"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.