In the Cedars Christian School 7th-grade math class I teach, someone got confused with 2^3and thought it meant 2 + 2 + 2 = 6, whereas it really means 2 · 2 · 2 = 8. That got us going as to how we might use exponential-like notation for all the arithmetic operations, not just multiplication. We might say that
I majored in mathematics in college, but still was surprised when I first learned about "tetration", which is repeated exponents. Likewise, "Pentation" is repeated tetration, ad infinitum...
My conclusion is that exponents are over-emphasized in the grade school curriculum, as any exponent other than 2 or 3 is almost never used in physics, and only has so much perceived utility because of computer modelling.
Maybe they are overemphasized. Where higher exponents are used is with base 2 and, especially, base 10-- scientific notation. That's worth the price of admission.
They are also good for teaching the idea of an inverse, a very hard idea to get across.
I like this :))
I majored in mathematics in college, but still was surprised when I first learned about "tetration", which is repeated exponents. Likewise, "Pentation" is repeated tetration, ad infinitum...
My conclusion is that exponents are over-emphasized in the grade school curriculum, as any exponent other than 2 or 3 is almost never used in physics, and only has so much perceived utility because of computer modelling.
Maybe they are overemphasized. Where higher exponents are used is with base 2 and, especially, base 10-- scientific notation. That's worth the price of admission.
They are also good for teaching the idea of an inverse, a very hard idea to get across.