Launching this month, Hawthorn Leadership School for Girls will offer sixth and seventh-grade girls a rigorous education in science, technology, engineering and math (STEM). But Hawthorn’s curriculum covers more than formulas and algorithms, said founder Mary Danforth Stillman.

“What makes us unique is not that we teach science and math – who doesn’t?” Stillman said. “It’s our approach. We are committed to developing the vital 21st-century skills of collaborating and problem-solving. We believe in learning...