Originally posted by: dullard
This is one of those areas in math where students can be destroyed by a bad teacher. Most teachers will try to quickly show the students 5-6 different methods to solve this same problem. They give each student a couple problems with each method, and then expect them to be able to solve the problem with any method. I've even seen the teacher give a 0 on a test for a student having the correct answer but whom did not a method that was taught in class.
What happens? The students get confused, don't know what method to use or why, and give up entirely on math. They think they are "bad" at math. But in reality, they had a bad teacher. And this is one point where many people make this decision to hate math forever.
Watch your daughter and her teacher. Make certain your daughter can solve that problem correctly with ONE method. Then have her use that method repeatedly. For the rest of her life, she'll be able to solve that type of problem correctly. Even if that means she is a bit less efficient - she can still solve it. And, she won't hate math.
I disagree. The elimination method leads to guassian elimination when working with 3 or more equations with 3 or more unknowns. However, that method will not work when solving a system of equations such as
y=x^2 + 3x -5
2x + 3y = 15
Furthermore, in the former case of a system of equations, the substitution method does not lend itself well to
2x + 3y + 4z = 12
3x - 2y +8z = 11
5x + 6y = 9z = 15
While I wouldn't necessarily give a student a zero for using the wrong method, I feel it's important to learn both of those techniques, along with a graphical approach (graph the lines, see where they cross.) I make my expectations very well known to the students - they need to know how to use each method, and if I say "use the elimination method" or "use the substitution method", they better know which way I mean. I'll give about 20% of the credit for a correct answer, 20% for checking the answer, and they'll lose 60% for using the wrong method. I also attempt to convey to them the reason that they need to use both methods (using two examples similar to what I have above.) I point out that the first of those two examples is something we'll be doing about a month later, and the second example is just a slightly more advanced version of the elimination method, but we won't touch it until pre-calculus (unless anyone wants to learn it during their lunch period.)
Of course, on a test with about 8 system of equations questions, I only dictate which way to solve the system of equations for one each of the two methods. 2 of the systems require a slight rearrangement to use either method (either line everything up, else divide by 2 or 3 to get an x= or a y=) And, of course, the other four problems are word problems.
edit: for what it's worth, my test on this topic is Wednesday this week. I have only 1 student who isn't capable of at least a 90 on this exam. He hasn't done a bit of the homework in 2 weeks. Refuses to pay attention, refuses to take notes, refuses to copy down examples, refuses to open his book, and refuses to come in for extra help during *my* lunchtime when I make myself available to anyone who needs even the slightest bit of extra help. I refuse to give him a high grade if he somehow gets the answers but can't show the work.
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