ALBANY, Ore. – It’s 7:15 on a cold gray Monday morning in May at Linn-Benton Community College in northwestern Oregon. Math professor Michael Lopez, in a hoodie and jeans, a tape measure on his belt, paces in front of the 14 students in his “math for welders” class. “I’m your OSHA inspector,” he says. “Three sixteenths of an inch difference, you’re in violation. You’re going to get a fine.”

He’s just given them a project they might have to do on the job: figure out the rung spacing on an external steel ladder that attaches to a wall. Thousands of dollars are at stake in such builds, and they’re complicated: Some clients want the fewest possible rungs to save money, others a specific distance between steps. To pass inspection, rungs must be evenly spaced to within one sixteenth of an inch, the top rung exactly flush with the top of the wall.

The exercise could be an algebra problem, but Lopez gives them a six-step algorithm that doesn’t use algebraic letters and symbols. Instead, they get real-world industry variables: tolerances, basic rung spacing, wall height.

Lopez breaks the class into five teams. Each team is assigned different wall heights and client specs, and they get to work calculating where to place the rungs. Lopez will inspect each team’s work and pass or fail the job.

Math is a giant hurdle for most community college students pursuing welding and other career and technical degrees. About a dozen years ago, Linn-Benton’s administration looked at their data and found that many students in career and technical education, or CTE, were getting most of the way toward a degree but were stopped by a math course, said the college’s president, Lisa Avery. That’s not unusual: Up to 60 percent of students entering community college are unprepared for college-level work, and the subject they most often need help with is math.

The college asked the math department to design courses tailored to those students, starting with its welding, culinary arts and criminal justice programs. The first of those, math for welders, rolled out in 2013.

More than a decade later, welding department instructors say that math for welders has had a huge impact on student performance. Since 2017, 93 percent of students taking it have passed, and 83 percent have achieved all the course’s learning goals, including the ability to use arithmetic, geometry, algebra and trigonometry to solve welding problems, school data show. Two years ago, Linn-Benton asked Lopez to design a similar course for its automotive technology program; they began to offer that course last fall.

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Math for welders changed student Zane Azmane’s view of what he could do. “I absolutely hated math in high school. It didn’t apply to anything I needed at the moment,” said Azmane, 20, who failed several semesters of math early in high school but last year got a B in the Linn-Benton course. “We actually learned equations I’m going to use, like setting ladder rungs,” he said.

Linn-Benton’s aim is to change how students pursuing technical degrees learn math by making it directly applicable to their technical specialties.

Some researchers think these small-scale efforts to teach math in context could transform how it’s taught more broadly.

Among strategies to help college students who struggle with math, giving them contextual curriculums seems to have “the strongest theoretical base and perhaps the strongest empirical support,” according to a 2011 paper by Columbia University Teachers College professor emerita Dolores Perin. (The Hechinger Report is an independent unit of Teachers College.)

Perin’s paper echoed the results of a 2006 study of math in CTE involving 131 CTE high school teachers and almost 3,000 students. Students in the study who were taught math through an applied approach performed significantly better on two of three standardized tests than those taught math in a more traditional way. (The applied math students also performed better on the third test, though the results didn’t reach the statistical significance threshold.)

So far, there haven’t been systematic studies of math in CTE at the college level, said James Stone, director of the National Research Center for Career and Technical Education at the Southern Regional Education Board, who ran the 2006 study.

Stone explained how math in context works. Students start with a practical problem and learn a math principle for solving it. Next, they use the principle to solve a similar practical problem, to see that it applies generally. Finally, they apply the principle on paper, in say, a standardized test.

“I like to say math is just like a wrench: It’s another tool in the toolbox to solve a workplace problem,” said Stone. “People learn almost anything better in context because then it has meaning.”

Linn-Benton dean Steve Schilling offers an example. Carpenters use a well-known 3-4-5 rule to get a square corner — lay out two boards at a square angle and mark one board at 3 feet and the other at 4 feet. Now a straight line joining the two marks should measure exactly 5 feet—if it doesn’t, the boards are out of square.

The rule is based on the Pythagorean theorem, a method for calculating the lengths of a right triangle’s sides: a² + b² = c². When explaining to students why the theorem describes the rule, the instructor uses math terms — “adjacent side,” “opposite side,” “hypotenuse” — that they’ll need to use on a math test, said Schilling. When using practical skills like the 3-4-5 rule on a project, “at first, they don’t even realize they’re doing math,” he said.

Related: Federal relief money boosted community colleges, but now it’s going away

Oregon appears to be one of the few places where this approach is spreading, if slowly.

Three hours south of Linn-Benton, Doug Gardner, an instructor in the Rogue Community College math department, had long struggled with a persistent question from students: “Why do we need to know this?” The answer couldn’t just be that they needed it for their next, higher-level math class, said Gardner, now the department’s chair. “It became my life’s work to have an answer to that question.”

Meanwhile, Algebra I was a huge barrier for many Rogue students. About a third of those taking the course or a lower-level math course failed or withdrew. That meant they had to retake the class and likely stay another term to graduate; since many were older students with families and obligations, hundreds dropped out, school administrators said.

For those who stayed, lack of math knowledge hurt their job skills. Pipe fitters, for example, are among the higher-paid welders, said welding department chair Todd Giesbrecht, but they need a solid understanding of the math involved. “Whether they’re making elbows, whether they’re making dump truck bodies, they’re installing steam pipe, all of those things involve math,” he said.

So, in 2010, Gardner applied for and got a National Science Foundation grant to create two new applied algebra courses. Instead of abstract formulas, students would learn practical ones: how to calculate the volume of a wheelbarrow of gravel and the number of wheelbarrows needed to cover an area, or how much a beam of a certain size and type will bend under a certain load.

Since then, the pass rate in the applied algebra class has averaged 73 percent while that of the traditional course has continued to hover around 59 percent, according to Gardner. Even modest gains like that are hard to achieve, said Navarro Chandler, a dean at the college. “Any move over 2 percent, we call that a win,” he said.

One day in May, math professor Kathleen Foster was teaching applied algebra in a sun-drenched classroom on Rogue’s wooded campus and launched into a lesson about the Pythagorean theorem and why it’s an essential tool for building home interiors and steel structures.

She presented the formula, then jumped to illustrated exercises: What’s the right length for diagonal braces in a lookout tower to ensure that the structure will hold? What length does the diagonal top plate for a stair wall need to be to ensure that the wall’s corners are perfectly square?

James Butler-Kyniston, 30, who is pursuing a degree as a machinist, said that the exercises covered in Foster’s class are directly applicable to his future career. One exercise had them calculate how large a metal sheet you would need to manufacture a certain number of parts at one time, a skill he’s used in the lab. “Algebraic formulas apply to a lot of things, but since you don’t have any examples to tie them to, you end up thinking they’re useless,” he said.

Related: Proof Points: Shop class sometimes boosts college going, Massachusetts study finds

Unlike at Linn-Benton, students at Rogue in any degree field can take this course, so some of the applied examples don’t work for everyone. Butler-Kyniston said he thinks applied math works better if it’s tailored to a specific set of majors.

Still, Foster’s class could rescue the college plans of at least one student. Kayla LeMaster, 41, is on her second try at a two-year degree. She had to drop out in 2012 after getting injured in a house fire. She’s going for a degree that will let her transfer to the University of Oregon to major in psychology; she hopes to eventually work as a school counselor or in some other job supporting kids.

But her graduation from Rogue hangs by a thread because she needs a math credit. She struggled in the traditional algebra class and had to withdraw, and the same happened in a statistics course. Applied algebra is her last chance. “When you add the alphabet to math, it doesn’t make sense,” she said. By contrast, in the examples in Foster’s class, “you get into that work mode, a job site somewhere, and you can see the problem in your head.” She got an A on her first test. “I’m getting it,” she said.

Gardner worries about the consequences of the traditional abstract approach to teaching math. When he was in college, “nobody ever showed me one formula that calculated anything really interesting,” he said. “I just think we’re doing a terrible job. Applied math is so fun.”

Oregon’s leaders appear to see merit in teaching math in context. In 2021, state legislators passed a law requiring all four-year colleges to accept an applied math community-college course called Math in Society as satisfying the math requirement for a four-year degree. In that course, instead of studying theoretical algebra, students learn how to use probability and statistics to interpret the results in scientific papers and how political rules like apportionment and gerrymandering affect elections, said Kathy Smith, a math professor at Central Oregon Community College.

“If I had my way, this is how algebra would be taught to every student, the applied version,” said Gardner. “And then if a student says, ‘This is great, but I want to go further,’ then you sign up for the theoretical version.”

At the level of individual schools, lack of money and time constrain the spread of applied math. Stone’s team works with high schools around the country to design contextual math courses for career and technical students. They tried to work with a few community colleges, but their CTE faculty, many of whom are part-timers on contract, didn’t have time to partner with their math departments to come up with a new curriculum, a yearlong process, Stone said.

Linn-Benton was able to invest the time and money because its math department was big enough to take on the task, said Avery. And both Linn-Benton and Rogue may be outliers because they have math faculty with technical backgrounds: Lopez worked as a carpenter and sheriff’s deputy and served three tours as a machine gunner in Iraq, and Gardner was a construction contractor who still designs houses. “I have up to 16 house plans in the works during construction season,” he said.

Back in Lopez’s class, on a sunny Wednesday, students are done calculating where their ladder rungs should go and now must mark them on the wall. One team struggles. “I don’t understand any of this,” says Keith Perkins, 40, who’s going for a welding degree and wants to get into the local pipe fitters union.

“I know, but you’re not doing the steps in the right order,” says Lopez. “Walk me through it. Tell me what you did, starting with step 1.”

As teams finish up, Lopez inspects their work. “That’s one thirty-second shy. But I wouldn’t worry too much about it,” he tells one group. “OSHA’s not going to knock you down for that.”

Three teams pass, two fail — but this is the place to make mistakes, not out on the job, Lopez tells them.

“This stuff is hard,” said Perkins. “I hated math in school. Still hate it. But we use it every day.”

This story about math in CTE courses was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for our higher education newsletter. Listen to our higher education podcast.

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ALBUQUERQUE, N.M. — As their teacher pounded his drums, belting the lyrics to the Native folk rock song “NDN Kars,” middle schoolers Eli, Izzy and Manin rehearsed new guitar chords for an upcoming performance.

“I got a sticker that says ‘Indian Power,’” teacher Luke Cordova sang. “I stuck it on my bumper. That’s what holds my car together.”

Inside a neighboring greenhouse, a group of school staff and volunteers prepared to harvest herbs and vegetables for students to use in medicinal teas and recipes during science lessons on local ecology. Meanwhile, in a 19th century schoolhouse next door, eighth graders in a Native literature class debated the consequences of racism on college campuses. “Remember,” teacher Morgan Barraza (Akimel O’odham, Kawaika, Apache, Thai) told them, “power is not all with the decision makers. You as a community have power, too.”

Once the site of an Indian boarding school, where the federal government attempted to strip children of their tribal identity, the Native American Community Academy now offers the opposite: a public education designed to affirm and draw from each student’s traditional culture and language.

The charter school, NACA, opened its doors in 2006. Today, it enrolls roughly 500 students from 60 different tribes in grades K-12, bolstering their Indigenous heritage with land-based lessons and language courses built into a college preparatory model. High schoolers at NACA graduate at much higher rates and tend to outperform their peers in Albuquerque Public Schools — which authorizes the charter — and throughout New Mexico. Over the past decade, NACA’s academic track record and reputation with families and tribal leaders has spurred the creation of a network of schools designed to overhaul education for Native students across the American West.

At 13 campuses in five states, the NACA Inspired Schools Network supports tribal communities that have found little support in traditional K-12 systems and want academic alternatives that reflect their hopes and expectations for the next generation. Each school approaches that mission very differently, and with varying results. Some have struggled to keep their doors open, testing the Albuquerque-based network’s ability to sustain its success beyond the flagship school. Still, network leaders plan to continue expanding and hope to present the NACA model as a way to grant Indigenous families the self-determination and sovereignty that has been denied to them for generations.

“In 150 years, we moved from a foreign, abusive, violent structure to now, where maybe our communities have something to say about where education is going,” said Anpao Duta Flying Earth (Lakota, Dakota, Ojibwe, Akimel O’odham), the network’s executive director. “We’re leading these schools. We’re in the classrooms. It’s not just maintaining status quo. It’s how we’re pushing the edge of what’s possible.”

Related: 3 Native American women head to college in the pandemic. Will they get a sophomore year?

NACA was born out of an urgent need to reimagine education for Indigenous youth: In 2005, 

three quarters of Native American students graduated on time in the Albuquerque school district, compared to 87 percent of all students, according to state data. Only about 1 in 4 students identifying as American Indian tested proficient in math, while proficiency rates in reading and science hovered closer to 40 percent. A string of suicides in the city’s Native communities, especially among youth, shocked educators.

In response, Native administrators within the district started meeting with families, college graduates and tribal leaders to discuss what a better education for Native students might look like. More than 200 people weighed in, often sharing their poor experiences in traditional schools, such as pervasively low expectations and a lack of cultural awareness among teachers. Community members prioritized three things in their dream school for Native youth: secure cultural identities, college preparation and holistic wellness.

Those conversations prompted Albuquerque Public Schools to authorize NACA as its first charter. Today, courses at all grade levels include Indigenous history, numeracy, land-based science and language classes in Keres, Lakota, Navajo, Tiwa, Spanish and Zuni. About two-thirds of the school’s teachers are Native American, with many alumni now leading classrooms. 

NACA requires students to take at least two college-level courses and earn internship credit. Last year, nearly 80 percent of graduates enrolled in college, up from 65 percent for the class of 2022. The school also tracks college completion rates, with 59 percent of the class of 2012 finishing within six years. Since then, the numbers have slipped to the single digits, with just 5 percent of the class of 2016 finishing within six years, according to a data analysis from the charter school network. (School officials said the decline is due to incomplete data.)

Younger students attend the K-8 campus on the former boarding school site, while the high school is located in a gleaming new tower nearby at the Central New Mexico College.

During a lunch break, 11th graders Joshua, a Navajo Nation citizen, and Tyshawn, from the Laguna Pueblo, volleyed a badminton birdie under the tower’s shadow. Both are recent transfers to NACA — Tyshawn from a private Catholic school and Joshua from a traditional public high school.

“There was nothing like this. No language class, nothing,” Joshua said of his previous school. Discussions of tribal culture were limited to a few isolated craft projects during a history unit and inaccurate portrayals of Indians at the “First Thanksgiving,” he recalled.

“Yeah, not at my school,” Tyshawn agreed, chuckling. “You had to learn that experience yourself.”

“I was the ‘only’ a lot,” added Joshua, referring to his Native identity. “We fill an entire school here.”

Related: Schools bar Native students from wearing traditional regalia at graduation

It’s only recently that the U.S. has fully acknowledged its long history of using education as a weapon against tribes. An investigative report released by the U.S. Department of the Interior in May 2022 identified more than 400 Indian boarding schools, across dozens of states and former territories, as part of a system that directly targeted children “in the pursuit of a policy of cultural assimilation.”

The investigation found evidence of at least 53 burial sites for children. Schools renamed students with English names, cut their hair and punished them — through solitary confinement, flogging and withholding food — for speaking Native languages or practicing their traditional religions. Manual labor was a predominant part of school curricula, but often left graduates with few employable skills.

“We continue to see the evidence of this attempt to forcibly assimilate Indigenous people in the disparities that communities face,” U.S. Secretary of the Interior Deb Haaland, a citizen of the Laguna Pueblo in New Mexico, said at the time of the report’s release.

According to a 2019 national survey, close to half of American Indian and Alaska Native students reported knowing “nothing” or only “a little” about their cultural heritage. A majority — between 83 percent and 91 percent — of fourth and eighth graders in the survey said they could not speak or read in their heritage language, or reported knowing a few words or phrases at most. Other studies have found significantly higher child poverty rates, lower graduation rates and lower performance on standardized exams for Native students.

As the state of education for these children continued to languish, the U.S. Department of Education in 2018 pushed for the expansion of high-quality charter schools meant to serve Native communities, among other groups it deemed educationally disadvantaged and underserved by the existing charter sector. It later published, in partnership with the National Indian Education Association, a guide to help founders and supporters of new Native American charter schools.

“The word just hasn’t gotten out about the ability to do this,” said Todd Ziebarth, a senior vice president of state advocacy and support at the National Alliance for Public Charter Schools.

In its tally of about 4,300 charter schools with at least one Native American student, the Alliance counts at least 16 schools specifically dedicated to Native American cultural affirmation. Only a handful offer classes taught in an Indigenous language.

Related: College tuition breaks for Indigenous students spread, but some tribes are left out

In one of those schools, about 90 miles northeast of Albuquerque, a dozen students walked into the front office of Kha’p’o Community School with stacks of books teetering in their hands.

They’d just cleaned the shelves at the Santa Clara Pueblo library, grabbing their favorite titles in Tewa, one of the languages spoken by the Pueblo people in New Mexico. The third graders juggled the books as they traversed a courtyard ringed by adobe houses-turned-classrooms, with teacher Paul Chavarria trailing them.

Back in their classroom, Chavarria, a first-year Tewa language teacher at Kha’p’o, commenced a lesson on the language. It’s a traditionally oral language, and speakers frown on any written form. Chavarria, though, scribbled a rough translation for “stone,” “trees” and “plants” on a whiteboard to help the students learn their heritage language.

For decades, the school (then known as Santa Clara Day School) was run by the U.S. Bureau of Indian Education, or BIE, which today operates 183 schools on 64 reservations. But in 2014, after the government-appointed principal barred a Tewa teacher from campus, tribal leaders took control of the school from the federal government, said Porter Swentzell, the school’s executive director and an enrolled member of the Pueblo. That same year, the school officially joined the NACA-inspired network as a K-6 charter school with a dual language immersion model. Today, it enrolls about 90 students. 

“In our hands, language is a sacred obligation. Our job is bigger than math or ELA,” Swentzell said.. “Our story doesn’t begin with us, and it certainly won’t end with us.”

Swentzell, who served on the school board when it shifted to tribal control, recalled a rocky start for Kha’p’o. The BIE withdrew the bulk of its support, he said. Teachers and staff had to reapply for their jobs, which no longer offered salaries at the federal level. In terms of school policies, technology systems, contracts and more, “we were starting from scratch,” Swentzell said.

Then, during the pandemic, Kha’p’o’s principal left, and enrollment plummeted from 120 students to 73, as multigenerational households kept their children at home. Half of the school’s teaching positions were unfilled, largely because of its remote location and lower salaries, according to Swentzell, who took over as head of school in 2022. 

Kha’p’o wasn’t the only school in the network to lose its leader during the pandemic. And each has since struggled to get academics and operations back on track, said Flying Earth, head of the charter network. The network has tried to help: In 2022, it created a fellowship program to nurture new leaders like Swentzell, a former professor at the Institute for American Indian Arts in Santa Fe. The fellows meet regularly on Zoom and gather in person once a year, along with a lead teacher or executive team member who could potentially become principal one day.

Related: How one Minneapolis university more than doubled its Native student graduation rate

Indeed, as the network has grown, it has confronted the difficulty of recreating the “NACA sauce” — as the flagship’s principal called it — in each new tribal community.

Six Directions Indigenous School opened the same year as Kha’p’o, in the western region of the state near the Navajo Nation and Zuni Reservation. Data from the New Mexico Public Education Department shows that 1 in 5 students at the charter school tested proficient in science. About 1 in 10 students perform on grade level in math, with a slightly better rate in reading, at 14 percent. 

Aside from academic problems, students at Six Directions have protested what they view as the school’s failure to fulfill its charter of serving Native youth. “It’s right there on all the signs: ‘This is an Indigenous school,’” said Caleb, a 14-year-old Hopi freshman. “This is supposed to be an opportunity for us to know our culture. These teachers weren’t doing that.”

At the start of the school year, in August, Caleb and other high schoolers at the K-12 campus staged an impromptu walkout to protest what they described as a revolving door of teachers hired from overseas and ongoing vacancies for language and culture classes. As of late fall, the entire school had just one core teacher, in science.

The walkout happened during Rebecca Niiha’s first week on the job as new head administrator of Six Directions. A former teacher who has worked on the Zuni and Navajo reservations, Niiha, who is Hopi, had admired Six Directions from afar. But she described finding its academic achievement and school climate as “degenerative” on day one.

After the walkout, two more teachers quit. Then the school’s current landlord announced it planned to sell the property, leaving Niiha unsure if she’d have to find a new location. In January, Six Directions received a warning from the state about its poor performance. 

The network’s support of struggling schools, like Six Directions, can only go so far. It does not directly authorize any charter and has limited ability to hold the schools accountable. 

Still, the network dispatches experts on finance, community engagement, student experience, curriculum and professional development. On a weekday last year, a team from the network met with Niiha to discuss options for the school’s location, training for teachers and an upcoming charter reauthorization. The network also recently partnered with AmeriCorps to place Indigenous educators in schools to offer classroom support, tutoring and mentoring, and has worked with individual tribes to certify teachers in heritage languages.

“Once a school’s created, we’re in it for the long haul together,” said Ben Calabaza, Kewa – Santa Domingo Pueblo and a spokesperson for the charter network.

Ultimately, the network wants to avoid being forced to close another of its member schools, as happened last year when Denver Public Schools shuttered the American Indian Academy. That school opened in fall 2020, at the height of the pandemic, and suffered from low enrollment and poor finances, according to the charter’s board of directors.

Flying Earth acknowledged the challenges of running a charter network that spans schools in several states. He said the charter model isn’t, on its own, a solution for poor educational outcomes for Native students. But he added that the NACA-inspired network has done what it promised: offered tribal communities a chance to have agency in building a dream school for their Native youth.

“How do we use the structures of education today, including charter schools, to lift up the genius that’s always been there, since time immemorial?” Flying Earth said, referring to the “genius” of traditional ways of knowing in Native communities. “The namesake school of NACA serves as an example of how one community did it.”

Many students, long after graduation, continue to contribute to that community. Some have returned as teachers and school staff. Emmet Yepa Jr., Jemez Pueblo, commuted two hours each way to attend NACA in downtown Albuquerque when he was in high school. Now, at 30, he sings every year at the school’s annual feast day — a traditional celebration among New Mexico pueblos.

“What attracted me to NACA was just the community,” he said. “They really emphasize your culture and holistic wellbeing.”

Yepa earned a Grammy Award as a child and later graduated from NACA as part of its inaugural class in 2012. From there, he went on to the University of New Mexico and now works for an Albuquerque nonprofit that includes land-based and outdoor education in civic leadership programs for young people.

Based on his positive experience, his siblings enrolled at NACA. His younger sister graduated  last year and now attends UNM, while his younger brother is a sixth grader.

“It’s hard to get into NACA now because there’s a waiting list,” Yepa said. “Thankfully he got a spot.”

This story about NACA schools was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter.

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Before she got to the math in her lesson on linear equations last fall, Sydney Kealanahele asked her class of eighth graders on Oahu why kalo, or taro root, is so important in Hawaii.* What do you know about kalo, she asked them. Have you ever picked it?

A boy who had never spoken in class, and never seemed even slightly interested in math, raised his hand.

“He said, ‘I pick kalo with my grandma. She has a farm,’” Kealanahele recalled. “He was excited to tell us about that.”

Class discussion got animated. Everybody knew about poi, the creamy staple Hawaiian food made from mashed taro. Others had even noticed that there were fewer taro farms on Oahu.

That’s when Kealanahele guided the conversation to the whiteboard, plotting data on pounds of taro produced over time on a graph, which created a perfect descending line. The class talked about why there is less taro production, which led to a discussion about the shortage of farm labor.

Kealanahele had taught eighth-grade math for six years at a campus of the Kamehameha Schools, but this was the first time she had started a lesson with a conversation about farming. The idea came from professional development she’d just completed, in ethnomathematics, an approach that connects math to culture by embedding math in a story about something relevant to students’ lives.

Ethnomathematics isn’t new, but until recently it was limited to a niche area of educational and anthropological research on how different cultures use math. Over the past couple of decades, it has evolved into one of several efforts to create more engaging and inclusive math classrooms, particularly for Black, Hispanic and Indigenous students, who tend to score lower on federal tests than their Asian and white peers. Ethnomathematics advocates say that persistent achievement gaps are in part a result of overly abstract math instruction that’s disconnected from student experience, and that there’s an urgent need for new approaches that recognize mathematical knowledge as it’s practiced outside of textbooks.

Many Black and Brown students don’t feel comfortable in math classes, said Shelly Jones, professor of math education at Central Connecticut State University. She said those classes tend to be “competitive” and that teachers “hone in on what Black and Brown students don’t know as opposed to honoring what they do know.” She added:  “We are trying to pull in students who have not traditionally felt they belonged in math spaces.”

That said, research on the impact of ethnomathematics is limited, and its practice is largely confined to individual classrooms — like Kealanehele’s — where the teacher has sought out the approach. And teachers who incorporate ethnomathematics without the right support and instructional tools risk stumbling into a cultural minefield, experts say. Most teachers in U.S. classrooms are white. If one of those white teachers decides their Hispanic students should learn base-20 Mayan numbers, and their students ask why, the teacher will have to come up with an answer, said Ron Eglash, a professor in the University of Michigan’s School of Information.

“Telling kids, ‘Because it’s your heritage,’ sounds really awkward from a white teacher,” Eglash said.

But experts say that high-quality ethnomathematics lessons boost student confidence and engagement when used by teachers (of any race) who have been trained and who allow students the time to explore the material on their own and through discussion.

Ethnomathematics falls under the same umbrella as culturally responsive math instruction. Experts say that teaching math this way requires teachers to get to know their students and create a learning environment where students can connect to math concepts. It involves developing lessons that reveal the math in everyday activities, like skateboarding, braiding and weaving. It can also include exploring the math involved in cultural practices, like beading.

“A lot of this work is about removing barriers or perceptions from a marginalized population that math is something the Greeks created and is imposed on me,” said Mark Ellis, a professor of education at California State University, Fullerton. He said that culturally responsive instruction takes other measures into account, besides academic outcomes, when determining impact. These include students’ attitude about math, sense of belonging in math classes and engagement in math discourses.

Related: Eliminating advanced math ‘tracks’ often prompts outrage. Some districts buck the trend

Traditional math instruction, Ellis said, is treated as if math were acultural, even though, as we know it in the U.S., math descended from the computational traditions of many places, including Mesopotamia (360-degree circles), ancient Greece (geometry and trigonometry), India (decimal notation, the concept of zero) and China (negative numbers). If these mathematical traditions are taught, Ellis and others ask, then why not Hawaiian calculations for slope, sub-Saharan fractal geometry and Mayan counting systems?

Eglash argues that ethnomathematics lessons aren’t just for students from the culture that the lessons draw from. It’s important that students explore math concepts from all cultures, including their own, he said.

Ethnomathematics, a term coined in the 1970s by Brazilian mathematician Ubiratan D’Ambrosio, first appeared in the U.S. about 25 years ago. That’s when Eglash and his wife, University of Michigan design professor Audrey Bennett, developed a suite of teaching modules by which students learn the history or context of a practice — braiding hair into cornrows, for example — and then use algebra, geometry and trigonometry to create their own cornrow designs with software.

Eglash and Bennett designed the teaching tools with the idea that students can use a module to create their work, which can mean mixing cultures. A Puerto Rican student used Eglash’s module about Native American beading to create a Puerto Rican flag simulation.

In 2009, Richmond City Public Schools asked Eglash and Bennett to teach a module called Cornrow Curves to a class of Black 10th graders. Eglash asked the class where cornrows came from. Their answer: “Brooklyn!” That led to discussion about the African origins of cornrows — where they indicated marriage status, religious affiliation and other social markers — and on through cornrows’ history during the Middle Passage, Civil Rights, hip-hop and Afrofuturism.

Only then did the students begin doing math, designing their own cornrows, noticing how the plaits get closer together or further apart depending on the values students enter in a simulation. One student created a design for straight-line cornrows by visually estimating how far to space them apart. In her presentation to class, Eglash recalled, she said that “there are 12 spaces between the braids on one side, which covers 90 degrees, so the braids are positioned every 7.5 degrees because 90/12 = 7.5.”

The Cornrow Curves module and other lessons like it have now been adopted by districts in 25 states. The Los Angeles Unified School District, for example, began offering a culturally responsive computer science curriculum in 2008 that incorporates ethnomathematics lessons that Eglash and Bennett developed. Some evidence indicates that this course helped boost student participation in computer science: An external evaluation found that enrollment in the classes rose by nearly 800 percent from 2009 to 2014.

In 2012, Chicago Public Schools adopted the same curriculum for an introduction to computer science course and invested in significant professional development for teachers. In 2016, the course became a graduation requirement for all Chicago high school students, and 250 teachers are trained each year on the curriculum.

An outside analysis of the Chicago program showed that students who took the course before taking AP computer science were 3.5 times more likely to pass the AP computer science exam than those who only took the AP course. A separate study in Chicago and Wisconsin showed that where the course was offered racial and gender achievement divides disappeared and that students were more likely to take another computer science class.

Related: Data science under fire: What math do high schoolers really need?

Keily Hernandez, 15, a first-year student at Chicago’s George Westinghouse College Prep High School, was happy to see the computer science course on her schedule this year, because she plans to major in computer science in college. At first, she found the cornrows module challenging — getting the designs to look the way she wanted them to look was difficult — but it was also fun, she said.

The class is collaborative, she said, and students often turn to each other or to the internet for ideas and help. Hernandez said that taking the class has relieved her doubts that she can be a computer scientist.

“The class made me reassured,” she said. “Math isn’t something that you just know, the same way that computer science isn’t something that you just know. You get better at it the more you do it.”

It’s students like Hernandez that Linda Furuto wanted to attract when she took the job as head of the math and science subdivision at the University of Hawaii West Oahu in 2007. At the time, student enrollment was so low that the school offered just two math courses. Furuto, who had grown up on Oahu and received her Ph.D. in math education from the University of California, Los Angeles, recalled thinking, “This isn’t working. We need to implement ethnomathematics here.”

Over the next six years, she began to integrate ethnomathematics into coursework, and student interest grew. By 2013, the university offered more than 20 math classes.

“Students would say things like, ‘I hated math. I felt no connection to it. But now I see that math is my culture and because of that I want to be a secondary math teacher,’” Furuto said. “Just knowing that the life of a student has in some way, shape or form been transformed speaks volumes.”

In 2018,  by then a professor of mathematics education at the University of Hawaii Manoa, Furuto established the world’s first ethnomathematics graduate certificate and master’s degree program.* So far, about 300 teachers have participated in the online program; about half are from Hawaii.

While teachers in Chicago get ongoing professional development in cohorts both before and while they teach the district’s ethnomathematics-based computer science course, educators who complete the University of Hawaii program are highly likely to be the only teacher at their school with this niche training.

Sydney Kealanahele, the teacher on Oahu, said that as inspired as she was by the ethnomathematics program, she doesn’t have time to teach using the method more than twice every three months.

“To create a really good lesson that feels authentic to me, and not just thrown together,” she said, “it takes time to do the research.”

For a teacher who doesn’t have colleagues in their school using the same approach, it can be hard to fit in something new like ethnomathematics, said Janel Marr, a math resource teacher in Oahu’s Windward School District. Marr was one of the first teachers to participate in the ethnomathematics graduate program, as an eighth-grade math teacher. Today she teaches in the graduate program.

“When you go back to the classroom, there are so many other things from all sides, from administration and curriculum to state tests,” she said. “It starts to get overwhelming. It’s not being implemented as much as we in the program would want it to be.”

Related: How one district diversified its advanced math classes — without the controversy

Ideally, said Eglash, ethnomathematics content should be related to real-world situations, even if that involves exploring painful periods of history. Where possible, content should connect with art, history, sports and math to provide multiple ways for students to interact. This is critical, he said, to address power dynamics and “identity barriers” in the classroom, like the race of the teacher. When teachers let students explore content individually and through group discussion, students gain control over their own learning.

“The teacher finds a way to use the tool that is authentic — which is something the kids pick up on and respect, even for white folks,” he said. “It’s when you are trying to be something you are not that teaching becomes awkward.”

Doing ethnomathematics right can also engage teachers, Marr said. She had been teaching eighth-grade math at Kailua Intermediate School for 13 years when she hit a wall. Her students would ask why they had to learn math, she said, and she didn’t have an answer. She was looking for inspiration when she heard about the University of Hawaii ethnomathematics program.

“My students would learn to work with the numbers and everything, but it wasn’t like they were making a connection of why there is slope,” Marr said.

After earning her master’s, Marr had the idea to approach linear equations in a new way. She showed her students a photo of a mountain with a long, bare line down its lush, forested side and asked if anyone knew what they were looking at. Most students didn’t.

She wrote a word on the whiteboard: holua. The path, students learned from research they did in class, was made of gravel pounded into lava rocks, and it ran down the side of the Hualālai Volcano on the east side of Hawaii. Elite members of ancient Hawaiian communities sledded down mountainside paths like this one as part of the extreme sport known as holua.

“We talked about those pictures and talked about, well what would the slope be? How fast might they be going? Because slope is really related to the rate of speed,” she said. “Math isn’t just theoretical. It’s having an experience of being part of the place.”

*Correction: This story has been updated with the correct spelling of Sydney Kealanahele’s name, and to clarify Linda Furuto’s role when she started the ethnomathematics program.

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Our country is facing a severe shortage of nurses, with many U.S. hospitals struggling to meet demands for patient care. By next year, we are expected to face a shortage of up to 450,000 nurses. Allied health professionals such as phlebotomists, pharmacy technicians and medical assistants are also in extremely high demand. 

Unless new policies are created to help attract and train new talent, we will never have enough healthcare professionals to fill the gaps in the workforce, and patient care will ultimately suffer. I believe it is critical for policymakers to create new pipelines for healthcare jobs — starting in high school. 

Many factors contribute to the growing healthcare workforce shortage, from policy and training barriers to high turnover and burnout. One of the most pressing challenges we have today is in building high school students’ awareness of and interest in the healthcare field, specifically in the many available nursing and allied health positions.  

Related: When nurses are needed most, nursing programs aren’t keeping up with demand

As a nurse educator and the mother of a high schooler, I know many young people who have high aspirations but aren’t familiar with the dozens of different paths to a rewarding career in healthcare.  

Surveys show that 58 percent of high school students are interested in jobs that require specific skills, like nursing. But many graduates feel unsure about what to study in college or what career path to pick. And some 30 percent are not following a planned career or educational path at all. 

This gap presents an opportunity for us to build students’ knowledge of and awareness about healthcare while they’re still in high school. That could mean sponsoring health education classes or hosting nurses to speak at job fairs. 

It could mean encouraging students to participate in educational programs to ensure they are academically prepared for the rigor of nursing school prior to their enrollment, or providing healthcare career-focused field trips so they can get a real sense of the many different roles that nurses play.  

Job-shadowing opportunities and simulation labs at local hospitals, healthcare facilities and colleges could also provide students with visual, in-person experiences that expose them to the array of opportunities in the field. 

There is often limited understanding of what it means to build a career in nursing or allied health, fields that include a rich tapestry of different roles and healthcare settings. For example, careers in nursing can range from being a certified nursing assistant in a nursing home to a registered nurse in an emergency room to a Ph.D. nursing educator in a classroom.  

For allied health, a career could mean being a medical coder in a doctor’s office, an EKG technician in a hospital or performing a variety of other roles.  

In short, there are many fulfilling ways to earn a living while bettering our communities — and not all of those paths require going to medical school or completing a four-year program.  

Quicker points of entry to the field, such as through training programs and associate degrees, are just as important for students beginning their healthcare professional journeys. 

Related: How one college is tackling the rural nursing shortage

By partnering with local hospitals, health systems, medical groups and even higher education facilities that offer degrees in healthcare, high school faculty and students can help develop a greater understanding of and interest in nursing as a profession.  

In some states, efforts are already underway. Maryland, Missouri and Florida — among other states — have invested in the future of the nursing workforce by providing grants that support nursing programs through recruitment and retention and enhance existing educational programs. In North Carolina, my local school systems have partnered with a grant-funded program to help high schoolers get credentialed and then intern at hospitals in their senior year.   

With the right support and investments, policymakers and schools can increase awareness of the critical role nursing plays in delivering quality, patient-focused care to our communities across our country.  

By starting early, we can help turn the tide on the nursing and allied health professional shortage and build a robust high school-to-healthcare-worker pipeline to ensure that all patients have access to high-quality care. 

Jade Tate, MSN, RN, CNE, is a NCLEX services manager at ATI Nursing Education. She is based in North Carolina. 

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ASTON, Pa.— In Jodie Murphy’s kindergarten class, math lessons go beyond the basics of counting and recognizing numbers.

On a recent morning, the children used plastic red and yellow dots for a counting exercise: One student tossed the coin-sized dots onto a cookie sheet while another hid her eyes. The second student then opened her eyes, counted up the dots and picked the corresponding number from a stack of cards.

The dots showed up again a few minutes later in a more complex task. Murphy set a two-minute timer, and students counted as many dot arrays as they could, adding or taking away dots to match a corresponding written number. Four dots next to a printed number 6, for example, meant that students had to draw in two extra dots — an important precursor to learning addition.

Kindergarten may be math’s most important year — it lays the groundwork for understanding the relationship between number and quantity and helps develop “number sense,” or how numbers relate to each other, experts and researchers say.

But too often teachers spend that crucial year reinforcing basic information students may already know. Research shows that many kindergarteners learn early on how to count and recognize basic shapes — two areas that make up the majority of kindergarten math content. Though basic math content is crucial for students who begin school with little math knowledge, a growing body of research argues more comprehensive kindergarten math instruction that moves beyond counting could help more students become successful in math later on.

Because so many students nationally are struggling in math — a longstanding challenge made worse by remote schooling during the pandemic — experts and educators say more emphasis needs to be put on foundational, early childhood math. But for a variety of reasons, kindergarten often misses the mark: Math takes a backseat to literacy, teachers are often unprepared to teach it, and appropriate curriculum, if it exists at all, can be scattershot, overly repetitive — or both.

Manipulating numbers in different ways, part of a supplemental math curriculum for Murphy’s whole class at Hilltop Elementary in this suburb of Philadelphia, is an attempt to address those problems. In an effort to improve math achievement district-wide, all elementary students in the Chichester School District get an extra 30-minute daily dose of math. In kindergarten, the extra time is spent on foundational skills like understanding numbers and quantity, but also the basics of addition and subtraction, said Diana Hanobeck, the district’s director of curriculum and instruction.

Related: You probably don’t have your preschooler thinking about math enough

Chichester district leaders say implementing the intervention, called SpringMath, along with other steps that include hiring a math specialist for each school, has brought urgent attention to students’ math achievement by bringing more students to mastery — and a lot of that has to do with how much students are learning in kindergarten. Student math achievement, which dropped to a low of 13.5 percent of students proficient or advanced during the pandemic, has more than doubled across grades since the intervention began, although still below the state average. Last spring, 47 percent of the district’s fourth graders were proficient or advanced in math on the Pennsylvania System of School Assessment test.

“The intervention is very targeted by skill and gives teachers data for each student,” said Hanobeck. “We are seeing it close gaps for students, and they are more able to access elementary school math.”

Murphy, the kindergarten teacher, said that while some students arrive at school able to do “rote counting,” others arrive with no prior knowledge or a very limited understanding of numbers and counting. The interventions have improved all students’ accuracy and fluency in more complex tasks, such as being able to count up or down from a number like 16 or 20, and adding and subtracting numbers up to 5.

“It used to take all year for some students to count on from different starting points, that’s actually really hard for kids to do,” Murphy said. “Students are meeting their goals far faster now. We are moving on, but also moving deeper.”

That deep thought is important, even in the earliest grades. Kindergarten math proficiency is especially predictive of future academic success in all subjects including reading, research has shown. In one study, students’ number competence in kindergarten — which includes the ability to understand number quantities, their relationships to each other, and the ability to join and separate sets of numbers, like 4 and 2 making 6 — presaged mathematical achievement in third grade, with greater number competence leading to higher math achievement.

It’s also the time when learning gaps between students are at their smallest, and it’s easier to put all students on equal footing. “Kindergarten is crucial,” said University of Oregon math education researcher Ben Clarke. “It’s well-documented in the research literature that gaps start early, grow over time and essentially become codified and very hard to remediate.”

But the math content commonly found in kindergarten — such as counting the days on a calendar — is often embedded within a curriculum “in which the teaching of mathematics is secondary to other learning goals,” according to a report from the National Academies of Science. “Learning experiences in which mathematics is a supplementary activity rather than the primary focus are less effective” in building student math skills than if math is the main goal, researchers wrote.

Related: Teachers conquering their math anxiety

The math students are taught in kindergarten often progresses no further than basic counting and shapes. In a 2013 study, researcher and University of Colorado Boulder associate professor Mimi Engel found that students who spent more time on the advanced concepts in kindergarten learned more math. Engel hypothesizes that exposure to more advanced content in kindergarten may help students in later grades when content grows more complex.

“We want some amount of repetition across grades in content,” Engel said. “There’s variation in kids’ skill sets when they start kindergarten, and, as a teacher, there are a number of reasons why you want to start with the basics, and scaffold instruction. But what I’m interested in is: when does repetition become redundancy?”

According to researcher Amanda VanDerHeyden, founder of SpringMath, breaking numbers apart and putting them back together and understanding how numbers relate to each other does more to help develop kindergarteners’ mathematical thinking than counting alone. Students should move from using concrete objects to model problems, to using representations of those objects and then to numbers in the abstract — like understanding that the number 3 is a symbol for three objects.

To improve students’ math skills, some schools and districts have recently upgraded the math curriculum and materials teachers use, so they are able to build increasingly complex skills in an organized, orderly way.

Kindergarteners in Hailey Lang’s classroom at Dr. William Burrus Elementary School in Hendersonville, Tennessee, were recently counting penguins — a digital whiteboard showed a photo of a mother penguin with seven fuzzy babies in tow.

“Can we make a math drawing about this picture? No details, you can just use little circles,” Lang said. Students drew one big circle and seven smaller circles on their papers to represent the penguins. Then they translated the circles into a number sentence: 1 (big circle) + 7 (small circles) = 8.

The lesson is new to students this year since they adopted the Eureka Math curriculum. It’s what Sumner County Superintendent Scott Langford calls “high-quality” instructional material, with lessons that move students beyond simply counting objects like penguins. Students look at penguins in a picture, translate them into representational circle drawings, then finally move on to their abstract number quantities.

Sumner County elementary coordinator Karen Medana said she appreciates the fact that the curriculum offers explicit guidance for teachers and builds on a sequence of skills.

One reason for redundancy in kindergarten math may be that classrooms lack cohesive materials that progress students through skills in an orderly way. A 2023 report from the Center for Education Market Dynamics showed that only 36 percent of elementary schools use high-quality instructional materials, as defined by EdReports, a nonprofit organization that evaluates curricula for rigor, coherence and usability. Eureka Math is one of several math programs that meet EdReports’ standards.

Related: How to boost math skills in the early grades

Often teachers are left to gather their own math materials outside the school’s curriculum. The Brookings Institution reports that large numbers of teachers use a district-approved curriculum as “one resource among many.” Nearly all teachers say they gather resources from the internet and sites like Teachers Pay Teachers — meaning what students learn varies widely, not only from district to district, but from classroom to classroom.

What students learn might not even be aligned from one grade to another. In a new, unpublished paper still in revision, researcher Engel found “notable inconsistencies” between pre-K and kindergarten classroom math content and how it is taught in New York City schools. Engel said results suggest that in many classrooms, kindergarten math might be poorly aligned with both pre-K and elementary school.

When teachers have access to well-aligned materials, students may learn more. At Marcus Hook Elementary, a Title I elementary school in the Chichester District, kindergarten teacher Danielle Adler’s students were deep into first grade addition, using numbers up to 12. They had already completed all the SpringMath kindergarten math skills in March, so she let them keep going.

“In the past we did focus more on counting, recognizing numbers and counting numbers,” Adler said, “But over the last three years I’ve seen the kids’ skills grow tremendously. Not only what they’re expected to do, but what they’re capable of doing has grown.”

What kindergarteners are expected to do at school has changed dramatically over the last 30 years, including more time spent on academic content. Adler and other kindergarten teachers agree that they hold higher expectations for today’s students, spend more time on teacher-directed instruction and substantially less time on “art, music, science and child-selected activities.”

Some worry that increasing time spent on academic subjects like math, and pushing kindergarten students beyond the basics of numbers and counting, will be viewed as unpleasant “work” that takes away from play-based learning and is just not appropriate for 5- and 6-year-olds, some of whom are still learning how to hold a pencil.

Engel said kindergarteners can be taught more advanced content and are ready to learn it. But it should be taught using practices shown to work for young children, including small group work, hands-on work with objects such as blocks that illustrate math concepts, and learning through play.

Related: How can you help your kids get better at math?

Mathematician John Mighton, the founder of the curriculum JUMP Math, said it’s a mistake to believe that evidence-based instructional practices must be laborious and dull to be effective. He has called on adults to think more like children to make more engaging math lessons.

“Children love repetition, exploring small variations on a theme and incrementally harder challenges much more than adults do,” he wrote — all practices supported by evidence to increase learning.

Simple lessons, when done well, can teach complex ideas and get children excited.

“People say kids don’t have the attention,” to learn more advanced concepts, he said, but he strongly believes that children have more math ability than adults give them credit for. Getting students working together, successfully tackling a series of challenges that build on each other, can create a kind of collective effervescence — a feeling of mutual energy and harmony that occurs when people work toward a common goal.

That energy overflowed in Adler’s classroom, for example, as students excitedly colored in graphs showing how many addition problems they got correct, and proudly showed off how the number correct had grown over time.

VanDerHeyden pointed out that, for young kids, much of a math intervention should look and feel like a game.

It’s often harder than it looks to advance kindergarten skills while keeping the fun — elementary teachers often say they have low confidence in their own abilities to do math or to teach it. Research suggests that teachers who are less confident in math might not pay enough attention to how students are learning, or even spend less time on math in class.

Teachers like Murphy have made some tweaks geared to engaging students. In class she calls SpringMath “math games,” and refers to timed fluency tests as “math races.” She even turned choosing a partner into a game, by spinning a wheel to see who students will get.

“We can do all these little things so they’re having fun while they’re learning,” Murphy said.

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Last April, an email went out to families in the Troy School District outside Detroit. Signed by unnamed “concerned Troy parents,” it said that a district proposal to end “basic” and “honors” math classes for sixth and seventh graders was part of a longer-term district plan to completely abolish honors classes in all of its schools.

Superintendent Richard Machesky and his team were stunned. The district was indeed proposing to merge separate sixth- and seventh-grade math tracks into what it said would be a single, rigorous pathway emphasizing pre-algebra skills. In eighth grade, students could opt for Eighth Grade Math or Algebra I. But the district had no plans for changes to other grades, much less to do away with high school honors classes.

Earlier that month, Machesky and a district team of curriculum specialists and math teachers had unveiled the plan during a series of meetings with parents of current and incoming middle schoolers. Parents had largely expressed support, said Machesky: “We thought we were hitting the mark.”

No matter. The email blast spurred opponents to show up at a board workshop and a town hall, and a petition demanding that the middle-school plan be scrapped got more than 3,000 signatures. At a packed board meeting that May, more than 40 people spoke, nearly all opposed to the plan, and the comments got personal. “Are you all on drugs?” parent Andrew Sosnoski asked the members.

It’s part of the skirmish over “detracking,” or eliminating the sorting of kids by perceived ability into separate math classes. Since the mid-1980s, some education experts have supported such moves, citing research showing that tracking primarily serves as a marker of race or class, as Black and Hispanic students, and those from lower-income families, are steered into lower-track classes at disproportionate rates. In the last 15 years, a handful of school districts around the country have eliminated some tracked math classes.

While there’s been ample research on tracking’s negative effects, studies of positive effects resulting from detracking are scant. In perhaps the only attempt to summarize the detracking literature, a 2009 summary of 15 studies from 1972 to 2006 concluded that detracking improved academic outcomes for lower-ability students, but had no effect on average and high-ability students.

Related: Data science under fire: What math do high schoolers really need?

Proposals to curtail tracking often draw fiery opposition, sometimes scuttling the efforts. The Portland school district in Oregon planned to compress two levels of middle school math into one starting in 2023, but after criticism, said the issue needed more study. Gov. Glenn Youngkin of Virginia, a Republican, won office in 2021 on an education platform that included protecting tracking, after an outcry over a state department of education plan that included language about “improving math equity,” which some interpreted as limiting tracking. The San Francisco Unified School District, which in 2014 detracked math through ninthgrade, recently announced that it’s testing the reintroduction of a tracked system, following a lawsuit from a group of parents who alleged that detracking hurt student achievement.

The pushback, often from parents of high-track students with the time and resources to attend school board meetings, is part of why tracking, especially in math, remains common. In a 2023 survey of middle-school principals by the Rand Corporation, 39 percent said their schools group students into separate classes based on achievement.

But some places have changed their math classes with minimal backlash, and also ensured course rigor and improved academic outcomes. That’s often because they moved slowly.

Evanston Township High School, in Illinois, started detracking in 2010, collapsing several levels in two freshman-year subjects — humanities and biology — into one.

Then, for six years, the school made no other changes. That allowed leaders to work out the kinks and look at the data to make sure there were no negative effects on achievement, said Pete Bavis, the district’s assistant superintendent for curriculum and instruction.

Teachers liked the mixed-ability classes and asked to expand them to other subjects, so in 2017 the school began detracking sophomore and junior English, Geometry and Algebra II.

At South Side Middle School and High School on Long Island, detracking went even slower, taking 17 years to fully roll out. The district started in 1989 with middle-school English and social studies, and progressed to high school math and chemistry by 2006.

The pace let parents see it wasn’t hurting their children’s achievement, said former South Side High Principal Carol Burris. During that period, the proportion of students earning New York’s higher-level Regents diploma climbed from 58 percent in 1989 to 97 percent by 2005. “I always told parents, when we started moving this through the high school, ‘Look, if this isn’t working, I’m not going to do it. I’m not going to hurt your kid,’” she said.

Related: How one district diversified its math classes – without the controversy

Those slow rollouts contrast with what happened in the Shaker Heights City School District in Ohio in 2020. That summer, school leaders needed to simplify schedules to accommodate a mix of online and onsite students because of the pandemic. They saw an opening to do something that had long been in the district’s strategic plan: end tracking in most fifth- through ninth-grade subjects.

But teachers complained last spring that it had gone too quickly, saying that they didn’t get enough training on teaching mixed classrooms, and that course rigor has suffered. Even supporters of detracking suggested it had happened so fast that the district couldn’t lay the groundwork with parents.

Shaker Heights Superintendent David Glasner said he understands those concerns. But he said he also heard from parents, students and instructional leaders in the district who say they’re glad the district “ripped the Band-Aid off.”

In Troy, despite the pushback from parents, the school board ultimately voted 6-1 for the change, noting that the district had spent four years studying options and that teachers and outside experts largely supported the plan.

Machesky said if he had it to do over, he’d communicate with parents earlier. The anonymous email took advantage of an information void: The district had communicated the proposal only to parents of current and upcoming middle schoolers. Most who turned out to oppose it had younger kids and hadn’t been told, he said.

Leaders in Evanston and South Side both say they also framed detracking as a way to create more opportunities for all students. As part of getting rid of tracks, Evanston created an “earned honors” system. All students enroll in the same classes, but they can opt into honors credit — which boosts their class grade by a half-point, akin to extra credit — if they take and do well on additional assessments or complete additional projects.

School leaders in South Side also ensured that detracked classes remained as challenging as the higher-level classes had been previously, Burris said. To make sure students succeeded, the school arranged for teachers to tutor struggling students in a support class held two or three times a week and in a half-hour period before school, changing the bus schedules to make that work. Teachers also created optional activities for each lesson that would push higher-achieving students if they mastered the material being covered.

“You have to make sure you’re not taking something away from anyone,” said Burris.

To prepare for pushback, Evanston also formed a “rapid-response team” that answered parent questions about the new system within 24 hours and developed dozens of pages of frequently updated FAQs. That took the pressure off teachers, letting them focus on the classroom, said math department chair Dale Leibforth. By the end of the first year of detracking, the school had gotten just three complaints, all requests for fixes to narrow technical problems rather than wholesale critiques, said Bavis.

“We imagined a catastrophe,” he said. “We asked, ‘what could go wrong?’” and mapped how to handle each scenario.

Related: Inside the new middle school math crisis

In response to continued critiques of its detracking effort, last fall Shaker Heights pioneered another idea: an evening immersion experience that lets parents sit through detracked classes. The four mock sessions — two in literature and two in math — were followed by questions and answers.

Parents were respectful but probing: How do teachers work together to make the new system work? Do kids know when they’re grouped with others who are struggling in a skill? Are the books we worked with really at sixth-grade level? While there’s no data on the session’s effects, Glasner says they “absolutely did move the needle” on community opinion.

Research from the Century Foundation, a progressive think tank, suggests that districts should focus on how detracking helps all students, rather than emphasizing that the efforts are aimed to advance equity and benefit students in lower tracks, said senior fellow Halley Potter. That approach gives parents of higher-track kids the idea that their own child’s academics are being sacrificed to help others.

That fits with what Machesky thinks happened last spring in Troy. “We kind of got caught up with the equity arguments that were raging in districts nationally at the time,” he said.

After last May’s board vote, opponents launched a recall petition against three board members who’d voted in favor of the change. To get on the ballot, it needed 8,000 signatures but got fewer than half that.

Since then, the opposition there has gone silent.

Last fall the district held “math nights” to talk about the new system and let parents ask questions. The students have settled in. “I have received zero negative communication from parents — no emails, no phone calls — zero,” said Machesky. 

Related: How can schools dig out from a generation’s worth of lost math progress?

Whether detracking spreads may depend on the experience of parents and students. Back on Long Island, parent Mindy Roman’s three children graduated from South Side High in 2009, 2012 and 2018, and she said she’s glad they were in classes with diverse groups of students. Her children didn’t have classes with a Black student until middle school because of the way elementary school lines were drawn, she said. And all three did well in the district’s detracked courses.

But Roman said she’s heard from current parents with the opposite experience. “It’s not ‘oh my God, my child is getting access to these unbelievable opportunities,’ but more like, ‘my kid is gonna get a 70 in a class when they could get a 90. I don’t want them to be put under that much pressure.’”

John Murphy, who was principal at South Side High from 2015 to 2023, said he started hearing around 2018 from people worried about the effects of the workload on their children’s mental health, and the school responded by giving less homework. Even so, “students are working way harder than they did 20 years ago,” said Murphy, now an assistant for human resources to Superintendent Matthew Gaven.

Still, academic outcomes at South Side have improved since the district eliminated tracking. In 2021-22, 89 percent of South Side graduates earned the highest-level diploma the state offers — the advanced Regents diploma — compared with 42 percent in New York state as a whole. Another 9 percent earned the Regents diploma.

That said, the district recently made an accommodation. Post-Covid, a small group of parents of middle schoolers told the district they didn’t think their children were ready for Algebra I because of the pandemic-era learning interruptions. So South Side Middle School retracked eighth-grade math starting in the 2023-24 school year, offering parents the choice of Algebra I or a grade-level math course. Gaven said that only around 7 percent of parents of eighth graders asked for that option, and that demand for it might taper as schools return to normal.

It’s an opt-in model far different from those that direct students into lower-level courses because of test scores or teacher recommendations, said Gaven. “We know our kids can handle algebra, but we respect our parents as partners and wanted to give them a voice and an option.”

This story about detracking was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter.

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There has been much talk and concern in recent months about making higher-level math more accessible to high schoolers, particularly low-income students from Black and Hispanic communities. Much of this discussion dwells on what is the best curriculum to use to teach Algebra I and other higher-level math courses.

The right curriculum is important, of course. A high-quality curriculum creates the foundation for success in math. A curriculum that values culturally responsive education enables teachers both to value the many kinds of experiences that students bring to classrooms and to push them academically while engaging them personally.

But properly implementing an Algebra I curriculum is at least as important as the curriculum itself. The core of implementation, meanwhile, is coaching each teacher for the specific challenges they will face in their classrooms. The key to success is ensuring that teachers understand the vision for how to implement the curriculum and are therefore motivated and prepared to use it to help children learn in ways that are relevant to them.

In a way, it’s like photography. The key to creating art with light and time is not the equipment. Although Hasselblad and Leica cameras and a metal case of Nikkor lenses are great in the hands of those who know how to use them, a great tool to create expressive photographic art can also be found in your purse or pocket. As with teaching algebra, the key is not the specific tool, but knowing the right approach and being trained well enough to be confident in using that approach.

Related: Kids are failing algebra. The solution? Slow down

I’ve seen a focus on implementation pay off in my own work as director of Algebra Success for the Urban Assembly. One of our coaches at the nonprofit, Latina Khalil-Hairston, encouraged teachers at Harry S Truman High School in the Bronx to tinker with their curriculum to encourage more student involvement.

They created a new lesson structure that focused more on getting students to help each other solve problems than on getting direction from teachers. While doing so, they were mindful of adopting this new structure within the challenging constraint of having only 45 minutes for each lesson. Teachers saw more participation and better results, which has been its own motivation.

Professionals in all fields need coaching and support — why would high school math be any different? We wouldn’t give a basketball playbook to a player and expect them to be LeBron James. Even LeBron James still practices and gets coaching feedback. Even the most accomplished among us need to see a vision of excellence.

Yet I have seen many schools fall into the trap of investing in a curriculum without giving teachers the most useful ways to implement it. Unsurprisingly, these schools fail to achieve the results they hoped for and then abandon one curriculum for another.

But the curriculum is just the camera. Training and coaching, personalized to each teacher, produce the art.

And that coaching should not only help teachers understand their tools, but also help them better understand the backgrounds of their students to ensure that their perspectives are part of the learning process. Knowing the nature of the student body can dramatically enhance understanding, retention and interest in math (or any subject).

Related: OPINION: Algebra matters, so let’s stop attacking it and work together to make it clearer and more accessible

I’ve seen the results. Just last year, we saw pass rates on the Algebra I Regents for schools participating in our Algebra Success program rise 13 percent over the previous year. College-readiness math results rose 14 percent.

It is time for schools and districts to abandon the search for the one perfect curriculum — it does not exist. Instead, they should focus on how to better implement the systems they have in an engaging, effective way. They should invest in the training and support of teachers to master the instruction of that curriculum. With these changes, we know students will find success in Algebra I, putting them on the path to higher-level math courses and postsecondary success.

Shantay Mobley is the director of Algebra Success for the Urban Assembly, a nonprofit that promotes social and economic mobility by innovating in public education. She previously was a math teacher, school leader and instructional consultant.

This opinion piece about teaching Algebra was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter.

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TULSA, Okla. — Amoni y Zoe esparcieron el contenido de una bolsa de sándwich llena de caramelos de frutas sobre sus escritorios como parte de una lección de matemáticas sobre proporciones.

“¿Qué significa tener el 50 por ciento?” preguntó su maestra, Kelly Woodfin, a los alumnos de sexto grado en su clase de matemáticas avanzadas. “¿Qué significa tener la mitad?”

Amoni y Zoe, ambas de 11 años, comieron solo un caramelo cada una, mientras convertían la proporción de manzanas verdes o fresas rosadas de su bolsa en fracciones, decimales y porcentajes. Cuando se quedaron perplejas con una estrategia para convertir un decimal en un porcentaje, inmediatamente levantaron las manos.

“Creo que hay que dar dos pasos hacia la izquierda”, dijo Amoni, su oración terminando en una pregunta.

“Has estado haciendo esto durante dos semanas, hermana”, la reprendió Woodfin en broma. “No sé por qué dudas de ti misma”.

Hace años, cuando Woodfin asistió de kinder hasta octavo grado en Union Public Schools, ella estudió en aulas bastante homogéneas. Woodfin recuerda que sus compañeros eran predominantemente blancos, un legado de que las familias blancas se mudaron a los suburbios cuando las escuelas de Tulsa empezaron a desegregarse durante los años cincuenta. Pero cuando ella regresó para enseñar en el distrito de Union en 2012, la población estudiantil blanca matriculado se había reducido a poco más de la mitad.

Sin embargo, hasta hace poco, los estudiantes en las clases avanzadas de matemáticas de Union seguían siendo en su mayoría blancos. Los estudiantes del itinerario acelerado en la escuela intermedia y secundaria procedían principalmente de escuelas primarias en vecindarios prósperos, donde los estudiantes tendían a sacar mejores resultados en la prueba de nivel de pre-álgebra para la cual tenían una sola oportunidad de tomarla en quinto grado. Pero en un día de invierno reciente, solo dos de los estudiantes de Woodfin se identificaban como blancos y más de un tercio todavía estaban aprendiendo el inglés.

La transformación en las clases de Woodfin representa más que un cambio general sobre quién asiste a las escuelas de Unión, donde hoy solo uno de cada cuatro estudiantes es blanco. También es el resultado de una campaña de años de duración para identificar y promover a más estudiantes de orígenes subrepresentados en los cursos de matemáticas más desafiantes del distrito.

En otros lugares, preocupaciones sobre quién puede acceder a clases de matemáticas avanzadas han llevado a los distritos a eliminar los sistemas de itinerarios (desagrupamiento) que separan a los estudiantes en diferentes clases de matemáticas según su capacidad percibida, o a eliminar las clases aceleradas por completo en nombre de la equidad.

Unión Public Schools, en cambio, ha intentado encontrar un término medio. El distrito, que se encuentra en partes de Tulsa y sus suburbios del sureste, continúa el sistema de grupos de clases de matemáticas separadas a partir del sexto grado. Pero también ha agregado nuevas formas para que los estudiantes califiquen para cursos de matemáticas de nivel superior, más allá de la prueba de nivel y ha aumentado el apoyo (incluyendo tutoría en las escuelas y períodos de clase más largos) para los estudiantes que han demostrado promesa en la materia.

Los datos de inscripción sugieren que el esfuerzo de hacer que las matemáticas de nivel superior sean accesibles para más estudiantes, habían comenzado a dar resultados antes de la pandemia. Pero han habido desafíos: en los últimos años, menos estudiantes se han matriculado en clases de matemáticas avanzadas en general, aunque el decrecimiento en número de estudiantes afroamericanos y latinos ha sido menos pronunciado que para otros grupos. Sentimientos anti-profesores, además de los bajos salarios docentes en Oklahoma, han dificultado la contratación de educadores de matemáticas, según administradores del estado. En Union High School, un puesto para enseñar Álgebra II permaneció vacante durante más de un año.

Pero el distrito sigue comprometido con sus cambios. Últimamente, directores de escuela y educadores de matemáticas veteranos han convencido a algunos exalumnos a que se unan a las filas docentes de Union. Shannan Bittle, especialista en matemáticas de secundaria en Union, dijo que los nuevos programas académicos del distrito, como aviación y construcción, podrían ofrecer a los estudiantes más formas de aplicar matemáticas avanzadas en empleos lucrativos.

“Nos esforzamos muchísimo para no dejar a la gente fuera” de las matemáticas aceleradas, dijo ella. “Pero hacemos todo lo posible para darles las herramientas para tener éxito”.

Tomar álgebra o matemáticas de un nivel superior en la escuela intermedia coloca al estudiante en el camino de tomar cálculo en la escuela secundaria, lo cual abre puertas a universidades selectivas y se considera un curso de entrada para muchas carreras STEM, las cuales son bien remuneradas. Datos federales sobre educación muestran que los estudiantes blancos en la escuela secundaria se matriculan en cálculo a una tasa casi ocho veces mayor que la de sus pares afroamericanos y aproximadamente el triple del promedio de los estudiantes latinos.

“Hay muchos estudiantes afroamericanos y latinos, y estudiantes procedentes de familias de bajos ingresos, que han demostrado aptitudes y anhelan más, pero sistemáticamente se les niega el acceso a cursos avanzados de matemáticas”, escribieron los autores “Esta práctica, y esta mentalidad, debe cambiar un informe de las organizaciones sin fines de lucro Education Trust y Just Equations”, publicado en diciembre del 2023.

Aun así, los enfoques que algunos distritos escolares han adoptado para aumentar la diversidad estudiantil en las clases de matemáticas han generado controversia.

En San Francisco, el distrito escolar eliminó clases de matemáticas aceleradas en las escuelas intermedias y secundarias en 2014 para poner fin a la segregación por capacidad, lo cual provocó protestas de padres. Tres años después, Cambridge Public Schools en Massachusetts comenzó a desmantelar su política de itinerarios de matemáticas aceleradas o de nivel de curso. Cerca de Detroit, el consejo escolar de Troy eligió eliminar las clases de matemáticas avanzadas para las escuelas intermedias empezando más tarde este año.

Asimismo, el año pasado la junta de educación del estado de California adoptó nuevas pautas curriculares que, entre otras ideas, alientan a las escuelas a posponer álgebra hasta el noveno grado. La junta insistió que el esquema “afirma el compromiso de California de garantizar la equidad y la excelencia en el aprendizaje de matemáticas para todos los estudiantes”. Pero los críticos, entre ellos profesores de matemáticas y ciencias, han opinado que hace lo contrario, al negar a los estudiantes la preparación académica que les hace falta para tener éxito.

“Veo el valor, en teoría”, dijo Rebecka Peterson, profesora de matemáticas de Union High y la Maestra Nacional del Año 2023, acerca de esfuerzos como el de California. Pero añadió: “Cada niño es distintivo, y como madre, una talla única no es lo que quiero para mi hijo”.

Peterson comenzó a trabajar en las escuelas de Union hace unos 12 años, impartiendo clases de matemáticas desde álgebra de nivel intermedio hasta cálculo de Advanced Placement. Desde el principio, Peterson notó la división demográfica en sus clases: “Somos un distrito con una riqueza cultural, y, sin embargo, mis clases de cálculo eran en su mayoría blancas”, dijo.

Decidió hablar con su directora de escuela en ese entonces, Lisa Witcher. Las dos descubrieron que, aunque Union High recibía a estudiantes de todos los 13 campus de primaria del distrito, los estudiantes de cálculo de Peterson venían principalmente de solo tres: los más blancos y ricos de las escuelas primarias de Union.

Poco después, oficiales administrativos del distrito recurrieron a Witcher para encabezar un nuevo programa de universidad temprana. Ella comenzó a reclutar estudiantes que habían tomado geometría en su primer año, pero descubrió que solo un décimo de los estudiantes afroamericanos de primer año en Union eran elegibles para inscribirse en esa clase. No habían tomado la clase requerida para entrar, Álgebra I, en octavo grado.

“Eso provocó algunas conversaciones incómodas”, dijo Witcher, quien se jubiló del distrito en 2021.

Al final, los administradores encontraron que la causa de la falta de diversidad estudiantil en las clases de matemáticas avanzadas de la escuela intermedia y secundaria se encontraba en el quinto grado. Ese era el año en el cual las escuelas administraban un examen mayormente basado en palabras, en el que los estudiantes tenían una sola oportunidad de aprobar. Los funcionarios del distrito dijeron que ese examen de gran peso perjudicaba a dos poblaciones en aumento en las escuelas de Union: los niños que todavía estaban aprendiendo el inglés y los niños de familias de bajos ingresos, cuyos padres no podían pagar tutores privados.

Este descubrimiento provocó una serie de cambios que comenzaron hace aproximadamente una década. El distrito escolar no eliminó el examen de quinto grado que servía como entrada a las matemáticas avanzadas, pero hoy los estudiantes pueden tomar el examen múltiples veces. Las escuelas primarias ofrecen tutores de matemáticas a partir del tercer grado, con programas extraescolares para estudiantes rezagados en la materia. Los maestros pueden recomendar a estudiantes prometedores a tomar matemáticas avanzadas de sexto grado, independientemente de su desempeño en el examen de nivel. Un administrador central también revisa las calificaciones de los estudiantes y el progreso en los exámenes de competencia para automáticamente inscribir estudiantes en clases aceleradas. (Se les envía una carta a los padres notificándoles sobre la inscripción automática y en ese momento pueden optar por que sus hijos no participen).

“Los perseguimos a todos los rincones del distrito escolar”, dijo Todd Nelson, ex profesor de matemáticas que ahora supervisa datos, investigaciones y pruebas del distrito.

Desde 2016, ha aumentado la diversidad de los estudiantes matriculados en los cursos avanzados de matemáticas del distrito. Ahora los estudiantes latinos representan el 29 por ciento de la matrícula total, antes representaban el 18 por ciento. Los estudiantes afroamericanos y multirraciales representan cada uno el 10 por ciento de la matrícula, en el 2016 representaban cerca del 8%.

Sin embargo, más recientemente la participación en matemáticas de nivel superior ha disminuido en todos los subgrupos de estudiantes en las escuelas de Unión. Las cifras del distrito muestran que esta tendencia comenzó antes de la pandemia, especialmente en las escuelas secundarias. Pero los administradores dicen que la interrupción debido a los cierres de las escuelas contribuyó a una persistente aversión a inscribirse en cursos desafiantes. Aun así, las proporciones de estudiantes afroamericanos, latinos y multirraciales que se matriculan en las clases avanzadas de matemáticas de Union han caído en tasas mucho más bajas que las de los estudiantes asiáticos y blancos.

“Consideramos que el trabajo que estamos haciendo es un proceso a largo plazo, a diferencia de solucionar el problema en un año”, añadió Nelson.

En la clase de sexto grado de Woodfin, Vianca, de 11 años, no estaba segura de cómo había terminado en la clase de matemáticas avanzadas. Recordó haber tomado un examen “súper difícil” cuando estaba en quinto grado y se registró para matemáticas estándar en la escuela intermedia.

“Parece que me colocaron aquí”, dijo.

Vianca dijo que la materia le ha sido un desafío este año. Pero un cambio reciente en los horarios de sexto grado que agrega más tiempo para las matemáticas significa que tiene 90 minutos con Woodfin cada día, en lugar de solo 45.

“Ella siempre va más despacio” cuando le parece demasiado, dijo Vianca sobre su maestra. “Puedo pedir ayuda”.

Duplicar la cantidad de tiempo para las matemáticas para los estudiantes de sexto grado en Union ha tenido un costo. Algunos padres se enojaron ante la reducción de actividades extracurriculares, como arte o música. El cambio requirió duplicar el número de profesores de matemáticas de secundaria, y los directores de escuela ya habían tenido dificultades para reclutar profesores para esas materias. (El año pasado, la tasa de rotación de docentes de Oklahoma alcanzó el 24 por ciento, la tasa más alta en una década, según datos estatales.)

La falta de diversidad docente también complica la misión general del distrito de incrementar la diversidad estudiantil en las matemáticas avanzadas, reconoció Bittle. Solo dos de aproximadamente 90 profesores de matemáticas de escuelas intermedias y secundarias se identifican como afroamericanos; y los esfuerzos para reclutar en Langston University, la única universidad históricamente afroamericana del estado, aún no han sido exitosos. Bittle añadió que los bajos salarios docentes en Oklahoma no ayudan. Las escuelas de los estados vecinos tienden a ofrecer mucho más que el salario inicial para profesores en Oklahoma de aproximadamente $40,000 anuales.

Las investigaciones acerca del debate sobre la eliminación de los sistemas de seguimientos demográficos presentan un panorama complicado. Casi al mismo tiempo que el distrito hizo sus cambios, un estudio internacional encontró que separar a los estudiantes dotados en clases aceleradas podría exacerbar la división entre ricos y pobres en las escuelas. Otro artículo, publicado por la Brookings Institution en 2016, encontró que los estudiantes afroamericanos y latinos en estados que utilizaron más sistemas de itinerarios para separar a estudiantes de octavo grado en diferentes niveles de habilidad en matemáticas obtuvieron mejores calificaciones en los exámenes de Advanced Placement.

“Esto seguirá siendo turbio”, dijo Kristen Hengtgen, analista senior de Education Trust. “El proceso de eliminar los sistemas de itinerarios parece tener buenas intenciones, pero todavía no hemos visto de manera concluyente que funcione”.

Sin embargo, Unión sigue comprometido con sus esfuerzos. Y en una clase de cálculo totalmente silenciosa, donde sólo el zumbido del sistema de climatización interrumpía el frotar de los lápices, los estudiantes permanecían comprometidos con sus propios trabajos.

Lizeth Rosas estaba sentada en la última fila. Vestida con bata azul brillante del programa de enfermería que tendría más tarde ese día, la joven de 18 años garabateó notas sobre cómo encontrar el valor promedio de fricción en un intervalo determinado.

“¿Alguna pregunta?”, dijo su maestra. “Hablen ahora o callen para siempre.”

Sólo ocho de los 22 estudiantes de la clase se identificaban como blancos. Rosas comenzó a estudiar matemáticas avanzadas cuando estaba en séptimo grado, dijo. El año pasado, para su sorpresa, un maestro le recomendó tomar el curso de Advanced Placement.

“Al principio me cuestioné, y, mucho”, dijo. “No sabía si estaba lista. Es mucho que procesar y nos movemos muy rápido”.

Rosas planea trabajar como enfermera práctica con licencia después de graduarse y supone que las conversiones de medicamentos y líquidos intravenosos requerirán matemáticas. Su padre, quien dirige su propia empresa de remodelación, no puede ayudarla con sus tareas de cálculo, dijo ella. Pero su programa de enfermería, parte de un programa de extensión de la escuela secundaria en el cercano Tulsa Technology Center, ofrece tutoría académica.

“No me hace tanta falta”, dijo Rosas. “Los profesores aquí son realmente atentos. Simplemente me ayudan. Me recuerdan que puedo hacerlo”.

Este artículo sobre equidad en las matemáticas fue producido por The Hechinger Report, una organización de noticias independiente sin fines de lucro centrada en la desigualdad y la innovación en la educación. Regístrese para el Hechinger newsletter.

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Universities, philanthropies, and even the U.S. government are all trying to encourage more young Americans to pursue careers in STEM,  an acronym for science, technology, engineering and mathematics. Many business sectors, from high tech to manufacturing, are plagued with shortages of workers with technical skills. In New York City, where I live, the subway is frequently plastered with advertisements carrying the message that STEM fields pay well. But studying STEM requires more than an interest in science or a desire to make good money. Students also need adequate training, even in elementary and middle school.

That’s why it’s concerning that high-achieving students, who’ve received less public attention than lower achieving students, were also set back by remote learning and pandemic uncertainty.  Fewer students with math skills shrinks the pool of people who are likely to cultivate an expertise in science, engineering and technology a decade from now. In other words, the STEM pipeline –  a metaphor for the development of future scientists, engineers and other high tech workers –  likely starts with a narrower funnel in the post-pandemic era.

The stakes are high not only for Gen Z, as they age out of school and enter the workforce, but also for the future of the U.S. economy, which needs skilled scientists and engineers to grow.

The leading indicators of STEM troubles ahead are apparent within the 2022 scores from a national test called the National Assessment of Educational Progress (NAEP). The immediate headlines from that first post-pandemic test focused on the fact that two decades of academic progress had been suddenly erased. Low-achieving children, who tend to be poor, had lost the most ground. An alarming number of American children – as high as 38 percent of eighth graders  – were functioning below the “basic” level in math, meaning that they didn’t have even the most rudimentary math skills.

Statisticians at the National Center for Education Statistics (NCES) have continued to dig into the 2022 data, and they’ve been also turning their attention to students at the top. These children are on grade level, but the eighth grade NAEP assessment shows that far fewer of them are hitting an advanced performance level, or even a proficient one. Math scores among top performers dropped as steeply as scores did among low performers. Even the scores of students at Catholic schools, who otherwise weathered the pandemic well, plummeted in eighth grade math. 

We don’t have data for other private schools because they have refused to participate in NAEP testing, but the eighth grade math declines among both high-achieving public school and Catholic school students are not good signs. 

NAEP tests reading and math in both fourth and eighth grades every two years in order to track educational progress. It’s one of the only tests that can be used for comparisons across states and generations. More than 400,000 students are specially selected to represent the regions and demographic characteristics of the nation. 

Among the four NAEP tests, eighth grade math showed the sharpest pandemic drop.  Math took a bigger hit than reading because kids can still read at home, while math is something that students primarily learn at school. If you didn’t read “The Hobbit” in your seventh grade English class because you were out sick with Covid, you can still be a good lifelong reader  But not getting enough practice with rates, ratios and percentages in middle school can derail someone who might have otherwise excelled. 

Why eighth grade math was hit harder than fourth grade math is a bit less obvious. One explanation is that the concepts that students need to learn are more difficult. Square roots and exponents are possibly more challenging to master than multiplication and division. And fewer parents are able to assist with homework as the math increases in complexity.

Yet another explanation is a psychological one. These eighth graders were in sixth grade when the pandemic erupted in the spring of 2020. This is a critical time in adolescent development when children are figuring out who they are and where they belong. A lot of this development occurs through social interaction. The isolation may have stunted psychological development and that ultimately affected motivation, study skills and the ability to delay gratification – all necessary to excel in math.

Let’s walk through the numbers together.

Highest achieving students lost ground in eighth grade math

This chart shows that the highest performing students, those at the top 10 percent and the top 25 percent, lost as much as low-achieving students at the bottom in eighth grade math. These eighth graders were in the spring of sixth grade when the pandemic hit in 2020, and it’s possible that they didn’t master important prerequisite skills, such as rates and ratios. These kids at the top are performing at grade level, but not as high performing as past eighth graders.

Fewer eighth grade students hit advanced and proficient levels

This bar chart shows that before the pandemic 10 percent of the nation’s eighth graders were performing at an advanced level in math. That fell to 7 percent. And the number of students deemed proficient in eighth grade math fell even more, from 24 percent to 20 percent. Before the pandemic, arguably, 34 percent of the eighth grade population was on track to pursue advanced math in high school and a future STEM career if they wanted one. After the pandemic in 2022, only 27 percent were well prepared.

Students at Catholic schools are generally much higher performing than students at public schools. In large part, that’s because of family income; wealthier students tend to have higher test scores than poorer students. Catholic school students tend to be wealthier; their families can afford private school tuition. In recent years, the Catholic Church has closed hundreds of schools that catered to low-income families, leaving a higher income population in its remaining classrooms. 

Catholic schools outperformed public schools but also dropped 

This chart shows that Catholic school students, depicted by the diamonds, outperformed public school students, depicted by the circles, in eighth grade math. But it was still a sharp five-point decline in eighth grade math performance for Catholic school students, almost as large as the eight-point decline for public school students. Scores of white students at Catholic schools declined five points; scores of students at Catholic schools in the suburbs declined seven points. Almost a quarter of Catholic school students are now functioning below a basic level in math for their grade. 

Despite the good academic reputation of Catholic schools and the praise Catholic schools received for resuming in-person instruction sooner, math scores suggest a problem. And it’s a problem that potentially extends to the whole private school universe, where 9 percent of students are enrolled, according to the most recently available data from 2019. 

I talked with Ron Reynolds, the executive director of the California Association of Private School Organizations, who explained that not just Catholic schools, but also many other private schools suffered even if they hadn’t been closed for long. Reynolds said that private schools were still hit by illnesses, deaths and absences and that might have affected instruction.

“Private schools are tightly knit communities in which teachers tend to be more intertwined in the lives of the children and families they serve,” he said. “When you have a crisis, and so many people experiencing stress and loss, that can certainly impact the teacher in some significant ways.”

Unfortunately, we don’t know exactly how other private schools fared during the pandemic because they have refused to participate in the NAEP tests for the past decade. Reynolds, who serves on the governing board that oversees the NAEP exam, has been trying to lobby more private schools to participate, but so far, to no avail.

Together private schools, selective public schools and affluent suburban schools have been important training grounds for the nation’s future scientists and engineers. Of course, it is possible that these high achieving students, now 10th graders, will catch up. Many of them are from wealthier families who can afford tutors, or attend well-resourced schools. But I am not seeing much evidence that schools have had the ability to think about the pipeline of advanced students when many students are so needy. And with post-pandemic grade inflation, students and parents may not be getting the signals they need to seek extra help independently. 

The administration of the 2024 NAEP test wrapped up in March, but results won’t be known for many months. I’ll be keeping an eye on eighth grade math and on SAT, ACT and Advanced Placement scores in the years to come.

This story about math scores was written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Proof Points newsletter.

The post PROOF POINTS: How Covid narrowed the STEM pipeline appeared first on The Hechinger Report.

COLOGNE, Germany — Neriman Raim, a 16-year-old student in this northwestern German city, thought that after finishing school she’d want to work in an office.

But two years ago, she did a two-week internship in an architect’s bureau, and it was tedious. Later, a placement working with kindergarteners led her to consider a career as a teacher — but not of kids this young. The next school year, she spent three weeks supervising older children as they did their homework.

Neriman now plans to become an educator working with grade-school children. After finishing school this summer, she’ll participate in a year-long placement to confirm that teaching is the right career for her before going to a technical college. Her internships offered a glimpse of what working life could look like, she said: “I could see what a day is like with kids.”

Neriman is taking part in Kein Abschluss ohne Anschluss (KAoA) — or “no graduation without connection” — a program that has been rolled out across the German state of North Rhine-Westphalia to help students better plan for their futures. Young people get support with resumes and job applications; in ninth grade, they participate in short internships with local businesses and have the option of doing a year-long, one-day-a week work placements in grade 10.

“You don’t learn about a job in school,” said Sonja Gryzik, who teaches English, math and career orientation at the school Neriman attends, Ursula Kuhr Schule. “You have to experience it.”

Germany and other Western European countries have long directed students into career paths at earlier ages than in the U.S., often placing kids onto university tracks or vocational education starting at age 10. Students in Germany can embark on apprenticeships directly after finishing general education at age 16 in grade 10, attending vocational schools that offer theoretical study, alongside practical training at a company. College-bound kids stay in school for three more years, ending with an entry exam for university.

The apprenticeship system, which is credited with keeping youth unemployment low, has drawn strong interest in the U.S. amid growing disenchantment with university education. Youth apprenticeships have begun to pop up in several U.S. states, and career exposure programs are expanding. “Many of the best jobs our country has to offer don’t require a college education,” wrote workforce training advocate Ryan Craig in his recent book “Apprentice Nation: How the ‘Earn and Learn’ Alternative to Higher Education Will Create a Stronger and Fairer America.”

But in Germany, the hundreds-year-old vocational system has faced headwinds. There is longstanding criticism that low-income students and those from immigrant backgrounds are channeled into vocational fields and away from more academic ones. More recently, despite the high demand for workers in the trades, students and their parents are increasingly hesitant about vocational education. Germany’s labor market has become digitized, and young people are keeping their options open before settling on a career path. Meanwhile, the pandemic had an outsized impact on vocational training, forcing many programs to close for long periods. And recent immigrants may be unaware of voc-ed’s high standing.

All this has led more students to choose to attend university. Yet many drop out: According to recent data, up to 28 percent of students fail to complete a degree. The figure for students in humanities and natural sciences is even higher, up to 50 percent. 

This high failure rate, coupled with labor market needs, has led policymakers to tweak traditional vocational models to make them more flexible. Students in the academic track increasingly have access to both apprenticeships and university, and some students who complete vocational qualifications can still go on to attend a university, where options for combining practical experience with academic studies are growing.

The program Neriman participates in, KAoA, is part of a wave of efforts to engage all students, not just those bound for vocational programs, in workforce preparation. All ninth and 10th grade students in North Rhine-Westphalia must do a three-week-long practical internship. Those on a vocational track begin apprenticeships after completing 10th grade, while students hoping to go to university attend academic high school for three additional years. The program encourages students from all backgrounds to think about their futures in concrete terms, said Bernhard Meyer, a teacher at Ursula Kuhr who coordinates KAoA in 11 towns across the Northwestern region.

“We have every type of possibility,” Meyer said. “And there’s not only apprenticeship or university, there are some studies in between.”

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At Ursula Kuhr Schule, students in the school’s woodworking lab build birdhouses and toy cars. A state-of-the-art kitchen lets students develop their culinary skills. An extensive garden, full of herbs, and boasting a hen house, offers an opportunity to test out horticultural skills.

Students take field trips to learn about different jobs. For example, on a trip to the airport they learn about positions such as flight attendant, fire service, security or aircraft mechanic. Employees from Ford, which has a plant in Cologne, visit the school to talk about their work with students and parents.

While university is free in Germany, students who study vocational fields can achieve financial security earlier on.

Businesses in Germany seem keen to participate in vocational training. Chambers of commerce and industry support company-school partnerships and help smaller businesses train their interns. Students are even represented in unions, said Julian Uehlecke, a representative of the youth wing of Germany’s largest trade union alliance.

The goal of apprenticeships is to offer training in the classroom and in the workplace. The system gives students “a pretty good chance of finding a well-paid stable job,” said Leonard Geyer, a researcher at the European Centre for Social Welfare Policy and Research.

Lukas Graf, head of the Swiss Observatory for Vocational Education and Training described the “basic principle” of Germany’s program as providing all-around training: “in the classroom, in the seminar room, and training in the workplace.”

Mile Glisic, a 15-year-old student at Ursula Kuhr Schule, is doing a long-term work placement at a hardware store and considering an apprenticeship in sales. Earning money while training for a career will help him understand financial planning, and prepare him for a future in which he has a house and family, he said. “I think it’s better because you start to learn what to do with your money when you’re younger,” said Mile.

While the KAoA program has rolled out across all 2,000 schools in this region of Germany, including those that focus on university preparation, Ursula Kuhr Schule prioritizes practical education. Students, more than half of whom come from minority backgrounds, begin career orientation when they are just 12 or 13.

Backers of vocational training say it supports social inclusion by giving young people training that allows them to secure well-paid, stable jobs. But, as in the United States, many argue it limits the prospects of students from marginalized backgrounds and reproduces generational inequalities. This is “a huge debate,” said Graf, of the Swiss Observatory.

To Graf, the value of either a university degree or practical study depends on the particular courses chosen. A university graduate in a field like philosophy, for example, might end up with fewer well-paid opportunities than someone with vocational education training, he said.

The pandemic deepened many parents’ ambivalence about vocational training. While university teaching continued through online platforms, on-the-job training came to a stop when companies had to shut down, said Hubert Ertl, vice president and director of research at Germany’s Federal Institute for Vocational Education and Training and professor of vocational education research at the University of Paderborn.

Parents have a big influence: Research by Ertl’s institute shows that when students express interest in a vocational program, their parents often talk them out of it and push them toward higher ed instead. “That’s often not doing the young people any favors,” he said.

His organization works with schools and parents to tackle preconceived ideas about vocational education. “We’ve started to engage with parents quite directly because parents often don’t know about the vocational programs at all, and they don’t know what opportunities they afford.”

Tim Becker, 20, is doing an IT apprenticeship after completing the university entry exam at his academically oriented high school in Cologne. At first, his parents, who worked for CocaCola, were uneasy. German parents usually want their children to go to university, “especially if they go to a gymnasium,” Becker wrote in an email, referring to academic high schools.

But in school, his career classes urged students to compare the benefits of university to a practical qualification. For Becker, who’d always loved computers, hands-on training beat out academic theory. “I am just not that guy that likes to sit all day in any lectures at some university,” he said. Some of his old classmates have already dropped out of college and are pursuing internships, he added.

Parents at Ursula Kuhr attend meetings, called “future conferences,” with their kids several times a year. Mile’s parents, who moved to Germany from Serbia when he was 9, have met his teachers frequently. “I know that they were very happy with it,” he said, referring to his career path. “They had some questions about it. But I think they’re thinking good about it because, I mean, it’s only doing good for us.”

Neriman’s mother, who is a nanny, “loved the idea” that her daughter would teach in grade-school, Neriman said. The teachers and staff at Ursula Kuhr help students gain confidence about their futures, she said. “The teachers do everything for us — they don’t want anyone to finish school and have nothing.”

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Other European countries are seeing similar labor market needs. Denmark, whose minister for education trained as a bricklayer, is facing a significant skills shortage in vocational fields, said Camilla Hutters, head of the National Center for Vocational Education, a Danish research organization.

In the 1960s, practical and project-based learning was common in Danish schools, Hutters said. That changed in the 1990s, when Denmark scored poorly on international rankings like the Program for International Student Assessment. Now, economic needs are causing a swing back to vocational and career education.

Today, Danish students as young as 6 might visit a workplace or spend a week learning about a particular career, she said, and discussions are under way to further integrate practical learning in primary school. Danish leaders also want to improve collaboration with business across the education system, including at the university level, Hutters said, where an increasing number of courses are likely to involve working with a company. Political leaders are discussing reforms that would “improve practical learning in the whole system,” she said.

But a tension between on-the-job training and academia persists in Danish thinking, she added. Although policymakers want to expand the practical element across all levels of education, university still remains the goal for many students and their parents. “This is a little bit of a mixed tendency at the same time, right now in Denmark,” she said.

Back in Germany, Becker will finish his internship in September 2024 with expertise in IT services and network security. Throughout his training, he has earned money — and will get up to €1,260 (roughly $1,360) per month in his final year — which has meant he could avoid taking on part-time work as some of his college friends have done.  “You don’t need to sit all day in university and go to work in the evening to pay your bills,” he said.

And it suits him. He grew up surrounded by computers, tinkering alongside his dad, and that love of technology persisted through his teens. He likes working with his hands and doing, “something where I can learn practical things,” he said.

This story about German vocational training was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter.

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