Whether or not the PE teacher is using sound pedagogy, the fact is that no child will leave that elementary school saying "I can't run" or "I can't do push-ups." Unless they have a serious physical ailment, they will all leave knowing that regardless of personal achievement level, basic athletic skills are a universal part of being human.
Many, many students reach middle or high school saying "I can't sing" or "I can't draw." These skills are no less universal than running or jumping jacks, but millions of adults and future adults believe they are somehow deficient.
Singing is universal. Making art is universal. We are failing our society by letting our children think otherwise.
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