THE D.C. school system’s experiment with a longer school day has produced encouraging results. Seven of eight schools with extended-day programming for the 2012- 2013 school year showed improvement in math and reading. As a group, students with an extended day posted gains on achievement tests that far outstripped those in schools with traditional hours.

None of that, though, seems to matter to the Washington Teachers’ Union. Nor does the fact that teachers in these schools willingly signed on to the new hours or that they were paid for their extra effort. For reasons that are impossible to fathom, the union is resisting — unfortunately, with some success — plans to expand this initiative.

Giving public school students more instruction time is a priority of D.C. Schools Chancellor Kaya Henderson. She set aside $5.1 million in next year’s budget for the effort. But, as The Post’s Emma Brown reported, the union, an affiliate of the American Federation of Teachers, is blocking the initiative by urging teachers not to approve the change and by preventing the issue from coming to a vote.

Let’s emphasize that last point: The union that is supposed to represent the interest of teachers won’t allow a vote in which teachers would decide for themselves, school by school, if they want a longer school day that would benefit students and for which they would be paid. A provision in the teachers’ contract, which expired in 2012 but is in force until a new agreement is reached, allows individual schools to adopt nontraditional scheduling if two-thirds of teachers approve.

It is a sensible approach that recognizes that not every school may need the extra hours and that schools should have flexibility in designing a schedule that best meets the needs of their students. As successful public charter schools have demonstrated, extra instructional time can help lift the achievement of poor and struggling students. Nonetheless, the union is opposed. Union President Elizabeth Davis claims it is “being cautious not to be [a roadblock] to reform.” We sure would hate to see what happens when it is being incautious.

Ms. Henderson called the union’s opposition “shortsighted” in that teachers whose students make gains because of extended learning stand to earn bonuses. We suggest that teachers’ jobs might also be in play, since the more students who are attracted to charter schools, many of which have longer school days, the less need there is for teachers in the traditional school system.

Teachers have rightly argued they should be treated like professionals, that they should be listened to and that they should be fairly compensated. It’s a case they need to make to their own union representatives.