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He and his students jointly pledge to bring "INTENSITY and DESIRE" to class, starting the year with a calculus banquet and a "circle of blessings" from parents. Yet Winn is strict. Every student signs a contract for the class, promising to review for the exam at school on a few Saturdays. He insists that homework has to be turned in before the bell rings.

One fear many educators have had about privatizing the community college model is that doing so might serve only wealthy, white students.

“Still, we wanted to ramp up our associate degree program but didn’t want to put start-up money into it. We thought we had an interesting concept and looked to partner with an investment group to get start-up funds and also get the enrollment moving along faster. We’ve always been a fairly entrepreneurial institution and have been willing to look at new options and opportunities.”

I wanted a partner that we would be comfortable with and for them to understand our commitment to keeping our reputation.”

All academic responsibilities and management, including course design and instruction, are controlled by Tiffin, which has hired additional faculty for Ivy Bridge. The “Cadillac enrollment management” of the college, as Slone calls it, is controlled by Altius.

he says his biggest challenge is determining how much remediation the institution should offer its least prepared students.

“Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.”

“Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning.”

“Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure,” and “Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and shortcuts.”

Missing entirely from the practice standards is a discussion of how to pose problems, and, more generally, how to ask powerful questions. This is a telling oversight. Unlike in school, real problems are not served up on a platter, fully formed. The standards-writers overlooked the most basic fact of people with genuine math expertise: They find problems!

Is it too late to change this? I hope not. Solving our problem of poor mathematics education depends upon it.

Tests are less relevant to concrete life and work skills than the ability to write a coherent essay, which requires being able to identify a problem, break it down to its constituent parts, analyze it from multiple angles and assemble a solution in a succinct manner to communicate across cultures and time.

The kids were so wedded to formulas that they couldn't step back and reason through a problem without them.

Mathematicians call it a lack of number sense, an intuitive feel for numbers and how they relate to each other.

To get kids thinking more deeply about math, Einstein started using new math textbooks this year. Instead of teaching students a new algorithm and drilling them on it in problem after problem, it poses open questions that can be solved multiple ways. That forces kids to figure out what strategies fit a problem, instead of just mechanically following steps.

"Now there are fewer problems — but they really have to think."

Einstein isn't the only school taking algebra on earlier. San Diego Unified is also changing its elementary school curriculum to ease younger kids into algebraic reasoning. Thousands of teachers have been trained in the new methods, which link algebra to every grade.

Mr. McAllister, the student blogger at Trinity, uses his iPhone's camera as a document scanner, with an app called JotNot Pro. After he takes a picture of a page of text, the app (which costs 99 cents), can turn it into a PDF file for easy review later.

A company named Inkling creates textbooks made for iPads, with interactive features and videos—things that paper volumes cannot do.

Brainstorming for classroom talks has gone high-tech with "mind mapping" software that encourages arranging thoughts and ideas in nonlinear diagrams. These programs have been available for years on laptops and desktop computers, but some professors say the touch-screen interface of smartphones or tablet computers enhances the process, letting scholars toss around ideas with a flick of the finger. Gerald C. Gannod, director of mobile learning at Miami University, in Ohio, recommends Thinking Space for Android devices, MindBlowing for the iPhone, and Popplet for the iPad. Mr. Delwiche, of Trinity University, likes MindJet.

And six middle schools in four California cities (San Francisco, Long Beach, Fresno and Riverside) are teaching the first iPad-only algebra course, developed by Houghton Mifflin Harcourt.