In suburban Howard County, Maryland, lots of students take calculus in high school. Or at least, lots of white and Asian students do. In 2011, African American and Hispanic students made up about 30 percent of the public school district's enrollment but only about 11.3 percent of calculus students, according to the U.S. Education Department.

Renee Foose, superintendent of the Howard County Public School System, recently asked Harvard's Center for Education Policy Research to investigate the disparity. The researchers tracked student test scores and course choices from senior year all the way back to elementary school.

"There's a remarkable finding here, which is that actually the achievement gap in Howard County, with regard to math, doesn't seem to grow over time," said Christopher Avery, lead author of the unpublished study. The district seems to be doing a good job enrolling strong math students in tough math courses.

But although the gap doesn't grow, it's persistent. And it emerges when children are young. "Success in the high school classes—the more advanced ones—actually has its roots in the third and fourth grade," Avery says.

Math experts disagree on whether calculus, usually a college course, should be taught in high school. In 2012, the Mathematical Association of America and the National Council of Teachers of Mathematics—two professional associations that focus on teaching—took the position that the goal of a K-12 math curriculum shouldn't be to get students through calculus but to give students a strong foundation that will prepare them for a range of college majors.

Even so, most educators agree that more students would benefit from a rigorous math background. Tracing the sequence of courses that leads to calculus in part reveals why it's so difficult to increase the share of students taking advanced high school math classes.

Here's how the pathway to calculus works in one school district, and what teachers and administrators are doing to make it more accessible. Howard County encompasses 76 schools and more than 50,000 children, nearly 20 percent of whom are low-income.

Foose has made elementary-school education a big priority. Last fall, the district's six most diverse elementary schools began to teach children in kindergarten through second grade using a new model: Instead of spending the day with a single teacher, students had one teacher for math and science, and another for reading and social studies.

When teachers have specialties, they can concentrate on improving instruction, administrators say. "It's more-focused professional learning," said Grace Chesney, a top district administrator. The elementary-school overhaul also includes an expansion of preschool at five of the six sites.

To be on track to take advanced math in high school, students need to leave third grade performing at or above grade level for math and enter it already up to par for reading, Foose said. "We know students will do better in math if they have a firm understanding of reading."

It's hard to measure how much math students know before third grade. But by that year, standardized-test scores show a racial and socioeconomic divide in math achievement. About 5 percent of African American, Hispanic, and low-income third-graders score in the top 25 percent of math test takers, the Harvard study found, compared with about one-quarter of Asian students.

After third grade, students start to be formally grouped according to their math ability. Howard County's school district offers two levels of acceleration: honors, which means students learn material one year above grade level, and gifted and talented, which means two. In the past, placement in fourth-grade gifted and talented math wasn't entirely objective; teachers selected certain students to take the placement test. Now, on top of making the test mandatory for all kids, the district is using additional data to track the students.

By the time they hit fourth or fifth grade, students always have the opportunity to transition in and out of accelerated math. But particularly when children are young, a lot of those transitions are dictated by parents. Parents can petition the school, hire private tutors, or enroll their children in summer school to try to move their child to a higher-level class.

Howard County teachers and administrators are trying to educate all families about the importance of math, so more parents can advocate for their children. They're also trying to eliminate bureaucratic decisions that might move students out of an advanced track unnecessarily. "When we made our fifth-grade teachers aware of what the impact was long term, immediately 1,000 more students were placed in a more rigorous [math] pathway," said Bill Barnes, who coordinates high school math programs for the district.

The Harvard study found that it's extremely rare for students who don't take their first algebra course in middle school to go on to take Advanced Placement (AP) calculus. The College Board's AP program includes two calculus courses: AB and BC, the latter covering more material.

The traditional progression to AP calculus begins with algebra and continues with one year of geometry, a second year of algebra, and a year of pre-calculus. Howard County students typically take AB before they take BC. So if you assume a student takes BC her senior year, and count backward, you'll find that she should really take algebra in the seventh grade.

Sure enough, the Harvard study found that students who take algebra in seventh grade are much more likely to take BC calculus. The study also found that students who take algebra in middle school were likely to be white, Asian, and affluent, and that standardized test scores in middle school tracked the same disparities that emerged in third grade.

High school isn't too late for students to accelerate in math. Students can double up, or take summer school courses; this might be a time when a student matures and starts to apply himself, or decides he wants to be an engineer. But those success stories are the exception rather than the rule.

If the goal is to get more kids to take AP calculus, or AP statistics, there has to be a systemwide effort, says Tom Sankey, the head of Mt. Hebron High School's math department. The Common Core math curriculum aligns well with calculus, which he thinks might help prepare students for the class.

He's hopeful that, with time, Howard County's calculus classes will reflect the district's racial and socioeconomic diversity just as they now reflect its gender balance. "This is my 35th year at Mt. Hebron. And I remember not that many years ago that women were the underrepresented groups," Sankey said. That's not an issue anymore.

"This is going to sound really idealistic. However, I think a huge factor in all this is the teacher and their passion for mathematics. And their belief in high expectations," he said. If teachers are totally in love with their subjects, and broadcast that to students, students can't help but get interested, too. That magic has to happen not just in 12th grade but also in 10th, and eighth, and fourth, and third.