Heffernan left teaching, hoping that some marriage of education and technology might help “level the playing field in American education.” He decided that the only way to close the persistent “achievement gap” between white and minority, high- and low-income students was to offer universal tutoring — to give each student access to his or her own Cristina Lindquist. While hiring a human tutor for every child would be prohibitively expensive, the right computer program could make this possible.

So Heffernan forged ahead, cataloging more than two dozen “moves” Lindquist made to help her students learn (“remind the student of steps they have already completed,” “encourage the student to generalize,” “challenge a correct answer if the tutor suspects guessing”). He incorporated many of these tactics into a computerized tutor — called “Ms. Lindquist” — which became the basis of his doctoral dissertation. When he was hired as an assistant professor at Worcester Polytechnic Institute in Massachusetts, Heffernan continued to work on the program, joined in his efforts by Lindquist, now his wife, who also works at W.P.I. Together they improved the tutor, which they renamed ASSISTments (it assists students while generating an assessment of their progress). Seventeen years after Heffernan first set up his video camera, the computerized tutor he designed has been used by more than 100,000 students, in schools all over the country. “I look at this as just a start,” he told me. But, he added confidently, “we are closing the gap with human tutors.”

Grafton Middle School, a public school in a prosperous town a few miles outside Worcester, has been using ASSISTments since 2010. Last spring, I visited the home of Tyler Rogers, a tall boy with reddish-blond hair who was just finishing seventh grade at Grafton and who used the program to do his math homework. (While ASSISTments has made a few limited forays into tutoring other subjects, it is almost entirely dedicated to teaching math.) His teachers described him as “conscientious” and “mature,” but he had struggled in his pre-algebra class that year. “Sometime last fall, it started to get really hard,” he said as he opened his laptop.

Tyler breezed through the first part of his homework, but 10 questions in he hit a rough patch. “Write the equation in function form: 3x-y=5,” read the problem on the screen. Tyler worked the problem out in pencil first and then typed “5-3x” into the box. The response was instantaneous: “Sorry, wrong answer.” Tyler’s shoulders slumped. He tried again, his pencil scratching the paper. Another answer — “5/3x” — yielded another error message, but a third try, with “3x-5,” worked better. “Correct!” the computer proclaimed.

ASSISTments incorporates many of the findings made by researchers who, spurred by the 1984 Bloom study, set out to discover what tutors do that is so helpful to student learning. First and foremost, they concluded, tutors provide immediate feedback: they let students know whether what they’re doing is right or wrong. Such responsiveness keeps students on track, preventing them from wandering down “garden paths” of unproductive reasoning.

The second important service tutors provide, researchers discovered, is guiding students’ efforts, offering nudges in the right direction. ASSISTments provides this, too, in the form of a “hint” button. Tyler chose not to use it that evening, but if he had, he would have been given a series of clues to the right answer, “scaffolded” to support his own problem-solving efforts. For the answer “5-3x,” the computer responded: “You need to take a closer look at your signs. Notice there is a minus in front of the ‘y.’ ”

Tyler’s father, Chris Rogers, who manages complex networks of computers for a living, is pleased that his son’s homework employs technology. “Everyone works with computers these days,” he told me later. “Tyler might as well get used to using them now.” But his mother, Andrea, is more skeptical. Andrea is studying for a master’s in education and plans to become an elementary-school teacher. She is not opposed to the use of educational technology, but she objects to the flat affect of ASSISTments. In contrast to a human tutor, who has a nearly infinite number of potential responses to a student’s difficulties, the program is equipped with only a few. If a solution to a problem is typed incorrectly — say, with an extra space — the computer stubbornly returns the “Sorry, incorrect answer” message, though a human would recognize the answer as right. “In the beginning, when Tyler was first learning to use ASSISTments, there was a lot of frustration,” Andrea says. “I would sit there with him for hours, helping him. A computer can’t tell when you’re confused or frustrated or bored.”