Monday, February 27, 2006
Factor Fear
I have been taken to task for using the term "Progressive Education" to describe the modern instructional practices. Progressive education is all about methods that work, since the methods I complain about don't work they are, ipso facto, not Progressive.
As my charges might say: whatever. I readily admit I don't know anything about Education, which is the academic study of how to teach. I am, however, starting to learn something about education, which is the practical art of teaching.
Every number can be written as the product of a unique set of prime numbers. For example the number 60 = 2 x 2 x 3 x 5 and that is the only product of prime numbers that equals 60, discounting permutation of course. This is known as the Fundamental Theorem of Arithmetic. Factors are wonderfully useful for finding common divisors and other basic arithmetical operations.
Note the word arithmetic, this is pretty basic stuff. Factors also show up in higher math, for example every polynomial can be factored into smaller polynomials.
We are learning about factors in the 6th grade special ed class. The kids, for the most part, grasp the concept of a factor and prime numbers but in order to seal the deal they need to practice.
Find the factors of 24. They are 1,2,3,4,6,12.
Is 7 a factor of 135? Divide 135 by 7 and you get a remainder of 2, 7 is not a factor of 135.
Here is my problem: These students do not know times tables. Every time you ask them what is 6 x 4 they must count to 24 by 4s. Using their fingers. Rote learning of times tables, when they were young, was not considered proper modern teaching procedure.
Since they can't do multiplication effortlessly then can't do division easily. Since they can't do division they can't quickly do factors. Without factors they can't do fractions. Without fractions they will fail at algebra. etc.
Learning 50 or so facts about numbers (2x2=4, 2x3=6, etc.) unlocks a whole chain of knowledge. Without those facts everything becomes difficult in math.
The lack of factual knowledge prevents children from learning new conceptual ideas.
Argh.
As my charges might say: whatever. I readily admit I don't know anything about Education, which is the academic study of how to teach. I am, however, starting to learn something about education, which is the practical art of teaching.
Every number can be written as the product of a unique set of prime numbers. For example the number 60 = 2 x 2 x 3 x 5 and that is the only product of prime numbers that equals 60, discounting permutation of course. This is known as the Fundamental Theorem of Arithmetic. Factors are wonderfully useful for finding common divisors and other basic arithmetical operations.
Note the word arithmetic, this is pretty basic stuff. Factors also show up in higher math, for example every polynomial can be factored into smaller polynomials.
We are learning about factors in the 6th grade special ed class. The kids, for the most part, grasp the concept of a factor and prime numbers but in order to seal the deal they need to practice.
Find the factors of 24. They are 1,2,3,4,6,12.
Is 7 a factor of 135? Divide 135 by 7 and you get a remainder of 2, 7 is not a factor of 135.
Here is my problem: These students do not know times tables. Every time you ask them what is 6 x 4 they must count to 24 by 4s. Using their fingers. Rote learning of times tables, when they were young, was not considered proper modern teaching procedure.
Since they can't do multiplication effortlessly then can't do division easily. Since they can't do division they can't quickly do factors. Without factors they can't do fractions. Without fractions they will fail at algebra. etc.
Learning 50 or so facts about numbers (2x2=4, 2x3=6, etc.) unlocks a whole chain of knowledge. Without those facts everything becomes difficult in math.
The lack of factual knowledge prevents children from learning new conceptual ideas.
Argh.
// posted by Old Math @ 3:32 PM 
