Some kids are ready to learn algebra, others haven’t figured out fractions and Johnny can’t add 2 + 2 and get 4. Their teacher is supposed to “differentiate instruction” for students at different levels in the same class. Get smart, writes the Math Curmudgeon. Differentiate by grouping students of similar readiness and ability in the same class.
If one-half of the room is “ready” for what you want to do and the other half is not, no amount of differentiation will cover that gap.
If the “simple” start for one group is too complex for the other, no amount of differentiation will cover that gap.
If “what is known” is too different, differentiation is futile. Those who start out ahead are held back and those who start behind are constantly trying to keep up, repeatedly reminded that “Masahiro and his friends” are the smart ones and that there is no point to trying to learn; one can only cling by the fingertips and hope for partial credit.
If the readiness gap is too wide, “algebra” will be two separate, simultaneous classes learning different things — and neither learning as much as possible, concludes the Curmudgeon. Or it might be three classes.