The proposal, which could go into effect as early as next school year, would allow four years of sports to count as elective credits toward graduation instead of the current maximum of two years.
The board's 10-5 vote followed often emotional debate, with both Dallas members - Republican Geraldine Miller and Democrat Mavis Knight - voting no.
Supporters said the move would keep kids in school and spur them to do well in academic courses. Critics charged that the plan would de-emphasize academics and return to the days of "football comes first."
Ms. Miller was among the most vocal opponents, insisting the plan would "completely dismantle" many of the education reforms enacted in Texas over the last two decades.
"This takes us back to the way things used to be," she said. "Our school reform movement put everything in perspective, with academics coming first. Now, we are opening the door to water down all the efforts we have made to strengthen standards in our schools."
But Craig Agnew, the Brenham High School coach and teacher who petitioned the board to adopt the rule, said an "unfair burden" exists for student athletes who must meet stringent course requirements to retain their athletic eligibility.
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