“After a few questions we could very quickly figure out what level you are at and the optimal piece of content for teaching,” Mr. Ferreira said. “The more you worked with the system, the better our profile of you got and the more we could give you better and better content.”

Nonetheless, Knewton ran into financial difficulties and was sold in May to the education publisher Wiley. Mr. Ferreira said the company’s troubles were not because its technology did not work, but because the company had relied heavily on one customer, which dropped Knewton in favor of an in-house system. Mr. Ferreira, 51, left to start Bakpax.

At its core, Bakpax is a computer vision system that converts handwriting to text and interprets what the student meant to say. The system’s auto-grader teaches itself how to score.

“Instead of handing your homework in, you just take a picture of it on your phone, and a few seconds later we can tell you what you got right and what you got wrong,” Mr. Ferreira said. “We can even tell you what the right answer is for the ones you got wrong.”

Mrs. Turner said her students loved the immediacy. The system also gathers data over time that allows teachers to see where a class is having trouble or compare one class’s performance with another. “There’s a lot of power in all this information that, right now, literally is just thrown in the trash every day,” Mr. Ferreira said.