Saturday, February 18, 2006
Sad Math
Here is how students are taught to multiply two numbers in the school district where I live. Consider the problem 12 * 34. We can write this as (10 + 2) * (30 + 4). Using the distributive law twice this can be written as 10 * 30 + 10 * 4 + 2 * 30 + 2 * 4 = 300 + 40 + 60 + 8 = 408. A helpful memory aide is FOIL, multiply the First, Outer, Inner and Last pairs of numbers.
Seems like a reasonable approach, and it can actually help to use this technique for mental arithmetic. If you are familiar with the “old” way of multiplication it goes like this: 12 * 34 = (10 + 2) * 34 = 340 + 68 = 408 (assuming the 34 was written above the 12).
The "old" and "new" methods have been around for centuries, but (until recently) the "old" method has been preferred because, well it works better.
The number of multiplications and additions for the new method scales with the number of digits in the bottom number. With the new number the number of operations scales with the number of digits squared (albeit they are simpler operations). If you are planning to multiply anything large than two digit numbers you want to use the "old" method.
Whatever the logic behind the switch the students in 6th grade do not know how to multiply three digit numbers and they do not know how to divide. (Long division? Are you CRAZY?). The curriculum simply does not provide for those two skills.
There are several root problems. Parents, for the most part, hate math. Elementary teachers, for the most part, hate math and it only takes one to ruin an entire cohort of students for the subject. The progressive education system rejects any kind of rote learning or systematic procedure like times tables or long division.
Net result is students do not know the basic math facts like 6*7, do not have any reliable algorithms to solve problems and get a near constant diet of negative feedback about the subject.
The oldest charter school in this district was started, in part, because parents were justifiably horrified by math education in the other public schools. That school emphasizes traditional math education. It has a large waiting list and ranks at the very top in all rankings of academic performance.
Seems like a reasonable approach, and it can actually help to use this technique for mental arithmetic. If you are familiar with the “old” way of multiplication it goes like this: 12 * 34 = (10 + 2) * 34 = 340 + 68 = 408 (assuming the 34 was written above the 12).
The "old" and "new" methods have been around for centuries, but (until recently) the "old" method has been preferred because, well it works better.
The number of multiplications and additions for the new method scales with the number of digits in the bottom number. With the new number the number of operations scales with the number of digits squared (albeit they are simpler operations). If you are planning to multiply anything large than two digit numbers you want to use the "old" method.
Whatever the logic behind the switch the students in 6th grade do not know how to multiply three digit numbers and they do not know how to divide. (Long division? Are you CRAZY?). The curriculum simply does not provide for those two skills.
There are several root problems. Parents, for the most part, hate math. Elementary teachers, for the most part, hate math and it only takes one to ruin an entire cohort of students for the subject. The progressive education system rejects any kind of rote learning or systematic procedure like times tables or long division.
Net result is students do not know the basic math facts like 6*7, do not have any reliable algorithms to solve problems and get a near constant diet of negative feedback about the subject.
The oldest charter school in this district was started, in part, because parents were justifiably horrified by math education in the other public schools. That school emphasizes traditional math education. It has a large waiting list and ranks at the very top in all rankings of academic performance.
// posted by Old Math @ 11:37 AM 
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This is paralleled in language arts by the omission of grammar & mechanics for pretty much the same reasons you give for math. What's weird is that while eschewing rote learning (parts of speech, distinct sentence structures, specific punctuation rules), the mandated assessments test for exactly that kind of material -- which is not in the curriculum.
I grew up on the new math, but after a while in college I started thinking in old math. It is easier to come up with the answer this way, and this is the reason some of the older mathematics teachers I have had, always could do math real quick in their heads.
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