In my view, yes, and Paul Tough agrees with me in his new book How Children Succeed: Grit, Curiosity and the Hidden Power of Character. To quote,
"Until recently, most economists and psychologists believed that the most important factor in a child’s success was the IQ. This notion is behind our national obsession with test scores. From preschool-admission tests to the SAT and the ACT—even when we tell ourselves as individuals that these tests don’t matter, as a culture we put great faith in them. All because we believe, on some level, that they measure what matters...But the scientists whose work I followed for How Children Succeed have identified a very different set of skills that they believe are crucial to success. They include qualities like persistence, curiosity, conscientiousness, optimism, and self-control. Economists call these non-cognitive skills. Psychologists call them personality traits. Neuroscientists sometimes use the term executive functions. The rest of us often sum them up with the word character.”
Critics argue that these skills cannot be taught, but the ironic thing is that teaching persistence requires, well, persistence, and an adult's inability to model this quality is half the battle. The other half consists of providing ample opportunities to try, fail, and try again, and to help kids build the skills that they need to manage that failure so that instead of crippling them it moves them forward.
Not only can persistence be taught, it should be of paramount importance in today's classrooms.