A new school year has begun with plenty of promise. Students are returning to classrooms ready to learn, build on what they know, and move one step closer to a diploma that opens doors.

Nationwide, too many students are crossing the graduation stage without the math skills they need for college, careers or financial independence.

On This Day in History — 2024

New Jersey is a powerful example. Though state leaders take a victory lap about a graduation rate above 90 percent, the state’s assessment shows that only six in 10 juniors are “graduation ready” in math.

“By lowering the bar for what it takes to graduate high school,” a new report found, the high graduation rate “is obscuring the fact that New Jersey, like some other states, has diminished what it means to earn a diploma.”

The report was commissioned by the Collaborative for Student Success.

New Jersey is hardly the exception. An independent 50-state analysis last spring found wide gaps between four-year graduation rates and math proficiency among high school students. California graduates 86 percent of students, but only 30 percent meet state expectations in math — a 56-point gap. Florida graduates 90 percent, while 44 percent meet or exceed standards in algebra and geometry. New York graduates 86 percent, but just 56 percent meet expectations on the Algebra I exam.

The list goes on. Alabama has a 67-point gap. Kansas has a 69-point gap. The District of Columbia has a staggering 71-point gap.

A diploma is supposed to signal that a student is prepared for what comes next, whether college, training or employment. Too often, it has become the bookend of a high school career, concealing unfinished learning. The result is a math deficit that gets punted down the road.

At Rutgers University, placement data reviewed in the New Jersey report show more incoming students beginning below calculus than before the pandemic, including larger shares assigned to elementary algebra, intermediate algebra and precalculus. Students who thought their high school grades showed readiness now face prerequisite courses that can delay or shut them out of majors in science, business, engineering, computer science and health fields.

Alex Kontorovich, the chair of the Department of Mathematics at Rutgers, says that many incoming students are hitting a wall.

“For them, it’s incredibly frustrating — not to mention costly — to learn that they have to take non-credit-bearing courses just to catch up, or even change majors entirely,” he said.

Costly in a big way. Median annual wages in math-focused occupations are more than double those across all occupations — $107,570 compared with $50,980 — and employment in those fields is projected to grow far faster over the next decade.

The solution is multifaceted.

First, states should maintain honest, comparable academic standards and resist lowering passing scores on statewide assessments to protect graduation statistics. Test results must reach parents and educators quickly enough to trigger tutoring or summer learning well before senior year.

Second, students who demonstrate readiness for advanced math should be enrolled automatically. Too many districts make students jump through unnecessary hoops, costing them opportunities to deepen their knowledge and prepare for demanding college programs and careers.

Third, districts should adopt high-quality math materials and invest in sustained teacher training. Weak curricula and uneven instruction compound math deficits.

Colleges and employers need graduates with durable math skills. Most of all, students need diplomas that open doors rather than hide the fact that schools left them unprepared to walk through them.