On Wed, Oct 24, 2012 at 5:41 AM, Robert Hansen <email@example.com> wrote: ... > I don't consider the teaching and learning of formulas to be algebra at all. > Just because it has letters in it doesn't make it algebra. >
I don't care what your definition of algebra is. Call using letters of the alphabet whatever you want.
This skill of being able to handle formulas or expressions in which even all the elements of the expression are letters of the alphabet should not be put off unnecessarily, for what should be obvious reasons.
> The teaching or learning of methods or techniques like being able to > solve for x in such as > > > 53/100 = 37/x > > in just one step is not algebra foolishness. (Equal fractions with one > of the denominators being 100 is a standard set-up in percent > > > > You meant to say "pretend to solve for x", right? Or are you pretending to > us that you just taught them to "solve"? This is my point. When you are > > walking through the steps to "solve" for x,
Although the phrase "solve for x" can and does have a number of different uses, one main use is simply through one or more transformations of equations to obtain an equation such that the variable in question is on one side of the equation and everything else is on the other side of the equation.
There is no pretend here. This skill in general is very important and there is nothing pretend about it, regardless of whether you want to call it an algebraic skill.
In fact, not being to perform this skill or at least quickly and easily is one of the main reasons people have problems in mathematics.
The vast majority of people that I have shown some of these quicker and easier ways with respect to this skill have responded positively to it. One adult student in particular told me that he would have had a much easier time of it in chemistry in high school had he discovered these methods on his own or been shown them. (This, since in chemistry and other sciences, needing to solve for an unknown - in the sense I mean above, transforming the formulas, so so present.)
> I am not against formulas for fraction arithmetic, but they must be > developed arithmetically, not algebraically. In your example above, the > student must "simply see" when and where to multiply or divide. >
There is a way of doing things with respect to isolating target variables that does not going through all that multiplying and/or dividing both sides of the equation to isolate the target variable. I shared some of these ideas at math-learn almost ten years ago - see all my posts in the following thread in 2003:
I suspect that you will show the same type of hostility to such ideas as these that make things so much easier and quicker for so many people, the same hostility I have received from so many in terms of making it easier and quicker to perform various skills. I wrote about this also at math-learn in 2005 - see not just this post but all my posts in this thread, including my post that started the thread: