4 ms·

Not sure what's the point of section 4.3 Factoring Trinomials introducing "trial and error (or guess and check) method", when this task can be solved easily wit

by Miiko 5y ago

Not sure what's the point of section 4.3 Factoring Trinomials introducing "trial and error (or guess and check) method", when this task can be solved easily without any trial and errors, by using 6.2 Quadratic Formula. Shouldn't section 4.3 at least mention that possibility? Is there something I do not understand here?

throaway46546 5y ago
Guess and check pissed me off so much back when I was in school.
- xphos 5y ago
  I think guess and check pissed you off because its taught as guess a random number and check they don't really teach you how to guess smartly and then you waste your time guessing in the wrong direction mindlessly. Its like teaching stands they should checkout every array slot when there are bits of knowledge that you can teach to do a binary search and get to an answer faster. And the math intuition to build the pattern of guessing is much less especially for high school level problems.
  - throaway46546 5y ago
    I just wrote a TI83 program to solve the equation and then spit out a couple randomized "guesses" so I could "show my work".
xphos 5y ago
Try factoring this with the quadratic formula x^5+5x^4+10x^3+10x^2+5x+1. Or try guess and check with -1,0,1. The issue with formula's is that they constrain the space of the problems and ones mind especially. the problem above is factoring is (x+1)^5 but there exists no (and there cannot exist) formula to that can tell you that from the equation. Algebra is taught poorly not because kids don't learn the steps but because it stunts people into viewing math as if you only had the formula its easier. I'm not saying you should know that there cannot exist a 5'th or greater degree integer formula for factoring equations because to say that is very hard. But when it leaves students with very little scaffolding to use when things go wrong / don't fit the formula neatly
- Miiko 5y ago
  > Try factoring this with the quadratic formula x^5+5x^4+10x^3+10x^2+5x+1. But this is not a trinomial and, of course, quadratic formula is not applicable here. My objection was specifically for section 4.3, which does not provide any clues how to extend the described method to more complex polynomials anyway. > The issue with formula's is that they constrain the space of the problems and ones mind especially. That I agree with - teaching only to use formulas is bad, - but how to find polynomial roots is not relevant here. The proper way to teach factorization is IMHO to show relations to roots first - which are not necessary to be found by quadratic formula, it may be the same trial and error method, - instead of introducing a special method that works only in very limited cases. > Algebra is taught poorly not because kids don't learn the steps but because it stunts people into viewing math as if you only had the formula its easier. Err... learning some steps (without explaining where they come from) is not a proper way to tech math anyway, and I surely do not advocate that. My point was different - instead of teaching some steps to solve particular problem (factoring trinomials), the better approach is to teach the underlying theory and real methods used in modern mathematics. That is, instead of using factorization as a method of solving polynomial equation, the proper approach is exactly the opposite, using equation roots for the factorization. Well, at least that's how they taught me to do things, and I do believe this is the correct way.

by Miiko 5y ago

throaway46546 5y ago

Guess and check pissed me off so much back when I was in school.

xphos 5y ago
I think guess and check pissed you off because its taught as guess a random number and check they don't really teach you how to guess smartly and then you waste your time guessing in the wrong direction mindlessly. Its like teaching stands they should checkout every array slot when there are bits of knowledge that you can teach to do a binary search and get to an answer faster. And the math intuition to build the pattern of guessing is much less especially for high school level problems.
- throaway46546 5y ago
  I just wrote a TI83 program to solve the equation and then spit out a couple randomized "guesses" so I could "show my work".

xphos 5y ago

Try factoring this with the quadratic formula x^5+5x^4+10x^3+10x^2+5x+1. Or try guess and check with -1,0,1. The issue with formula's is that they constrain the space of the problems and ones mind especially. the problem above is factoring is (x+1)^5 but there exists no (and there cannot exist) formula to that can tell you that from the equation. Algebra is taught poorly not because kids don't learn the steps but because it stunts people into viewing math as if you only had the formula its easier. I'm not saying you should know that there cannot exist a 5'th or greater degree integer formula for factoring equations because to say that is very hard. But when it leaves students with very little scaffolding to use when things go wrong / don't fit the formula neatly

Miiko 5y ago
> Try factoring this with the quadratic formula x^5+5x^4+10x^3+10x^2+5x+1. But this is not a trinomial and, of course, quadratic formula is not applicable here. My objection was specifically for section 4.3, which does not provide any clues how to extend the described method to more complex polynomials anyway. > The issue with formula's is that they constrain the space of the problems and ones mind especially. That I agree with - teaching only to use formulas is bad, - but how to find polynomial roots is not relevant here. The proper way to teach factorization is IMHO to show relations to roots first - which are not necessary to be found by quadratic formula, it may be the same trial and error method, - instead of introducing a special method that works only in very limited cases. > Algebra is taught poorly not because kids don't learn the steps but because it stunts people into viewing math as if you only had the formula its easier. Err... learning some steps (without explaining where they come from) is not a proper way to tech math anyway, and I surely do not advocate that. My point was different - instead of teaching some steps to solve particular problem (factoring trinomials), the better approach is to teach the underlying theory and real methods used in modern mathematics. That is, instead of using factorization as a method of solving polynomial equation, the proper approach is exactly the opposite, using equation roots for the factorization. Well, at least that's how they taught me to do things, and I do believe this is the correct way.