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Now, lets convert back: It is absurd that a high school biology teacher had not learned how to change centimeters to meters; -- unless he too, had been taught by the rule for idiots: "move the decimal two places", in which case, it is predictable. Similarly, 2.365 dollars and 2.365 can be converted to 236.5 cents and 236.5%, resp. "Ratio" and "Proportion" basically, mean that we can set up tables, (as in the previous problems) and then it is valid to multiply or divide a line by a number. Jack and Jill went up the hill to pick apples and pears.The new 1999 California Standards require that students learn this in Grade 4. Jack picked 10 apples 15 pears and Jill picked 20 apples and some pears.
("Right Teacher, Wrong Class", Washington Post, February 15, 1999)This instruction (above) to "move the decimal two places" is what I call an "Avoid-thinking-by-excessive-memorization-of-overly-specialized-procedures" method of mis-education. That students forget much, over the summer, is a good excuse for the next grade's book to be largely a copy of this grade's.
It is popular with traditional textbooks because it is an easy way to teach. Similarly, 236.5 (236 and a half) cents and 236.5% can be converted to 2.365 dollars and 2.365, resp.
This report will present simple, conceptual-understanding based arithmetic methods that will allow students to solve a wide variety of problems.
These better methods of instruction are in the spirit of my version of KISS , that is "Keep It Simple for Students", while emphasizing conceptual-understanding.
Correctly, multiplying numbers when multiplication is not justified is wrong.
Darcy Conant wrote: "Many students -- even 'good' high school students have difficulty with rate problems.
Next is the same type of problem, except that the word "proportion" is used instead of the word "ratio". Physics tells us that weights of objects on the moon are proportional to their weights on Earth. The parenthetical phrase "[on Earth]" is (of course) omitted from instruction.
It must be a complete mystery to them as to why a weight on the moon should be any different than the weight on Earth.
The ratio of apples to pears picked by both Jack and Jill were the same. Solution Jack 10 15 Jill 20 30 Thus, Jill picked 30 pears.
Let's redo this problem with less nice numbers: Problem 10.