needs to determine ‘y.’”
So it went for the next 20 minutes in Scott’s Algebra I class, as students worked in groups of three around 10 whiteboards and practiced substitutions as they learned how to solve systems.
The method Scott was using is called vertical learning, a building thinking classrooms process where students work in groups on vertical surfaces such as chalkboards or whiteboards. The idea is to make the process visible as students work together to solve problems, and to assure that all understand.
Such was the case with Alexis, Addie and sophomore Abbi Borisch, who talked through the problem as Addie wrote out the steps to get to the solution. The group did the same when it came to Abbi’s turn to determine the answer for “y.”
“It really helps me to practice more,” Addie said. She added that it was nice to not be sitting at a desk the entire class time.
Head Up, Stand Up
“This is how I learned,” Scott recalled. “You were at your desk with your head down, working on your problems.”
In some math classes of the past, teachers wrote sample problems on the board and students would copy them, said Katie Austin, Comstock Park’s curriculum director and instructional coach. Then students would do a few problems on their own and ask questions. Before the end of class, students would get a homework sheet, do a few problems at school and complete the rest at home. They’d return to class the next day to check their work, and the process would repeat with the next lesson.
During the 2022-2023 school year, the district updated its sixth- through 12th-grade math resources to be a little more rigorous and to increase student interaction and accountability. They found it in enVision Mathematics, which uses problem-based and visual learning to create fun and engaging lessons that encourage inquiry and discovery. The updated resource also provides examples and projects that feel more current both to students and staff.
“We were looking for something that was going to allow our students to interact a little bit more with each other as well as with the content,” Austin said, “and (to) focus even more so on their number sense and their math IQ and provide a deeper understanding of the content — as opposed to just memorizing different algorithms and processes and procedures.”
Teachers also wanted to build student confidence in doing math.
“You hear a lot of students and adults say, ‘Oh, I’m not a math person, I’m not good at math,’” Austin said. “We are trying to change that mindset for the students a little bit, in that anybody can be a math person, and give them multiple entry points into the topic so it is accessible for all and (so) all students could feel successful.”
With the new curriculum, the secondary math team discovered that students were not used to talking or engaging in academic conservations about math. A focus for the team this year has been working with Kent ISD math consultants to help students with that.
“It is hard for students, because they have to be vulnerable,” Austin said. “They have to talk to their peers and they have to be OK with maybe saying something that isn’t correct, and (ask themselves) ‘How can I learn from that error, or what can I pick out that was the right path?’”
Educators also have been attending programs hosted by Michigan Mathematics Educators, a network that provides professional training. Scott discovered vertical learning via that network.
“There has been a lot more risk-taking,” she said. “When you’re in a math class you are scared to get things wrong, but with the vertical learning, students are more willing to take the risk because it is easy to erase, so it is like it didn’t happen.”
While she has only been using vertical classrooms for about two months, Scott said she has already seen benefits and plans to explore other vertical learning possibilities.
Scribe, Speaker, Manager
Back in class, Scott had each student pick a playing card to determine who was in which group. Randomness provides opportunities to learn from different students how they solve a problem, she explained.
In each group there’s a scribe who writes on the board; a speaker who speaks for the group; and a manager who makes sure the group stays on track. Scott has students switch roles so that everyone has a chance to work on the problems, and she checks in throughout.
Sophomore Alyssa Phillips said being able to get out of her seat and in front of a whiteboard has helped her focus more on what she is learning. Alyssa said she also has enjoyed working with other students during the lesson.
Said freshman Bristol Bennett: “It definitely helps me understand the problems and how to do it better.”
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