July 1, 2015

In the 1990s, the Math Wars pitted two philosophies against each other. One side argued for content-based standards -- that elementary school students must memorize multiplication tables by third grade. The other side argued for students to discover math, unfettered by "drill and kill" exercises.

When the new 1994 California Learning Assessment Test trained test graders to award a higher score to a child with a wrong answer (but good essay) than to a student who successfully solved a math problem, but without a cute explanation, the battle was on. New-new math was quickly dubbed "fuzzy crap." By the end of the decade, repentant educators passed solid math standards.

Yet the Math Wars continue in California, as well as in New Jersey, Oregon and elsewhere. In Palo Alto, parent and former Bush education official Ze'ev Wurman is one of a group of parents who oppose the Palo Alto Unified School District Board's April 14 vote to use "Everyday Mathematics" in grades K-5. Wurman recognizes that the "fuzzies" aren't as fuzzy as they used to be, but also believes that state educators who approve math texts "fell asleep at the switch" when they approved the "Everyday" series in 2007.

The "Everyday" approach supports "spiraling" what students learn over as long as two or more years. As an "Everyday" teacher guide explained, "If we can, as a matter of principle and practice, *avoid anxiety about children 'getting' something the first time around*, then children will be more relaxed and pick up part or all of what they need. They may not initially remember it, but with appropriate reminders, they will very likely recall, recognize, and get a better grip on the skill or concept when it comes around again in a new format or application -- as it will!" Those are my italics -- to highlight the "fuzzies'" performance anxiety.

Becki Cohn-Vargas of the Palo Alto schools told me that a majority of a district committee recommended "Everyday Math" after "a very extensive process." "Spiraling" helps students because "it goes deeper each time." Also, the district will closely observe where the new series needs to be supplemented. "We have a lot of confidence in our teachers," she added and the district's high test scores support that.

"Everyday" dissenters object to the program's emphasis on teaching different algorithms to solve equations. A fourth-grade manual supports "low-stress" partial-quotients algorithm, which demonstrates a longer way to divide 158 by 12, by noting that 10 is a partial quotient that yields the number 120, and then encourages students to use other partial quotients -- 2 or 3 -- to find the answer.

"Partial-sums addition" tells students to add 6,802 plus 453 by adding 6,000 and 1,200 (which is 800 plus 400) plus 50 plus 5. Why? Because: "One way is not better than another."

Now, I understand why a teacher would demonstrate these methods to students -- even the ultra-complicated "lattice" method of multiplication (which is even more tedious to explain, so I will spare you). Different approaches can provide students with other ways to understand why 6 times 9 equals 54.

But making students use slow, labor-intensive algorithms is, to me, the sort of mind-numbing exercise likely to instill hatred of math in students. So you see the dividing line in the Math Wars: The fuzzies think that children will crumble and turn on math if you make them memorize math facts in early grades, while traditionalists think students will fall behind in math if they don't learn basics thoroughly and early. Besides, elongating and verbalizing math exercises is the classroom equivalent of getting your teeth drilled.