New York City’s attempt to change how schools teach math is facing some early roadblocks—and generating debate that cuts to the core of long-standing scientific and philosophical questions about how students best learn the subject.
The school system, the largest in the country, is in its second year of a new initiative aimed at raising persistently low math achievement in the city. Two-thirds of New York City’s Black and Latino students are not performing at grade level in math on state tests.
The initiative, NYC Solves, proposes using common curricula to achieve this goal—ensuring, district officials have said, that all kids have consistent access to grade-level instruction.
All high schools will eventually be required to adopt Illustrative Mathematics to teach Algebra 1, a program that prioritizes a problem-based approach. Students learn primarily through grappling with, and discussing, real-world scenarios that involve math. Middle schools can choose from a short list of pre-approved programs.
But this school year, as Illustrative Mathematics rolled out to more schools across the city, the teachers’ union started pushing back, citing concerns from educators. The curriculum moves too fast, they said, there’s not enough support for struggling students, and teachers don’t have the flexibility they need to differentiate for kids coming into class with varied abilities.
(These critiques come amid an uneven and at times, rocky, rollout of the city’s similarly ambitious attempt to reimagine reading instruction.)
In response to the union’s advocacy, on Feb. 5, the department of education offered some flexibility for teachers in attempts to make the curriculum easier to implement. They can slow down the pace of units and discard some of the program’s assessments. And the city will make more professional learning and resources to differentiate instruction available, according to a letter from the schools chancellor, the United Federation of Teachers president, and the president of the city’s union for school leaders.
Still, some teachers say these options don’t go far enough.
“The changes that were announced are relatively minor,” said Bobson Wong, an Algebra 2 teacher at Bayside High School. Wong doesn’t use the curriculum in his class, but has reviewed the materials and taught Algebra 1 last year.
“So many of the questions are so overwhelming for kids, because they don’t allow for kids to process the information,” he said. “They don’t allow for kids to practice the requisite skills they need to solve the equations.”
This analysis—that the lessons put too much focus on developing deep understandings of math concepts, and not enough on practicing math skills—touches on a foundational divide in the ongoing “math wars.”
The perennial question: Should math class prioritize conceptual understanding or procedural fluency?
As the creator of Illustrative Math sees it, learning to do math is like learning how to ride a bicycle.
Kids don’t watch adults ride and pick up the skill that way; they have to get on and pedal themselves, said William McCallum, the co-founder of the curriculum and an emeritus professor of math at the University of Arizona.
“There is an underlying principle that we believe in, that kids learn math by doing math rather than by watching someone else do math,” he said.
This is one theory in math education: Give students complex problems that they might not know exactly how to solve, and ask them to work through them, with the support of their peers and their teachers. Proponents say this leads to deep conceptual understanding of math topics.
Another approach relies more on explicit instruction. Teachers model new skills, students practice them with teacher guidance, and only then do they apply them on their own. Those who use this “I do, we do, you do” method say that it shores up the crucial foundational skills students need to tackle higher-order concepts.
Research suggests that students might do well with some of both—in math, conceptual understanding and procedural fluency develop in tandem and build off of each other. But there’s not much consensus about how to structure lessons and units in ways that attend to both of those two goals.
McCallum said Illustrative Mathematics embrace one path. “We believe that conceptual understanding and procedural fluency are both incredibly important,” he said. “Our approach is that kids will remember the procedures for longer, and they will last with them for life, if they understand how those procedures work.”
Wong agreed that math curriculum shouldn’t prioritize one set of skills over the other. “You have to do both. You do both simultaneously,” he said.
But in Wong’s estimation, Illustrative Mathematics “goes too far to the idea of discuss and think first, and then do,” he said. “You can’t do that. Math is a language. You learn a language by observing patterns and applying them.”
Students need more time than the curriculum provides to observe and process these patterns, he said. He gave an example of one problem in the Algebra 1 curriculum.
The problem asks students to determine the relationship between two columns of numbers in a table, and then justify whether each of four given equations could be used to represent the relationship.
“This is actually a very rich question. Because if you do it correctly, you can address a lot of misconceptions that kids make,” Wong said.
But addressing all of those potential misconceptions would take more time than the five minutes allotted for the activity, he said. And the inclusion of “difficult numbers” in the table—some of the numbers are decimals and fractions rather than whole numbers—could sidetrack kids with weaker prior knowledge, he added. (Decimals and fractions—staple concepts of the middle school classroom—are well known tripping-up points for students in math.)
Other teachers have raised similar concerns. One Brooklyn math teacher quoted in Chalkbeat said he struggled to make students’ discovery of math concepts “sticky” without repeated practice.
In Philadelphia, where city schools adopted the curriculum in the 2023-24 school year, an evaluation study found that educators had trouble moving through the lessons at the recommended pace and differentiating for struggling students.
“The idea is that we’re trying to find practices that meet students where they’re at and also gain them basic skills, so for the students that I work with, they have already enough discomfort,” said one principal in the study.
“Sometimes, continually doing productive struggle all the time is not always the answer,” the principal said, referencing the idea that letting students try—and sometimes fail at—challenging problems on their own can accelerate learning.
Some criticize a problem-based approach
Listening to teacher feedback like this is key to making any large-scale implementation work, McCallum said.
Illustrative Mathematics plans to do “customized” support for New York City teachers, he added, noting that one district superintendent in the city had asked if the organization’s trainers could prepare the schools’ math leaders to run professional learning. But seeing results from new programs also takes time, he said.
Still, some math educators and parents have called into question the very idea of a problem-based approach.
In Wake County, N.C., for example, a pitched battle has raged for the past eight years over the district’s use of the Mathematics Vision Project in its high schools, a curriculum that emphasizes problem-solving and collaboration, with teachers expected to act as facilitators. Parents argued that their children weren’t getting enough explicit instruction to understand new topics.
The back-and-forth between the most vocal critics and the company became so heated that the Mathematics Vision Project sued one Wake County parent for libel and slander.
In 2021, a group of professors and math educators formed a “science of math” movement, claiming that struggling in the math classroom isn’t always productive. These researchers, many of whom study students experiencing math difficulties, cite studies showing the benefits of explicit instruction and scaffolded practice.
On its website, this group takes issue with productive struggle, which they say can “lead to frustration and cause students to develop misconceptions.”
McCallum, though, doesn’t see these advocates as launching a counter-movement to the kind of complex problems that Illustrative Mathematics centers. “I don’t think it has to be either/or,” he said.
