But new I led found that difficulties with advanced topics often stem from earlier gaps in understanding. Because mathematics is cumulative, students who struggle with algebra, for example, may be facing with fractions, number sense or other skills typically developed in earlier grades. When these deficiencies go unaddressed, they persist and create bigger problems down the road. 

These deficiencies are shaped by instructional choices made in classrooms every day. Chief among them is the ongoing debate over whether students are being equipped with a genuine understanding or merely trained to follow steps. 

In reality, requires both. Students must know how to carry out procedures, but also need to understand why they apply to specific problems. Like a chef, mastering math is not just about following a recipe or executing techniques correctly; it is about understanding how elements work together so that, when faced with something new, students know how to reason through the problem and build on previous knowledge.

And this imbalance often begins . For example, in early elementary grades, the pressure to focus on rote memorization of addition facts and subtraction 鈥渢ricks鈥� can occur at the expense of number sense. When memorization is prioritized over understanding the quantities involved, we set the stage for the conceptual disconnect that becomes a crisis in later grades.

In many traditional math curricula, procedural knowledge . Students memorize steps and by middle school, that can become their entire conception of math. When students understand the steps through conceptual knowledge, they can explain and justify their work. In a classroom, this may look like a student understanding that the area of a triangle is half that of a rectangle because they can visually decompose the shapes, rather than simply reciting the formula A=12bh. This can help them make connections and understand the 鈥渨hy鈥� behind the process. even points to conceptual understanding improving procedural knowledge more than vice versa.

The focus on procedural knowledge could be driven in part by the need for schools to meet goals for standardized test scores. Standardized testing rewards correct answers more than understanding, which may reinforce the imbalance of conceptual and procedural learning. Many reduce teacher performance to student test scores, despite these scores failing to capture a complete picture of student learning. Under this pressure, many teachers may feel compelled to 鈥�,鈥� prioritizing procedural accuracy to ensure their students can answer the basic multiple-choice questions that dominate these exams.

Declines in NAEP scores may intensify the urgency, fueling a climate where short-term gains matter more than long-term mathematical understanding. In a standardized testing-focused environment, conceptual knowledge can feel like a risk.

Addressing this imbalance does not require eliminating standardized tests, nor does it demand that every lesson become an exhaustive explanation. Instead, it requires an intentional approach to integrating conceptual knowledge into math instruction. Procedural knowledge remains essential, but it should be grounded in meaning and understanding, not memorization alone.

For this to happen, educators must be supported in teaching conceptually. Professional development that emphasizes conceptual explanations, student reasoning, and common misconceptions can bridge this gap.

Teachers also need tools that make conceptual knowledge manageable within real classroom constraints. Diagnostic assessments, formative checks and student work analysis can reveal where understanding breaks down, allowing teachers to target specific concepts not well understood. When instruction focuses on the ideas students struggle with most, conceptual knowledge can become feasible.

Tools that use diagnostic questions to identify where students鈥� understanding of math concepts falls short 鈥� what researchers call 鈥溾�� or 鈥渋nstructionally relevant errors鈥� 鈥� can help educators gain insight into how students think about and approach math problems. Rather than spending valuable instructional time trying to infer misunderstandings, educators can focus on addressing them. 

A randomized controlled trial across 20 schools and 3,000 students found that students who used one such tool achieved in a single school year. The tool was developed with support from the , which assists learning engineers in the development of AI-based tools that will significantly improve middle school math learning.

Math is hard 鈥� but perhaps that is because it is often taught without meaning. Many students learn the steps to solving a problem without ever understanding why it works. Procedures alone are not enough. Memorization can only take students so far; true learning happens when knowledge can be applied. If we want students to reason, problem-solve and build their math knowledge, conceptual knowledge cannot be optional.

This story was originally published by Chalkbeat. Sign up for their newsletters at .

New York Gov. Kathy Hochul wants to revamp the way the state鈥檚 schools teach math.

Hochul announced the plan in her annual State of the State address on Tuesday, along with several child care and education initiatives she has previewed over the past week. The governor鈥檚 broader agenda includes funding a ; expanding pre-K and child care vouchers statewide; growing a ; bolstering the state鈥檚 teacher training pipeline; and building on free community college for adults who want to train for high-demand careers.

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The governor鈥檚 office released few details about the plan to overhaul math, but in its outlining Hochul鈥檚 priorities for the year, state officials compared it to existing efforts to revamp literacy instruction. The governor has worked with teachers and school districts to adopt evidence-based 鈥渟cience of reading鈥� practices that focus on phonics and explicit reading instruction, state officials wrote.

Similarly, Hochul said in her Tuesday speech that it is time to get 鈥渂ack to basics鈥� in math. 鈥淢y hope is for New York students to be the most academically prepared in the country,鈥� Hochul said.

To that end, she will introduce legislation to require the State Education Department to provide school districts with best practices for teaching math and guidance on selecting math curriculums that align with state standards.

The state will also require the State University of New York and the City University of New York to offer extra training in evidence-based math instruction to teachers, especially in New York鈥檚 districts with the lowest math performance.

鈥淲ith these proposals, New York parents can rest assured that there is no better place for their children to learn and thrive than here in our state,鈥� Hochul said.

New York City is already several years into an experiment in mandating and standardizing school curriculums in the name of evidence-based teaching practices. Well before the state rolled out its curriculum recommendations, former Mayor Eric Adams introduced a teaching overhaul called NYC Reads, which required elementary schools to use one of three city-approved reading programs.

At the same time, under a math reform called NYC Solves, the city required high schools, and later some middle schools, to adopt a standardized curriculum for algebra.

Some educators and experts contended that it didn鈥檛 make sense to introduce a math overhaul in high school, and lacked the vocabulary or tools to follow what was being taught.

New York City鈥檚 new schools chancellor, Kamar Samuels, seems to agree.

Math reform should start with elementary schools, he 鈥淚f we don鈥檛 do math well,鈥� Samuels added, students won鈥檛 鈥渂e ready for the jobs that exist, much less the jobs that don鈥檛.鈥�

Samuels also argued for a balancing a 鈥渂ack-to-basics鈥� approach to math that emphasizes memorization and math facts with a focus on creative problem-solving. Conceptual understanding is important, Samuels said, but parents 鈥渓ook back at me and say, 鈥楳y kid is in fourth grade and doesn鈥檛 know the times tables.鈥欌��

鈥淲e think of [times tables] as an old thing, but we absolutely need to incorporate it so that our parents can believe in what we do again,鈥� Samuels said.

The jury remains out on whether New York City鈥檚 curriculum mandates have improved performance. The Adams administration they said were evidence of positive results, but education experts say it鈥檚 too soon to draw conclusions.

Chalkbeat is a nonprofit news site covering educational change in public schools.

These are the telltale signs of math anxiety creeping back into my classroom, and it鈥檚 heartbreakingly common. Between experience a decline in math skills over the summer across elementary grades. By the time they reach fifth grade, students can lag behind their peers by two to three years.

That means students are missing out on crucial math skills that form the foundation for everything that comes later. As many teachers can attest, math remains one of the hardest subjects to teach because the basics aren鈥檛 always as black and white as they seem.

I鈥檝e had to look for new ways to break down those barriers and ease the pressure. That鈥檚 why I鈥檝e leaned into game-based learning. It takes something stressful and makes it approachable. In teaching math, that makes all the difference.

I first brought games into my math block because I wanted to try something different. A student suggested we review a concept with a math game he had used, and I decided to give it a shot.

There are plenty of games: Math Reveal, Quizizz and Coolmath among them. In my class we use Prodigy, which allows students to play as wizards exploring different fantasy worlds. They progress through the game by engaging in math-based quests and battles, answering a series of math questions to power spells, cast attacks or heal their wizard. Behind the scenes, the platform analyzes each student鈥檚 strengths and gaps, then adjusts and tailors content to the appropriate learning level.

The benefits were clear almost immediately, and the atmosphere in my classroom shifted. Kids who normally avoided eye contact were leaning in, laughing and actually asking to do math. It was a small change at first, but it began breaking down the anxiety that had been holding students back.

Their anxiety turns into curiosity, and their avoidance shifts into active participation. Students knew they could make mistakes, try again and keep moving without the fear of failure they often carried into traditional lessons.

Over time, I鈥檝e learned that these games weren鈥檛 just fun. They were powerful teaching tools. Game-based learning platforms helped students review after new lessons and revisit older concepts to keep their skills sharp. As a result, when we moved on to fractions or multi-step problems, they weren鈥檛 burdened by forgotten fundamentals.

Now, I incorporate game-based learning throughout my curriculum. I may introduce a new lesson with a quick round or have students partner up to practice and reinforce a concept. Before a test, I can assign relevant game modules that give students a low-stakes way to practice and prepare.

I noticed students catching up quicker than in previous years. At the start of one school year, I had eight students who were pulled out of my class for extra math help. By the end of the year, only two needed the extra support.

And let’s be honest: These tools have helped me, too. Teaching math can be overwhelming, especially with constant pressure to get every student up to speed and prepared for benchmark tests.

Game-based learning became a comforting resource for me because it offers new ways to personalize lessons and celebrate small wins. As students play, I can track their learning in real time to see which skills they鈥檝e mastered, where they鈥檙e struggling and how their performance is shifting over time. Students can move at their own pace now, and I can step into the role of guide rather than taskmaster.

Like any classroom tool, game-based learning works best when you use it with intention. Over the years, I鈥檝e learned some strategies that make it more than just 鈥減lay time.鈥�

• Play along: When I first started using game-based learning platforms, I didn鈥檛 fully understand how each game worked or the way they built in rewards, challenges, and storylines that keep kids engaged.
  
  That changed when I created my own character and began playing alongside my students. Suddenly, when a student shouted, 鈥淚 just beat the Puppet Master!鈥� I knew exactly what that meant, and I could celebrate and learn with them.
  
  By experiencing the games myself, I learned how to implement them in the classroom. I could see firsthand how to weave them into lessons, when to use them for review versus pre-teaching, and how to keep the fun from becoming a distraction.

• Assign with purpose: I don鈥檛 just let students log in and click around. I strategically tie games to the key concepts we鈥檙e learning that week or use them to revisit skills. For example, I might assign a short warm-up where they tackle problems from earlier in the year so they鈥檙e never losing touch with old material. Cyclical practice helps build long-term retention while lowering the stress of new concepts.

• Differentiate lessons: One of the biggest wins with game-based learning is how easy it is to differentiate and personalize learning. In any classroom, I have students at wildly different levels: Some need extra review, others are ready to race ahead. With games, I can assign work that meets each child where they are.
  
  That flexibility saves me time, but more importantly, it saves students from unnecessary stress. They can master concepts step by step, and I can gently move them up without overwhelming them.

When I first introduced game-based learning, I didn鈥檛 know what to expect. It felt like one more thing to manage. But I let students guide me, and the results spoke for themselves. They were more engaged, less anxious and more willing to try.

For teachers who are unsure, my advice is simple: Give it a chance. Watch your students light up when math feels less like a hurdle and more like a game. For me, the greatest reward has been seeing kids who once dreaded math start to relax, build confidence and move from 鈥淚 can鈥檛 do this鈥� to 鈥淐an we play again?鈥�

Game-based learning isn鈥檛 about replacing rigor. It鈥檚 about sparking curiosity, reducing fear and creating the kind of engagement that fosters a genuine love of learning. Most of all, it reminds us 鈥� and our students 鈥� that math can, and should, be fun.

A attempts to untangle the policy pendulum swings and provide states and districts with concrete evidence for what鈥檚 most effective. But to really understand what鈥檚 at stake, consider a history lesson  鈥� more a cautionary tale, really 鈥� set in San Francisco schools.

Nationally, only 16% of eighth-grade students took Algebra I in the mid-80s 鈥� and as one might imagine, the well-resourced schools that offered the advanced math subject in middle school overwhelmingly catered to wealthy white students. The 90s was marked by efforts to address those inequities and increase access to Algebra I, which was seen as a gateway to academic success and college access but one that often . 

Swept up in California鈥檚 鈥淎lgebra for All鈥� push in the late 1990s, San Francisco schools shifted away from placing high-achieving students on advanced math tracts and attempted to enroll all eighth-graders in Algebra I. But the results were lackluster at best. By significantly increasing enrollment, including students who were not academically prepared for the subject, achievement plummeted. Some research even suggests a harmful backsliding for the lowest-performers, who often had to repeat the course. 

So, San Francisco course-corrected once again. In 2015, they rolled out new and rigorous math standards, but took away the ability for students to take Algebra I in eighth-grade, making it a ninth-grade subject. Then, after a wave of criticism from parents fearing their kids weren鈥檛 being challenged or properly prepared for more advanced mathematics, they reintroduced Algebra I to eighth-graders this year, piloting three different ways of offering the subject in middle school to pinpoint the most effective way to do so. 

San Francisco isn鈥檛 alone in its Algebra I pendulum swings 鈥� not by a long shot. Today, the subject has become a bellwether for equity and college access, and unexpectedly, one of the most hotly debated topics in American education. 

With district and school leaders clamoring for more meaningful guidance about who should take the class, when, and with what types of support, a new report from and the tackles those issues head-on.

鈥淥ver the past few decades, the research that has come out of those policy swings 鈥� from everyone should take it in eighth grade to no, we should make everyone take it in ninth grade 鈥� has kind of shown that that one-size-fits-all uniform push to algebra one is not meeting the needs of all students,鈥� says Elizabeth Huffaker, a fellow at Stanford University鈥檚 Center for Education Policy Analysis and author of the report. 鈥淎 lot of states and districts are experimenting with new models, and we wanted to bring to bear what we do know as states and districts try to do that.鈥�

Here鈥檚 what the report found and what state, district and school leaders should examine as they think about the most effective ways to set students up for success with Algebra I and beyond. 

How to Determine Algebra Readiness

In deciding who should take algebra, districts should attempt to strike a balance between expanding early access to the subject in 8th grade and ensuring students are academically ready. The goal should be to broaden participation while preventing course failure, disengagement, and long-term setbacks. 

shows that long-term academic success is higher when students are enrolled in Algebra I based on academic readiness rather than grade level. But whether schools should embrace acceleration among students with uncertain readiness depends on the level of academic support a district can provide as well as the proportion of students considered borderline ready. Enrolling too many students who aren鈥檛 fully ready can be disruptive and ineffective, whereas a small number who are also bolstered by tutoring programs, for example, would likely be successful.

Students who are not academically ready need significant support to be successful.

When it comes to making placement decisions, shows the best way to do so is with a combination of test scores, rather than relying solely on subjective referrals or a single test score. This has been shown to improve participation and achievement, especially for historically underserved students. For example, when schools in Wake County, North Carolina, replaced subjective placement factors with a cutoff score based on multiple academic measures, it led to increased enrollment, especially among Black, Hispanic, and low-income students. 

Tracking v. Mixed Classrooms

鈥淭racking,鈥� the practice of assigning students to courses based on their proficiency level, is controversial since it assumes students have fixed academic abilities. That鈥檚 a narrative that鈥檚 particularly harmful for low-income students and students of color who come into K-12 with far less access to advanced coursework. 

Yet the practice is widespread, especially in older grades and for placement in advanced classes: Nationally, about 25% of 4th graders and 75% of 8th graders attend schools that use tracking. Supporters argue that it improves learning by targeting instruction to students鈥� individual needs, and seems to bear that out, with classrooms grouped by proficiency levels allowing more targeted instruction.

However, research also shows that tracking tends to benefit higher achievers while also widening achievement gaps and increasing segregation. Moreover, students in lower tracks are typically aware of their placement, which can hurt confidence, motivation and effort. 

Meanwhile, mixed-proficiency classrooms offer all students access to rigorous coursework, but risk discouraging lower achievers by introducing material that鈥檚 too advanced while also slowing progress for high achievers because the material isn鈥檛 advanced enough. And while differentiated instruction can benefit all students, effectively supporting a wide range of academic abilities requires teachers to have advanced skills.

Evidence-Based Strategies to Help Kids Catch Up

The best approach is to provide extra support to students who aren鈥檛 quite ready for algebra through tutoring, offering two periods of math each day (also known as 鈥渄ouble-dose鈥�) or providing summer programs, research shows. 

Tutoring, especially when delivered in small groups, multiple times per week, and during the school day, is one of the most effective short-term and long-term academic interventions. A of 21 randomly controlled trials found that math tutoring generates about a 10 percentile learning gain, on average, which is a large effect for an educational intervention. 

鈥淒ouble-dose鈥� algebra gives students two math periods a day and has been shown to improve outcomes. When Chicago Public Schools required underprepared 9th-grade students to take two periods of algebra instead of one, student test scores increased. It also led to longer-run gains in college entrance exam scores, high school graduation rates, and college enrollment rates.

also shows that summer bridge programs help students build the study skills and confidence needed for success in algebra. One 19-day Algebra I bridge program in California raised the share of algebra-ready students from 12% to 29%.

Where to Go From Here

Increasing enrollment in Algebra I in middle school involves nuanced decision-making that includes evaluating the readiness of students and educators and the capacity of the district to provide support.

What districts should avoid, the research shows, are policy shifts that either delay Algebra I for all students or accelerate them without strong, integrated support, and enrollment policies that rely on one static test score or subjective teacher recommendations.

鈥淭here should be an emphasis on raising the floor, not lowering the ceiling when we’re thinking about balancing access and achievement,鈥� Huffaker says. 

Most recently, districts have been turning to auto-enrollment policies, which allow students to opt out and support those who may not be academically ready with either tutoring or a second math class. Research shows that it increases participation and completion rates, particularly among underrepresented students. 

Bottom line, Huffaker says, is that there are always going to be trade-offs when it comes to how and when to introduce Algebra I. 

鈥淲e always say that supported acceleration is a great way to get all or most of your students on an advanced pathway. And it sounds really great to have everyone kind of on that early Algebra I one trajectory. But districts face significant resource constraints and staffing. So I think our real goal here was to provide a framework where districts could come in with their local priorities and resources mapped and see what鈥檚 realistic for them.鈥�

Nearly half of 1,471 education leaders who responded to the analytics company鈥檚 December query reported that the task was “very challenging” and far worse than finding strong English language or social studies applicants.

鈥淭he pool of certified math teachers is small, and the demand is high, particularly for candidates who are ready to support student learning from day one,鈥� said Nicole Paxton, assistant principal and athletic director of Mountain Vista Community School in Colorado Springs. 鈥淚n our district, we鈥檝e experienced a growing number of math openings with only a handful of candidates to consider 鈥� many of whom are international applicants requiring sponsorship or visas.鈥�

Another lends insight into a possible reason why: Only 1 in 8 elementary teacher preparation programs nationwide devote adequate time to teaching fundamental math content topics, including numbers and operations, algebraic thinking, geometry and measurement 鈥� plus data analysis and probability. 

The National Council on Teacher Quality, which released the teacher preparation study April 8, found 鈥嬧�媡he average undergraduate program dedicates 85 hours of instructional time to foundational math content knowledge 鈥� 20 hours short of what the organization recommends. 

Graduate programs devote even less time to the topic 鈥� 14 hours total 鈥� with only 5% meeting or approaching the minimum recommendation of 150 hours. The council said 22% of undergraduate programs earned an 鈥淔鈥� for their performance in this area: More than 80% of graduate level programs also earned this failing grade. 

鈥淭eachers need to know how to do more than just follow the steps in math to get the right answer,鈥� Heather Peske, the organization鈥檚 president, said in a statement. 鈥淭hey need to know why those steps work. It鈥檚 like the difference between a basketball player and a coach. The player can learn their role and follow directions, but the coach needs to understand the bigger picture, the why behind every move.鈥�

Michael Rubin, principal of Uxbridge High School in Massachusetts, roughly 60 miles southwest of Boston, said finding high-quality teachers of any subject is difficult, particularly in math and science.  

鈥淲hen we deal with even more advanced levels of mathematics, with highly specialized content, the number of educators is even more limited,鈥� he said. 鈥淢y father was a math teacher for 39 years, and not a year has gone by since he retired nine years ago where a principal has not reached out and asked him if he is willing or able to come in to teach, tutor or substitute.鈥�

Indeed, Gallup poll responders said the problem was even more acute in later grades where the math curriculum gets harder: 64% of principals said this was 鈥渧ery challenging鈥� at the high school level versus 56% at the middle school and 23% at the elementary level.

The struggle can also be seen in lower-income and rural communities, like Sheridan County School District #3 in Clearmont, Wyoming, which enrolls just 83 students K-12. Chase Christensen, who serves as both superintendent and district principal, said staff are frequently asked to take on other roles.

Next fall, he said, a physical education teacher will lead advanced mathematics classes 鈥� they will focus on pre-algebra, geometry, statistics and probability 鈥� at the middle school level while he works toward earning his certification in that subject. Christensen said he鈥檚 grateful for his staff鈥檚鈥� flexibility. 

鈥淲hen we all sit down and take a hard look at what the needs of the school are, people just step up and we figure out how it is going to work,鈥� he said.  

Stephanie Marken, a senior partner at Gallup leading its U.S. custom research division, said schools鈥� trouble finding quality math instructors is particularly concerning because these teachers play a pivotal role in making this often tough subject palatable.  

鈥淚f you have a highly engaged teacher who鈥檚 really committed and qualified in that subject area, we know that it brings math education to life in a way that you just can鈥檛 do otherwise,鈥� Marken said. 

Math anxiety, the fear that students 鈥� 鈥� share about this subject further harms their opportunity and ability to succeed in it. 

鈥淲e know that a lot of students have negative emotions surrounding math and that there鈥檚 a lot of pressure that math places upon students,鈥� Marken said. 鈥淲e know that the teacher makes a big difference in breaking down math and making it feel really relevant and achievable.鈥�

Paxton, of Colorado Springs, said her district employs several strategies to manage the problem. It supports teachers on visas and those coming from alternative certification pathways through monthly meetings that focus on best practices, classroom management and cultural assimilation. 

It also works with which has, for three decades, recruited college graduates to teach in high-need schools for two years. Plus, it’s built a solid relationship with its local university鈥檚 teacher training program and has launched a 鈥済row your own鈥� pipeline to support teacher aides in earning their bachelor鈥檚 degrees, completing internships in the district and ultimately becoming licensed teachers there.

鈥淭hese layered supports and creative recruitment efforts are our response to a national challenge,鈥� Paxton said. 

Gallup鈥檚 Math Matters Study went beyond schools鈥� issues with hiring to families鈥� experience on campus: While roughly a third of the 808 parents who responded said their children receive some math tutoring, only 13% received such help more than weekly. Gallup notes that prior research shows  high-quality math tutoring can improve achievement by an additional three to 15 months of learning, 鈥渂ut the most impactful tutoring programs must include frequent sessions 鈥� three times a week or more.鈥�

Roughly a third of parents said they would enroll their child in tutoring if it was available or more accessible.

Parents also reported a lack of communication about the subject on the part of educators: One in six said they 鈥渘ever鈥� hear from their child鈥檚 school about the goals for their child鈥檚 math learning or what their student is learning in math class. 

The survey showed, too, a lack of understanding 鈥� and consensus 鈥� among educators about what constitutes high-quality instructional materials, curriculum aligned to college- and career-ready standards: 37% of all education leaders said they were 鈥渘ot at all familiar鈥� with or 鈥渘ot very familiar with鈥� the concept. 

Sixty-eight percent of school superintendents and 46% of school principals said their building or district had no official definition of the term. But when supplied with a definition by Gallup, which identified high-quality instructional materials as those 鈥渨hich are standards-aligned and use evidence-based practices for the content area,” 69% said most or all of their math curriculum qualified. 

Professional development proved an added challenge. Thirty-nine percent of educators surveyed rated their own school鈥檚 math-related professional development as 鈥渇air鈥� or 鈥減oor.鈥� This statistic was worse at the high school level where 6% said it was poor and 39% said it was fair. 

The Gates Foundation sponsored the Math Matters Study and provides financial support to 社区黑料.

That鈥檚 one of the top-line findings from a from the Urban Institute, which sought to understand whether devoting resources to children鈥檚 health and social development yields greater benefits than devoting resources to their cognitive development; the study also looks at what aspects of a child鈥檚 cognitive development play relatively larger roles in their adult outcomes.聽

Researchers found that math scores have a significant predictive impact on earnings into adulthood. That finding holds true for children of all races and ethnicities 鈥� including for Hispanic children who consistently experience the largest gains 鈥� and for girls, who tend to see a higher earnings boost than boys. 

鈥淢ath scores seem to matter a good bit,鈥� says Gregory Acs, vice president for income and benefits at the Urban Institute and one of the lead authors of the policy paper. 鈥淓verything matters a little, but cognitive skills seem to matter a lot.鈥�

The findings, which replicate a longstanding correlation between math and adult success, come as school districts across the country consider ways to provide more effective math instruction, especially in the early elementary years, and build a stronger connection in the K-12 setting to local workforce needs.

Specifically, the analysis shows that improving math scores by 0.5 standard deviation for children up to age 12 is associated with larger increases on earnings by age 30 than other equivalent improvements. 

The impact also increases as children get older. For example, a half standard deviation increase in preschool math scores raises earnings by 2.5 percent, while a half standard deviation increase in middle childhood raises earnings by 3.5 percent. A 3.5 percent increase corresponds to about $1,200 a year in additional earnings for the average adult. Notably, girls see a greater increase in adulthood earnings from an improvement in math scores than boys 鈥� more than three-quarters of a percentage point at every life stage.

The same cannot be said for the earnings impact of improving reading scores, which actually diminishes as students get older, falling from 0.9 percent (about $300) to 0.5 percent (less than $200) from ages 5 to 11. Meanwhile, the impact of health and social relationships are consistent but modest as children get older. 鈥淚t鈥檚 not an enormous impact, but it鈥檚 an impact,鈥� Acs says. 鈥淲ould you pass up a 3 percent raise?鈥�

鈥淚t consistently shows that things you do early in life do ripple through,鈥� he continued. 鈥淎nd even when you might not see a clear causal pathway,鈥� he says, 鈥渋t鈥檚 a good framework for understanding how early life stuff matters.鈥�

The analysis bolsters previous research touting a correlation between math and earnings later in life and gives policymakers much to think over as they choose among interventions aimed at benefiting children in the short or long term, as well as when might be the most effective moment to unleash those targeted interventions. 

鈥淚t is useful to see what are the curricular options and where you can intervene in kids鈥� lives early on if you want to have a long term impact,鈥� Acs says. 鈥淎nd it does show that improvements in childhood and elementary school do matter and carry on into earnings.鈥�

For example, Acs says, it may be worth making bigger investments in math in later grades given that improvements in middle school have a more significant impact on earnings than in preschool. And for school leaders looking to make a dent in the earnings gap between men and women, it鈥檚 important to know that increasing math scores in childhood consistently raises the adult earnings of girls by a greater percentage than those of boys 鈥� even if in absolute dollar terms, increasing math scores raises boys鈥� earnings, too. 

In the wake of the recent 鈥渟cience of reading鈥� overhaul that shifted how educators teach students to read, policymakers are increasingly setting their gaze on math pedagogy. improved slowly between 1990 and 2013 and then plateaued, only to fall sharply during the pandemic. On average, students lost in math between 2019 and 2022. The most vulnerable students fell even further behind, exacerbating racial and socioeconomic inequities. 

Recovery has been stubborn and slow. Students recorded the largest drop ever in math scores on the National Assessment of Educational Progress last year, to their lowest levels in more than three decades.

鈥淲e always talk about this amazing predictive power of early mathematics,鈥� says DeAnn Huinker, professor of math instruction at University of Wisconsin-Milwaukee and director of the Center for Math and Science Education Research. 鈥淎nd I think we’ve taken math identity and agency away from kids, and just squashed the love that you find in 3-, 4- and 5-year-olds when they鈥檙e exploring numbers. Kids just really get turned off of mathematics, so I think we’re fighting that right now.鈥�

Education policy experts, lawmakers and business leaders agree that the nation needs to drive improvements in K-12 math to remain competitive in an increasingly technical global economy. On the most recent internationally benchmarked , known as the PISA, Americans scored lower than students from 36 other countries. And Defense Department officials are concerned about Americans鈥� contempt for math, warning that it has serious implications for national security, including .

Looking ahead, the Bureau of Labor Statistics shows that the number of jobs in so-called 鈥渕ath occupations鈥� is set to increase by 29% by 2031, or by roughly 30,000 jobs per year 鈥� a faster clip than for other occupations. 

Though the debate over how to correct course is ongoing, experts say that the way schools are currently teaching math doesn鈥檛 work very well; further complicating the problem is the fact that many teachers who seek out positions in early elementary grades 鈥� the important foundational math years 鈥� do so because they don鈥檛 like math. Teachers should move away from procedural learning that involves rote memorization, Huinker and others say, and focus instead on conceptual understanding, which helps students recognize underlying math relationships, and developing a positive math identity.

鈥淭he number one goal is to really get at this deeper understanding of mathematics,鈥� she says. 鈥淲e want kids to make sense of the mathematical ideas that they’re exploring and learning about. So not rote learning, not memorizing, not worksheets. We do a lot that still is perhaps bad practice in early mathematics.鈥�

Huinker says she hopes research like that from the Urban Institute鈥檚 analysis crystalizes for policymakers and school leaders the importance of getting math instruction right 鈥� especially in the early years.

鈥淥ne thing that鈥檚 starting to really be more acknowledged is the importance of early mathematics and its predictive power for the long term,鈥� she says. 鈥淭here’s so much emphasis on reading and literacy, which is super important, but it kind of always overshadows mathematics. The crux of all of this early childhood, elementary and middle math is ensuring that kids feel empowered with agency to make sense of mathematics, to question, to explore, to really think of themselves as confident in that.鈥� 

鈥淗ow many do you have? One鈥wo..three鈥our,鈥� Johnson says, before they place another bear in the row. 鈥淲hat if we add more? What comes after four?鈥�

Johnson smiles when Mayeda replies with 鈥渇ive.鈥� The stealth math lesson is working. Mayeda 鈥渁dded鈥� a bear and is starting to understand, in subtle ways, the very early basics of addition.

鈥淭hey think it’s play,鈥� Johnson said, stepping away to let Mayeda line up bears on her own.. 鈥淭hey don’t always understand that they’re actually learning things.鈥�

Math lessons like this, disguised as a fun activity playing with colorful bears, should be a regular part of preschool, math experts say, especially as older students across the U.S. struggle with math after the pandemic.

But such lessons are a rarity. Preschools devote just five percent of time to math skills, after observing 77 preschool classrooms in seven states 鈥�  Arizona, California, Massachusetts, Nebraska, North Carolina, Ohio and Virginia. 

The researchers from four universities also found math instruction between 2018 and 2020 rarely went beyond the most basic math skills, like learning numbers, counting and identifying shapes, which are important for students to learn, but stop short of what most four-year-olds can do. 

鈥淭hey鈥檙e getting hardly any math,鈥� said Michelle Mazzocco, a professor at the University of Minnesota鈥檚 Institute of Child Development and co-author of the study. 

While some may see doing basic counting for a few minutes a day as the right thing for most preschoolers, Mazzocco and other national math advocates say it鈥檚 a lost opportunity.

With falling scores on math tests such as the international Programme for International Student Assessment (PISA) tests – which dropped between 2018 and 2022 by two-thirds of a year鈥檚 worth of learning – teaching basic math in preschool, if done well, can make it easier to understand advanced lessons later, Mazzoco said. When presented as games or play, even four-year-olds can learn basic concepts behind math tasks like measurement, geometry,  addition and subtraction.

鈥淪ome of those children who struggle with math are struggling because they got off to a slow start,鈥� Mazzocco said. 鈥淭hat can be diminished.鈥�

鈥淲e need to make sure that preschoolers have more opportunities to engage their natural inquisitive interest in math, to do so regularly and frequently in developmentally appropriate ways,鈥� she said.

Latrenda Knighten, the president-elect of the National Council of Teachers of Mathematics, agreed students can learn math concepts at a young age and preschools should teach much more of it. She doesn鈥檛 expect a math learning revolution similar to the 鈥渟cience of reading鈥� across the country, but wants math to be a priority, even in preschool.

Though there are vigorous debates over how preschool gains in all subjects fade over time, Knighten said. But if students learn more math early on, and kindergarten and later grades build on that knowledge, not just re-teach it, scores should go up, she said. Preschool math also provides an early start on learning critical thinking, problem-solving and recognizing patterns that pays off later, she said.

鈥淵ou hear a lot about literacy, literacy, literacy,鈥� said Knighten, a former elementary school math coach. 鈥淚n an ideal world, you maybe turn those wheels and give math the focus that we’ve had on reading for so long.鈥� 

Historically, preschool math has been a low priority, both because of the traditional focus on reading but also because preschool is often viewed as child care or play-based more than an academic program. States don鈥檛 require preschool and few pay for it, so just 35 percent of four year olds nationally attend preschool, according to the National Institutes for Early Childhood Research at Rutgers University.

There鈥檚 also no national consensus on what students at that age should be taught. The nation鈥檚 last attempt at setting national education standards, the Common Core movement, faced opposition to its kindergarten through 12th grade standards and skipped preschool altogether.

Even the National Council of Teachers of Mathematics promoted math skills starting in kindergarten from 1980 to 2000, before adding preschool in 2000.

The council and many states now have specific recommendations about what preschoolers should learn about numbers and shapes and measurement.

Consider counting, for example. Counting can be just memorizing and reciting a list of names assigned to each number. But the council and states also want preschoolers to learn that each number stands for a real quantity of items. They can be taught that each item should be counted once 鈥� not a few times or counting several items as one 鈥� which is a common mistake four-year-olds can make.

They can also be taught that the count of one group can be more than or less than the count of another. 

Doug Clements, a professor at the University of Denver and co-author of the highly-regarded Building Blocks preschool math curriculum, said it is easy to underestimate what preschoolers can learn.

鈥淭here’s a common misunderstanding that in preschool you learn to count, then in kindergarten you count higher, and then in first grade you can learn arithmetic,鈥� he said. If you give students a narrative, a story behind a problem, he said, and let them use objects to see things physically, they can understand math concepts well.

鈥淧eople think that arithmetic is a vertical – a three, then a plus sign, two, bar under it, then fill in the numeral 鈥� which is not what I’m talking about,鈥� he said.

Teachers can ask four-year-olds, for example, if they have five toys and give a friend two, how many they have left.

The colored bears in Johnson鈥檚 class, a common tool for preschools,  offer a chance to show, without any lecture or worksheets, that objects can be sorted by color or size, that a row of six bears, for example, is larger than a row of four bears and that 鈥渁dding鈥� another bear to a row changes the number to a higher one.

It sounds simple, but teachers need to be intentional about how they handle 鈥減lay鈥� like this, Knighten said.

鈥淚t takes the teacher understanding what’s happening and knowing the right questions to pose to student,鈥� she said. 鈥淢aybe ask them, 鈥榃hat can you tell me about how you’ve arranged these bears or these cars or whatever they’re playing with? Do you have more of one than you have the other? How do you know you have more?  How can you show me?鈥� And that鈥檚 not even bringing out paper or pencil, it’s just understanding the math that a child at ages two, three or four is capable of understanding and how to provide opportunities for them to explore those things.鈥� 

The counting bears are one of dozens of toys and games packed into the math closet at the Fairmount Early Childhood Center in Beachwood, Ohio, just a few miles from Johnson鈥檚 Head Start class.

There, students count off jumping jacks and toe touches to reinforce quantity. Children at one table glue decorations to printouts of the number one to reinforce how the number looks. In another classroom, three-year-olds pick through a box of different-colored blocks of different shapes and line them up in rows by shape and color, counting how many they have placed in each row as they go. 

Teacher Rosanne Stark guides students nearby in the earliest stages of another math skill 鈥� measurement. Today, three-year-olds pick between shorter and longer rectangles of colored paper and glue them to a sheet under columns labeled 鈥渟horter鈥� or 鈥渓onger.鈥�

鈥淲ould you say that’s on a long strip or a short strip?鈥� Stark asks a student. 鈥淟ong. Good job. So we’re going to glue it on.鈥�

Clements said comparing lengths with activities like this is a good start.

鈥淭hen we move on to actual measurement, which is assigning a number to the length of something,鈥� he said. That can happen first by attaching several, say five, blocks together to see if something is longer or shorter than five blocks, then 鈥渁dding鈥� or subtracting blocks to the right size.

鈥淭hey can show you in the count of cubes,鈥� he said. 鈥淚t’s a very concrete measurement. It’s very easy to understand conceptually for kids, because it makes sense to them.鈥�

How much impact preschool math has, though, is unclear. Researchers can point to multiple studies showing preschool math leads to better math performance in kindergarten and in elementary school, sometimes as late as eighth grade. But as with preschool overall, other studies show students taking preschool math don鈥檛 end up further ahead than other students in later grades. This so-called 鈥渇ade鈥� plagues most debates over whether preschool is worth the effort or cost.

Tyler Watts, an assistant professor at Columbia University鈥檚 Teachers College who is researching the effects of early math, said advantages sometimes nearly vanish by fifth grade. He and others are trying to figure out why.

鈥淚 don’t think it’s totally clear, to be honest with you,鈥� he said. 鈥淚 think it’s a hard problem to figure out.鈥�

While he鈥檚 still a supporter of preschool and preschool math, Watts believes 鈥� like Mazzocco and Knighten suggested – that it can be the first of many steps in improving math lessons over several years.

鈥淚f the goal is improving, say, math achievement in grade eight, I think you’re going to need to work on that all the way from PreK through grade eight,鈥� he said. 鈥淚 don’t think PreK is going to work as kind of like a low-cost silver bullet for that problem.鈥�

There鈥檚 another challenge to making preschool math better and more common 鈥� preparing teachers. Knighten said that in her time as a math coach in Louisiana, she found many gravitate toward teaching reading because they thought they were 鈥渂ad at math鈥� when they were in school and view it as an ordeal, Knighten said.

That鈥檚 why the council partnered with the National Association for the Education of Young Children this year to offer for teachers on topics like and .

鈥淚f we actually provide teachers with more confidence in their ability to teach mathematics to students,鈥� Knighten said. 鈥淭hen, of course, that means that they’ll spend more time on those activities with students, and students will actually get more of those beginning, foundational experiences.鈥�

The survey, conducted by the research and public relations firm Global Strategy Group, was commissioned by the Bill & Melinda Gates Foundation. Many of its themes 鈥� including the necessity of math skills in both promising career paths and the demands of everyday life 鈥� by the Foundation over the past six months, after its leaders announced a major refocusing of resources toward post-pandemic math recovery last fall. Standardized tests like the National Assessment of Educational Progress have shown steep declines in math achievement during the COVID era.

Angela Kuefler, a partner at Global Strategy Group, said on a call with reporters that existing methods of teaching math were regarded as 鈥渦nengaging, outdated, not connected to the real-world experiences that kids are having or will have.鈥� 

鈥淧arents especially鈥on’t feel like their kids are getting fully adequate preparation for what they will need to succeed later in life,” Kuefler said.

Asked to choose among a list of academic subjects, 60 percent of the survey sample (over 730 teachers and 800 parents) named math as either 鈥渆xtremely important鈥� or 鈥渧ery important,鈥� more than for any other discipline. Ninety-three percent of parents (and 94 percent of teachers) also agreed that 鈥渨hen students succeed in math, they are more likely to succeed later in life.鈥�

But math was also the most frequently named subject that needed 鈥渦pdating and improvement鈥� in how it is taught, according to respondents; 56 percent listed math, far more than career and technical education (41 percent), social studies and history (36 percent), English (35 percent), science (31 percent) and the arts (14 percent).

In the main, complaints about math education related to its applicability to the world that students live in. While over 60 percent of the survey鈥檚 participants said that math should be relevant to the real world, just 21 percent said that it currently is. The subject was similarly described as less useful and engaging than it ideally would be, while sizable minorities of parents and teachers described our current approach to math as complicated, boring, useless and irrelevant.

Some of those sentiments were echoed in accompanying focus groups that Global Strategy conducted with parents of varying racial and socioeconomic backgrounds. Participants cited by the Foundation described their children鈥檚 math coursework as 鈥渁 chore, instead of a challenge,鈥� noting that compelling instruction 鈥渄oes not reach all students.鈥� 

The influential philanthropy has already embraced the task of overhauling math education, awarding large grants to organizations like the and the that aim to make math more culturally relevant to disadvantaged and minority students. Some of those efforts have also come under criticism from some conservatives, that the project could weaken math standards and harm student outcomes.

But Bob Hughes, the Foundation鈥檚 director of K鈥�12 education, cited the 鈥渁bysmal鈥� data on student learning loss as evidence that more dramatic interventions were necessary.

鈥淧arents, teachers, and the general public see a disconnect between the math education they believe our young people need to thrive and the one that students are actually experiencing in too many classrooms,鈥� Hughes said. 鈥淧arents and educators point to a solution: Making math education more relevant for students and more connected to the real world.鈥�

I know, looking to our state for inspiration isn鈥檛 generally a natural instinct. After all, we ranked 52nd in the nation in elementary math on the in 2019. On the 2022 assessment, however, Alabama . Furthermore, the state’s fourth-graders lost no ground in math even as students nationally saw steep declines amid the pandemic.

This progress isn’t happening by chance. Alabama’s leaders and educators are working hard to bring about continued positive change. In 2019, they improved the state standards, making them more rigorous and aligned with those used to develop the Nation鈥檚 Report Card, also known as the National Assessment of Educational Standards. Districts then started moving to better, standards-aligned instructional resources. 

The state also created a that is aligned with those standards, and some schools used pandemic relief funding for digital math tools and math specialists. Last spring, policymakers passed the , designed to improve math instruction in a comprehensive way.

While many states have laws aimed at improving literacy, Alabama , few have taken similar steps to systematically improve math instruction.

The hope is that the new math law will drive continued progress among Alabama students, much as the literacy law has led to reading . The law establishes a state task force that will ensure teachers get strong training and evidence-based resources in their classrooms to improve math instruction. The task force is sharing information about high-quality curriculum and assessment systems and is designing professional development programs to ensure teachers have substantial math knowledge and teaching practices. 

All elementary schools will get math coaches to provide ongoing, on-site support for teachers. K-5 schools serving more than 800 students will get two coaches. The state is also developing an initiative to help qualified classroom teachers become math coaches.

As an elementary school principal and former middle and high school math teacher, I鈥檝e seen firsthand how much teachers need this kind of help. The math taught today is much more rigorous than the math many of us learned as kids. There is greater emphasis on understanding concepts and the application of math, rather than simply memorizing rules and procedures. Teachers need to fully understand math concepts themselves to effectively teach it. 

I鈥檓 fortunate that my school is among those that already has a math coach. I tapped her recently to work with a teacher who just wasn鈥檛 as confident teaching math as she was in reading and other subjects. They worked together over time on areas in which the teacher was struggling, and the improvement was visible.

The coach recently watched one of the teacher’s students perform well on a challenging task. The child鈥檚 eyes lit up; though she had previously struggled in math, confidence was visible on her face. When the teacher and coach discussed the student鈥檚 progress, the teacher cried with joy and explained that before, she would have given the student less rigorous work. She realized the difference she was now able to make in the classroom and in her students鈥� lives because of the coaching she had received.

Moments like these make me so proud of the progress we鈥檙e making.

Other provisions of the new law include improving training for aspiring teachers enrolled in education schools and for principals, especially those in low-performing schools. And there’s a new summer program for fourth- and fifth graders who struggle with math. Grades K-3 students who attend reading literacy camp will also have opportunities to address math gaps 鈥� especially important as summer slide can be a

To gauge the law’s impact, an outside reviewer will study and evaluate these efforts. 

Alabama would not be the first Southern state with high poverty rates and low education rankings to provide inspiration when it comes to addressing an urgent problem facing the schools. Our neighbors in Mississippi led the nation with the passage of a in 2013 that improved reading instruction and propelled the state from last in reading instruction to seeing the in the country.
It takes this kind of systematic, coordinated and funded state support to see large-scale student academic growth across the state. It will also require all who care for children and their education to develop a growth mindset and truly believe that all students can be successful in learning mathematics. Given the pandemic鈥檚 impact on student learning, all states should act now. Although Alabama鈥檚 Numeracy Act is in its infancy, I hope other states will follow our lead.

Here鈥檚 a typical scenario 鈥� a student thrives in elementary math, enjoying manipulatives, games and kid-friendly word problems. Then, the tides change. When more abstract thought enters the equation, the student鈥檚 once-favorite class becomes a source of anxiety and defeat.

In middle school, students also can hit a learning wall due to unaddressed learning gaps. Even before the pandemic, students were arriving in middle school with learning gaps in basic math concepts, according to Shelly Burr, who supports 42 Allegheny County, Pennsylvania, school districts through the Allegheny Intermediate Unit and serves as a certified coach through Harvard. Those basics that weren鈥檛 create barriers to learning new, more complex skills.

Filling those skill gaps while moving through grade-level content is tough.  鈥淚t鈥檚 challenging for teachers to be able to be teaching grade-level content,鈥� Burr says, noting that sometimes they are having to reteach skills from two or three grade levels prior. Middle school math timelines typically involve learning a new skill daily, which doesn鈥檛 account for the progression of skill acquisition, she says.

 While a fresh approach to teacher training is part of the solution, innovative classroom teachers are already making strides in the right direction. Their strategies include using concrete tools to help young minds grasp abstract concepts, giving students choices and shifting mindsets to see mistakes as part of the process.

Teachers Need Guidance to Focus on Key Skills

Burr points out that teachers aren鈥檛 necessarily trained to identify the must-have skills at each grade level to remain math-proficient later. If teachers must prioritize mastery of certain skills over others, knowing which are most essential is key.

 A by the Regional Educational Laboratory Program alongside some Missouri education leaders identified five broad categories: ratios and proportional relationships, the number system, expressions and equations, geometry and statistics/probability. Mastery in these areas was most associated with Algebra I success. 

Burr says, 鈥淭he biggest predictor of algebra success is all the way in terms of their number sense.鈥� 

Concrete tools build abstract understanding

It鈥檚 less likely you鈥檒l see students in middle school playing with tiles, making art and working with their hands, but students at this age still need such activities to succeed in math. Burr encourages teachers to use manipulatives, even during middle school, to help students transition from concrete to abstract understanding. She points to tools like base 10 blocks through fifth grade, a fraction manipulative to help kids 鈥渟ee it in different ways鈥� and . 

If a school could choose only one hands-on tool for middle school, she says, algebra tiles are a must-have for everything from helping to visualize integers to solving multi-step equations. The pandemic also showed educators that virtual algebra tiles could work too.  

Classroom Snapshots Light the Way

We took a look at top practices in middle schools around the country, where teachers are actively working to engage students in math and close learning gaps. Here are some of their go-to strategies for reaching middle-schoolers:

Give Gen Z the immediate feedback they鈥檙e used to 鈥� mistakes and all

Kat Abe, eighth-grade math teacher, Northbrook Middle School, Houston

Using tech tools without direction is like using a Tesla without knowing your destination, Abe jokes. Instead, intentional and immediate feedback through tools like NearPod and Socrative increases engagement and timely improvement in her classroom. She anonymously displays multiple students鈥� work at once with these tools, working with students to identify what went wrong.

鈥淭hey鈥檙e used to being stimulated by technology and wanting that instant feedback, that immediate gratification that comes from some of these tech tools I鈥檓 using,鈥� she says. For Nearpod, she uploads all her lessons, giving feedback in real time. 鈥淭hat鈥檚 a lot different from pen and paper 鈥� where I鈥檓 not reaching all 30 students in the classroom.鈥� She says catching mistakes immediately leads to 鈥渋ntentional discourse鈥� around their work, rather than presenting her own. 

Building a culture where 鈥淢istakes Are Totally Hot,鈥� a math acronym she uses, is normalized because every day students see both mistakes and exemplars. The tech tools she uses lend themselves to naturally catching mistakes as they happen, so students are used to both making them and getting that immediate feedback. She also doesn鈥檛 use homework, as students get so much practice and feedback during class.

Drawing from non-math subjects to make the abstract concrete 

Elisa Murphy, director of teaching and learning, New York City Charter School of the Arts

Negative numbers can be challenging for middle-schoolers, Murphy says. 鈥淚t鈥檚 really hard to understand why when you subtract a negative number, it becomes positive 鈥� that doesn鈥檛 make any sense.鈥� But it鈥檚 easier when kids have concrete analogies like submarines going underwater, or making soup hotter or colder with ice cubes. 

Kids also are encouraged to create their own real-life examples of math in action, often with a music or art connection. For example, seventh-grade math teachers wanted students to use proportions in a project. Some used scale factors to enlarge their own drawings. Others played a piece of music to demonstrate  intervals, or the ratio of frequencies in the pitches that make up a musical chord. In a third option, students scaled up a recipe to feed the entire class and then cooked it for everyone to enjoy.

In eighth grade, math teachers used an art project to cement students鈥� understanding of transversals, lines that intersect two parallel lines, and the angles they create. Students had to look outside the classroom to find examples of transversals in their home or neighborhood. After photographing their example, they used an online protractor to measure the angles formed, observing whether they were complementary or supplementary to each other.

Solving real-world problems 

Jeanne Huybrechts, chief academic office, Stratford School, with multiple California locations

According to a 2022 student poll conducted by Gradient Learning, over usually don鈥檛 see the relevance of what they are learning in school. 

鈥淲hen Stratford middle school students ask their math teachers, 鈥榃hy do we have to learn this?鈥�  we think they deserve an answer,鈥� Huybrechts says. 鈥淭eachers regularly integrate real-world problems that illustrate the usefulness of the principles, thus making the math courses seem much more relevant.鈥�

For example, one popular exercise is to design a smartphone and calculate the amount of storage needed.  In another unit, students design a solar panel-covered roof, calculating the pitch necessary to optimize energy capture. She says this helps to alleviate the abstractness of both algebra and geometry courses in middle school.

Setting goals and tracking mastery

Sarah Breslin, assistant principal, Brooklyn Lab Middle School, New York

When Breslin saw a discrepancy between students鈥� classroom 鈥渆xit tickets鈥� and their interim assessment performance, she worked with teachers to build a professional development plan. The program, called Shift the Lift, refers to moving the mental load of solving the problems from the teacher to the student. It鈥檚 designed to help teachers spot the specific standards that stump students most often and to help them embrace a growth mindset as they work to master them.

Teachers set 鈥渉yper-specific goals鈥� for each student, push independent practice and use exit tickets two to three times a week to measure progress toward those goals, she says. The exit tickets measure how well students master the topic at hand and evaluate their work habits. Breslin says that when students begin Shift the Lift, on average, only about 55% meet expectations. Just five weeks later, that number routinely grows to 89%.

Letting students decide how to demonstrate their understanding

Ashley Barattini and April Regan, eighth-grade co-teachers, The Urban Assembly School for Leadership & Empowerment, Brooklyn

It鈥檚 not every day you see a summative assessment in the form of a podcast, brochure, Tik Tok or sewing project. But that鈥檚 the norm for Barattini and Regan鈥檚 students, where choice is a fundamental aspect of increasing engagement in middle school math. Barattini recalls a student last year who looked at the options for testing and instead proposed an embroidery project demonstrating her new math knowledge. The teachers were more than happy to oblige. 

From scavenger hunts to stations, mini-lessons with the whole group to smaller learning groups, 鈥済iving them options to show their knowledge and show the way they鈥檙e learning math and making sense of it鈥� is key, Regan says. Lessons in their classroom last a maximum of 10 minutes, and they give homework only every few weeks, around five to six questions, one from each lesson they鈥檝e recently taught for extra practice. 

Says Regan, 鈥淚 love hearing at the end of an activity, a student being like, 鈥楢ctually, this was really fun today.鈥欌��

This piece originally appeared on .

The scores offer more discouraging evidence from NAEP, often referred to as 鈥渢he Nation鈥檚 Report Card.鈥� Various iterations of the exam, each tracking different subjects and age groups over several years, have now shown flat or falling numbers. 

The latest release comes from NAEP鈥檚 2020 assessment of long-term trends, which was administered by the National Center for Education Statistics to nine- and 13-year-olds before COVID-19 first shuttered schools last spring. In a Wednesday media call, NCES Commissioner Peggy Carr told reporters that 13-year-olds had never before seen declines on the assessment, and the results were so startling that she had her staff double-check the results.

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鈥淚 asked them to go back and check because I wanted to be sure,鈥� Carr recalled. 鈥淚’ve been reporting these results for…decades, and I’ve never reported a decline like this.”

The eight-year gap between 2020鈥檚 exam and its predecessor, in 2012, is the longest interval that has ever passed between successive rounds of the long-term trend assessment; a round that was originally scheduled for 2016 was for budgetary reasons. Given the length of time between exams and the general trend of increasing scores over multiple decades, observers could have expected to see at least some upward movement.

Instead, both reading and math results for nine-year-olds have made no headway; scores were flat for every ethnic and gender subgroup of younger children 鈥� with the exception of nine-year-old girls, who scored five points worse on math than they had in 2012. Their dip in performance produced a gender gap for the age group that did not exist on the test鈥檚 last iteration.

More ominous were the results for 13-year-olds, who experienced statistically significant drops of three and five points in reading and math, respectively. Compared with math performance in 2012, boys overall lost five points, and girls overall lost six points. Black students dropped eight points and Hispanic students four points; both decreases widened their score gap with white students, whose scores were statistically unchanged from 2012.

In keeping with previous NAEP releases, the scores also showed significant drops in performance among low-performing test-takers. Most disturbing: Declines among 13-year-olds scoring at the 10th percentile of reading mean that the group鈥檚 literacy performance is not significantly improved compared with 1971, when the test was first administered. In all other age/subject configurations, students placing at all levels of the achievement spectrum have gained ground over the last half-century.

鈥淚t’s really a matter for national concern, this high percentage of students who are not reaching even what I think we’d consider the lowest levels of proficiency,” said George Bohrnstedt, a senior vice president and institute fellow at the American Institutes for Research.  

Tom Loveless, an education researcher and former director of the Brookings Institution鈥檚 Brown Center on Education Policy, said that the reversals in math performance were particularly disappointing because they defied NAEP鈥檚 recent trends. For roughly the last three decades, even as politicians and education policy mavens have emphasized literacy instruction, comparatively rapid growth in math scores have made that subject 鈥渢he star of the show,鈥� Loveless said. 

鈥淣ow it almost appears as if those gains are now unwinding, they’re going away. And I don’t think anyone has been able to identify why that’s happening.” 

Bohrnstedt who has followed NAEP for much of his career, said the declines in 13-year-old math performance was notable for another reason: The long-term trends assessment, which been administered by NCES for a half-century, differs substantively from from the content found on other versions of the test. Reflecting the way math was taught in the 1970s, the assessment features more naked math problems and less complex problem-solving than the so-called 鈥渕ain NAEP,鈥� which is administered to fourth- and eighth-graders every two years.

“For the most part, it’s a more basic kind of math than is being taught today, so it’s disappointing to see that we’re still seeing this poor performance by large percentages of our children,” Bohrnstedt said.

Overall, Loveless said, the combination of flat scores on the biennial 鈥渕ain NAEP鈥� and significant declines on this version of the test indicates that American math instruction changed direction over the last decade in a way that may have stymied learning. While hesitating to blame the Common Core curricular reforms that spread during the Obama administration 鈥� he recently wrote on the oft-maligned learning standards 鈥� Loveless called for further research to investigate possible causes.

鈥淭o me, it suggests that beginning a decade or so ago, something went wrong with how we teach math to younger students,鈥� he said. 鈥淢y own hypothesis is that an emphasis on conceptual understanding has gone too far, that without computational skills to anchor math concepts, students get lost.鈥�

Michael Petrilli, head of the reform-oriented Thomas B. Fordham Institute and a defender of the Common Core standards, said that the results could reflect an alternative theory: That the social and financial overhang of the Great Recession profoundly disrupted skills formation for children who are now reaching their teen years. 

鈥淎ssuming that Common Core wasn’t implemented until about 2013, the 13-year-olds wouldn’t have been exposed to it until about second grade,鈥� Petrilli wrote in an email. 鈥淭he nine-year-olds, on the other hand, got it from kindergarten. So why are the 9 year olds holding steady?鈥�

鈥榁ery Discouraging鈥�

Perhaps the most striking revelation from the release is the continued divergence in scores between students at the top and bottom of the performance distribution 鈥� a phenomenon that Commissioner Carr called 鈥渨ell-established鈥� during Wednesday鈥檚 media session. 

Throughout all four age and subject configurations, when average scores for most students were stagnant, scores for the lowest-performing students were down; when scores for most students were down, scores for the lowest-performing plummeted.

In nine-year-old reading, where average scores remained unchanged from 2012 鈥� and scores for the top-performing students ticked up a point 鈥� those for students scoring at the 10th percentile fell seven points. The same students lost six points in math, while 13-year-olds scoring at the 10th percentile dropped five points in reading and an astonishing 12 points in math.

Even comparatively low-performers at higher levels lost ground in some respects. Nine-year-olds marked at the 25th percentile dropped four points in math, while 13-year-olds at the 25th and 50th percentiles lost eight and five points, respectively, in the subject. 

“It’s very discouraging to see this steep drop at the 10th percentile in both reading and mathematics, but especially in mathematics,鈥� Bohrnstedt concluded. 鈥淚t also confirms what we’ve seen with respect to the high percentage of kids performing at the ‘below basic’ level in the main NAEP.鈥� 

The long-term assessment is a crucial piece of data for another reason: It was administered to students between October 2019 and March 2020, making it a final snapshot of academic trends before the emergence of COVID-19. Loveless said he hoped future analyses of how kids learned during and after the greatest disaster in K-12 history wouldn鈥檛 overlook the 鈥渄eeper,鈥� persistent stagnation that preceded it.

鈥淭hese scores represent the last valid, national assessment of student achievement pre-pandemic. For that reason, they will take on historical significance as a baseline measure when future analysts attempt to gauge the impact of the pandemic on student learning.鈥�