Sometimes
teaching polynomials drive me nuts. It
seems like there are a number of “rules” textbooks want them to memorize, and a
number of procedures that are kind of archaic in the age of graphing
calculators.
So for starters:
Factoring the Sum of Cubes or Difference of Cubes.
It seems like the
books want them to memorize this formula for this, and normally I have fallen
in line with this, in some respects it’s not that difficult. But I tried a new plan yesterday – just kind
of struck me as I started to cover this section in class.
I’ll do it here
first with the general case then look at it for a specific case. I decided to see what would happen if I used synthetic division, granted you have to know the binomial factor
but that is virtually staring you in the face. So here we go.
And yes I know I really should factor out the last term, but the purpose of this was to show how synthetic division could be use for this situation. I don't know if this a better process or a more confusing process. I guess I kind of would like feedback on what people think.
Now on with my
continued rant teaching polynomials. Is
it really necessary in this day and age to talk about the Rational Zero Theorem
(p/q rule), Descartes's Rule of signs?
I'm not convinced those are really important any more.
I do believe End
Behavior is important and understanding the essence of the Fundamental Theorem
of Algebra, that polynomials have the same number solutions as the degree of
the polynomial is important, and knowing that complex conjugates come in pairs
is good to know. While I can't say I have completely dissected Common Core, but I get the impression some of of these nitty-gritty details are not part of Common Core, and for the life of me, I'm not sure they are necessary.
What do you think, are these skills necessary? Or are there other skills we need to know with respect to polynomials, their zeros, local minimums and maximums, especially when these features can be found with a graphing calculator?
What do you think, are these skills necessary? Or are there other skills we need to know with respect to polynomials, their zeros, local minimums and maximums, especially when these features can be found with a graphing calculator?
Just curious.
Just finished teaching this. I made students memorize factoring two cubes, but your way makes sense. I had them look at the change of signs of y in a table as to why there would be a zero there so they can have a little bit of an idea what they are doing on their calculator when they tell it to find the zero. I did not do rational zero theorem. I used to and then, I was like why? So, I don't. They are doing well with the unit and liking it. Testing today.
ReplyDeleteThanks for your input. I find the rational zero theorem intriguing, but I'm like you, I just think teaching it or at least testing over it is kind of outdated now that we have graphing calculators. I'm old enough to remember being taught in the 7th grade how to calculate square roots by hand before calculators came along. Yuck! Never used it since, and don't remember nor care to know how it was done.
ReplyDeletebravo
ReplyDelete