Let’s learn from local bright spots how to teach kids math

By Nataliya Yufa

Friday, May 2, 2025

Originally published in Cambridge Day

Growing up in Ukraine, I would occasionally hear stories from my grandmother’s youth. One thing she was upset about, 50 years later: being asked to act as a teacher to fellow students in math. Grandma happened to just get math intuitively, and she had no idea how to explain it to a classmate who didn’t think like her and needed more support. It was extremely frustrating to both of them.

It was a Ukrainian researcher, Lev Vygotsky, who first formalized the idea of knowledge being represented as three concentric circles – the inner one being things a student knows extremely well, the middle being where they can currently learn and the outer one being knowledge they are not ready for. Intuitively, this makes sense, especially when we relate it to something like a new language. When I started to learn Spanish, reading novels was definitely out of reach, but the alphabet was something I was solid on; somewhere in the middle is where my teachers would meet me.

Math is akin to a different language. If someone is a novice, they are not going to make progress by being asked to do tasks completely outside their reach. At the same time, asking a student to do things that they are already very comfortable with results in frustration, too – students ask, justly, what is the point?

What does this have to do with math education in Cambridge? As a teacher in Cambridge Public Schools, I saw firsthand a sixth-grader who struggled with basic computations on the way to solving a grade-level problem proclaiming to himself “I’m bad at math” and a classmate who was doing calculus at home. Through a grassroots nonprofit, The Cambridge Math Circle, my colleagues and I find math that both types of students can explore outside of the school curriculum. But when we teach curricular math, there is no single way that works well for both types of students – teaching at the place where either student is ready to learn will be out of place for the other, and teaching in the middle will fail both, because neither one happens to be at this level.

What should we do instead? This is a question that’s being asked and answered by many local educational institutions – The Algebra Project, the pilot program at Cambridge Street Upper School, Girls’ Angle, the Young People’s Project and Harvard University’s math department, as well by as the city’s Steam Initiative, to name a few, in addition to the Math Circle. What do all these programs have in common?

Three things: Meeting the students where they truly are, not where they theoretically should be; showing students that the instructors authentically care about them, to help them through the tough stretches of learning;  and providing interesting, challenging and joyful work to all students, regardless of whether they are behind or ahead.

Math is a very politicized topic in the United States. Last month even the White House weighed in on its incorrect understanding of what Harvard University is teaching in some of their intro math courses. Here is the groundbreaking way Harvard is meeting the needs of students whose learning suffered because of the pandemic: It is building extra time into the course for students with missing prerequisite knowledge. 

With this, rather than taking a first college math course, failing, having to retake the entire course and deciding they are not “math people,” students are able to succeed the first time.

This is different from how many colleges deal with struggling students – either offering remedial classes that take extra time and tuition and do not meet graduation requirements, or having students take a class to try to master some of the content when they are not ready for it – then drop it at the end and do it all over again the next semester to try to pass. Students, of course, are not robots, and it makes a huge difference to them whether they are able to pass a class on their first try.

We should learn from the understanding of all of the great work being done in our city and make sure all of our students get the joyful math experience they deserve. It is something that will benefit them for the rest of their lives and what they will remember 50 years later.