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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.

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.

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.

Students spend more time on things they don't understand and less time on things they have already mastered.

Students get assistance when they encounter problems.

Students are required to do math.

Lord Kelvin once made the observation, “If you can measure that of which you speak and express it in numbers, you know something about your subject; but if you cannot measure it, your knowledge is of a very meager and unsatisfactory kind.” If he is correct, then our knowledge about how, and to what extent, the use of information technology in teaching and learning affects outcomes—both learning and cost—is meager indeed.

Hispanic students who were part of the College Assistance Migrant Program (CAMP) historically had been unsuccessful in math courses. During the fall 2002 semester, however, students in the redesigned Intermediate Algebra course had an unprecedented 80 percent pass rate, compared to a prior 70 percent rate

SIX MODELS FOR COURSE REDESIGNSupplemental: Add to the current structure and/or change the contentReplacement: Blend face-to-face with online activitiesEmporium: Move all classes to a lab settingFully Online: Conduct all (or most) learning activities onlineBuffet: Mix and match according to student preferencesLinked Workshop: Replace developmental courses with just-in-time workshops http://www.theNCAT.org/PlanRes/R2R_ModCrsRed.htm

FIVE PRINCIPLES OF SUCCESSFUL COURSE REDESIGNRedesign the whole course.Encourage active learning.Provide students with individualized assistance.Build in ongoing assessment and prompt (automated) feedback.Ensure sufficient time on task and monitor student progress. http://www.theNCAT.org/PlanRes/R2R_PrinCR.htm

At Alabama, the success rate (grades of C– or better) for African-American freshmen in the redesigned course was substantially higher than for white freshmen, despite the fact that the African-American students were less prepared when they entered the course (on a math placement exam, 20 percent of Caucasian freshmen scored less than 200, versus 41 percent of African Americans). In fall 2000, 71.4 percent of African-American freshmen were successful, versus 51.8 percent of Caucasian freshmen; in fall 2001, it was 70 percent versus 65.3 percent.

Students learn math by doing math, not by listening to someone talk about doing math.