Don't knock rote mathematics. 'Busy Work' in most other fields is called 'practice'. And like all things, practice is the key to improving a skill. Repetition, memorization and muscle memory are all key fundamentals.
If your son wants to be a quarterback, you practice throwing a football. Over and over again with slight variations to the angle, distance and speed. A meaningless procession of skill building that builds the muscle memory and "know how" required to be successful at the more complex task of managing a game and leading an offence, which is what a quarterback really does. You can't be good at throwing to a receiver on a button hook or on a screen play if you are still mastering how to manipulate the speed and position of the ball as it leaves your hand.
We would laugh in the face of anyone that suggests otherwise.
Your brain is no different. It needs practice in the basics before it can progress to more advanced topics. You need to spell before you can write a story, and you need to know addition and multiplication before you can perform calculus. The basics for math need to be implanted in your brain for immediate retrieval, so that your processing power can focus on the higher level task.
It's not enough just to know that "there" can be spelled three different ways. To be a good writer, you need to know instantly which one to use when, otherwise you just simply aren't very efficient. Likewise, a person needs to know instantly that 8 and 64 have a distinct factor/product relationship to be able to understand that a rectangular floor with an 8 foot length, 3 foot width and total area of 64 square feet cannot possibly exist and has been measured incorrectly before you proceed to buy all that carpet.
The most skilled in any field have the greatest mastery of the basics. Mathematics is no exception.
Don't knock rote mathematics. 'Busy Work' in most other fields is called 'practice'. And like all things, practice is the key to improving a skill. Repetition, memorization and muscle memory are all key fundamentals.
If your son wants to be a quarterback, you practice throwing a football. Over and over again with slight variations to the angle, distance and speed. A meaningless procession of skill building that builds the muscle memory and "know how" required to be successful at the more complex task of managing a game and leading an offence, which is what a quarterback really does. You can't be good at throwing to a receiver on a button hook or on a screen play if you are still mastering how to manipulate the speed and position of the ball as it leaves your hand.
We would laugh in the face of anyone that suggests otherwise.
Your brain is no different. It needs practice in the basics before it can progress to more advanced topics. You need to spell before you can write a story, and you need to know addition and multiplication before you can perform calculus. The basics for math need to be implanted in your brain for immediate retrieval, so that your processing power can focus on the higher level task.
It's not enough just to know that "there" can be spelled three different ways. To be a good writer, you need to know instantly which one to use when, otherwise you just simply aren't very efficient. Likewise, a person needs to know instantly that 8 and 64 have a distinct factor/product relationship to be able to understand that a rectangular floor with an 8 foot length, 3 foot width and total area of 64 square feet cannot possibly exist and has been measured incorrectly before you proceed to buy all that carpet.
The most skilled in any field have the greatest mastery of the basics. Mathematics is no exception.