Correction: An earlier version of this column incorrectly referred to the number of AP exams with passing scores at each school. Blake's students passed 660 AP exams across all subjects and Columbia's students passed 524 AP exams across all subjects. The column incorrectly attributed those numbers only to AP calculus.

Walter Fields’s 15-year-old daughter is a sophomore at Columbia High School in Maplewood, N.J. She scored advanced proficient on state math tests in middle school and received an A in algebra in eighth grade.

For reasons that mystify Fields and his wife, their daughter was not recommended for the ninth-grade geometry course that would keep her on the track to Advanced Placement calculus her senior year. Only when they contacted the principal and the math department chair was she placed in that advanced course. The geometry teacher encouraged her dream to become an engineer. She had a B most of the year but slipped to a C because of the demands of lettering in basketball and track, her father said.

Now she is in a fix. Her Algebra 2 teacher made clear on Parents Night, her father said, that “she did not like school sports and suggested students needed to choose between being involved in a sport and being enrolled in her course.” The teacher has proved to be, her father said, very discouraging. His daughter has struggled.

“The teacher’s response to our questions regarding our daughter’s performance was ‘she just doesn’t seem to get it,’ ” Fields said. “When we pressed the teacher she curtly suggested that maybe this wasn’t the right class for our daughter.” Her geometry teacher was apparently so alarmed that she told Fields’s daughter to come see her if she needed help. Fields and his wife are well-educated African Americans. He thinks Columbia High is hindering his daughter’s progress because of her race. He and other parents are preparing to file a lawsuit on that issue. Fifty-six percent of Columbia students are black, but just 14.4 percent of AP calculus students in the 2011-12 school year were of that race. Seventy-three percent were white.

Race is probably a factor, but there is more to it. Consider the difference between Columbia’s AP program and those of Washington area high schools with similar demographics. In the latest Washington Post America’s Most Challenging High Schools list, Columbia had a rating of 1.487, the ratio of the number of AP tests to the number of graduating seniors last year. The AP participation ratio for Blake High School in Montgomery County was 59 percent higher, even though its 29 percent portion of low-income students was similar to Columbia’s 23 percent. Blacks are the largest ethnic group in both schools.

Columbia’s AP exam passing rate is 85 percent. Blake’s is 64 percent. Like many U.S. schools, Columbia restricts access to AP. That produces very high passing rates. Fewer average students are allowed to stretch themselves in an AP course, despite research suggesting that even students who flunk AP exams do better in college because of the experience.

Nearly every public school in the Washington area has opened its AP courses to all students. Fields’s daughter would have no trouble getting into AP calculus at Blake, and she would find teachers at every level eager to help her. At her school, according to her father, she has a teacher who apparently doesn’t care how much she might learn in calculus and prefers to deny her that challenge. She is taking AP history and will take AP English, but her dreams of a career in science or engineering require more math.

South Orange-Maplewood school Superintendent Brian G. Osborne seems interested in his schools becoming more like Blake.

“We recognize the need to encourage all students who want to work hard to take AP classes,” Osborne said. “The high passage rate of 85 percent does indicate that we need to do more to increase access, eliminate barriers and encourage students. Open access to AP courses is one strategy under active consideration.”

Columbia and Blake are nearly identical in size. Blake’s open door last year produced 660 students with passing scores on AP exams across all subjects. Columbia’s restricted-access policy yielded 524. If we as a nation want and need more students in science, math and engineering courses, doesn’t it make sense to encourage more students to challenge themselves in those subjects?