>Sounds like a return to the "New Math" to me. > >Kent >
Does it really?
My feeling is that *understanding* is far more important than retention of numerical facts. This is hardly "new math." Indeed, I've seen "new math" binary number flashcards, indicating that, even in the era of new math, some teachers were still emphasizing the memorization of computational results.
I've posed questions to junior high students, high school students, and college students such as "Is .95 x 73 going to be larger than 73, smaller than 73, or equal to 73?" It bothers me a great deal that a number of students at each of these levels don't know the answer to this question. It bothers me a lot more than it would to find out that *all* of them have forgotten 7 x 9 = 63.
I am curious to know, Kent, which you feel is more important: that a student knows 7 x 9 = 63, or that a student understands that multiplying a whole number by a factor between 0 and 1 will result in a number that is smaller than the original whole number?
Perhaps my point is clearer when considering division. There are a *lot* of students out there (at various levels of education) who believe that 4 / 36 = 9. They have completely missed the underlying concepts of division. Any student who thinks 4 / 36 = 9 clearly can't picture (either mentally or on paper) what is going on in division. For, how on earth could you divide 4 objects among 36 groups so that there are 9 objects in each group? Perhaps the problem in their thinking stems from the fact that they drill and drill and drill the fact that 36 / 4 = 9, but never (or only briefly) work with modelling division, and exploring properties of division.
If you take a look at some of the old "new math" books, I think you will find that your comparison is not really fair.
Norm Krumpe Indiana University of Pennsylvania Indiana University at Bloomington