On a recent visit to a Concord park, Berkeley teacher Laura Kretschmar noticed that something was off with a generic sign ordering people to social-distance.
The stick figures on the state-issued advisory were not actually standing the mandatory 6 feet apart from one another.
Kretschmar teaches math and science at King Middle School, and, like others in her profession, she’s trained to see everything as a potential “teachable moment.” So she wondered if the students at the North Berkeley school might be able to catch the error too.
It didn’t take long for 11-year-old Cruz Foster to figure out what was wrong. Within two weeks of Kretschmar’s park jaunt, the student was emailing California’s secretary of health and human services to propose a better and accurate design.
“I realized that if people start seeing these signs and don’t take the liberty of figuring out what’s wrong, then the coronavirus is going to keep spreading,” Cruz told Berkeleyside.
In the original adult-designed sign, four stick figures are standing at the four corners of a square. Labels on the sign show that the hypotenuse, or the diagonal line from one corner to another, is 6 feet long. But that means that the sides of the squares are actually less than 6 feet long, or dangerously short.
The sixth graders in Kretschmar’s class haven’t learned that kind of math yet, so the assignment was a “challenge problem,” an extra-credit task due any time during the week. Kids were encouraged to work on it with an adult.
“I wanted students to struggle with this,” Kretschmar said. “I knew Cruz would be into this problem. He’s such a self-starter and very creative.”
Foster loves math, so he thought the assignment “looked like a fun challenge. And with COVID-19 going on, it seemed like a relevant problem,” he said.
The student had already spent some of his downtime during the pandemic poking around on educational websites, at one point watching a video on trigonometry.
“I had discovered the Pythagorean theorem, so I kind of used that, and I figure out that the people adjacent to each other were not 6 feet apart,” he said. Foster took out his calculator and got to work on a revised sign design where the math checks out.
When the student sent in his work, “it made my day,” said Kretschmar. “I was so excited.”
For the 20-year veteran teacher, who recently came to King from an Oakland charter school, the shift to “distance learning” has introduced brand new challenges. Kretschmar is used to carefully watching her students in class, constantly assessing what’s engaging them and what they’re struggling with, and reshaping her lessons based on her observations.
“It’s so hard to know during this time as a teacher if you’re having an impact,” she said. “Those lightbulb moments are hard to capture.”
Talking on Zoom with Foster, the teacher suggested he try to make some good come out of his discovery. They decided to write to the state.
“My first thought was, definitely let’s do this, at least so they don’t put more of these signs up and possibly so they change them,” Foster said. In his cordial letter, he tells Secretary Mark Ghaly he has some “feedback.” It’s probably too late to replace all the signs, the student acknowledges, but “perhaps you could share with your staff in the spirit of teaching and learning!”
California’s Health and Human Services Agency did not respond to Berkeleyside’s inquiry about whether staff had read Foster’s letter or redesigned the erroneous sign.
In Kretschmar’s class, mistakes are a frequent topic of conversation. She’s taught her students to expect and respect them — and to politely point them out when they notice them (even when the teacher is the responsible party).
Foster said he also attends and “owes a lot to” the Berkeley Math Circle, a UC Berkeley-run program introducing K-12 student to theoretical mathematics. In those meetings, Foster said, the point is to only understand 30% of what you’re learning and get lots of problems wrong.
“It’s really fun, and I feel like it’s a lot of the reason why I’ve been able to do things like watch trigonometry videos and not get really confused,” he said.
Both the math program and a version of his King classes have continued online, but for Foster and many of his classmates, adjusting to school closures has been strange.
“I was never someone who felt like, ‘Oh, my God, I wish I didn’t have school,'” Foster said. “It’s weird mostly because part of why I like school so much is the social aspect, and we don’t really have that now. But it makes it so that when we are on a Zoom call with each other, it’s a better experience. In class we see each other all the time so people aren’t going out of their way to be nice and in with the program.”
If those classmates do run into Foster “IRL,” they can count on him staying a safe and calculated distance away.