See quotes below; I have to jump in with what I know about this issue. (I have taught algebra to community college students for over 20 years; some of these students -- about 20% -- never had algebra previously.)
I think we are missing some key points. A variable is not simply a letter standing for a number. When we say "P = 2L + 2W", we are making a statement about a relationship between quantities, any one of which might be a "variable". Furthermore, not all "variables" imply that we will find a solution. Both of these issues are challenging to the first time student, but are critical if there is any hope of being able to apply algebra.
Further comments are given below the quotes.
firstname.lastname@example.org wrote: > > Hi Bonnie, I would definitely start with concrete things. Remember the > blocks with hexagons and paarallelograms? You could use them or cuisenaire > rods or anything. After getting comfortable with the rrelative sizes > between them, assign a nmber value to a few. Then have her grab a handful > and count them up, i.e., four yellows, three orange ones, two greens. Then > write that out. 4Y +3O +2g. I've seen this work. Eventualllly she will > substitute with no fear. You will robabyl have to trick her into this by > tellling her it's parenting and not math so the anxiety doesn't get > triggered. Or tell her it's geometry, not algebra. > > Have fun!! Martha> Point: This transition is fairly easy, but is entirely too dangerous. A student says that "4Y" means "4 yellow ones", and makes two assumptions: 1) That the variable is always 1. 2) That the variable is a label. Hopefully, you can see the danger in the first assumption. For the second, look at the situation of working with money invested in accounts earning interest (say, at 5%). The "label" interpretation is that x is 5%; when I tell the student that the interest is ".05x", the student tells me this can't be true! If you use this type of transition to variables, you need to provide a corrective package later to make sure the student has a more complete understanding of "variable."
> >Has anyone run in to a case like the student I have had who seems unable > >to do any math that has unknowns or variables in it? She is mid 40s, > >very bright, English major going on to a Masters program. She can do all > >sorts of computations including fractions, percentages, ratios, and word > >problems are some of her favorite things to do. But as soon as you give > >her something like 4 + 2x - 6 + 5x= 95, she is totally frozen. She can't > >get past go when trying to combine like terms, and reacts physically > >(anxiety, tears, etc.) She has recently been tested (instrument unknown > >to me at this point) by our local Special Ed teacher to see if there is > >some way to pinpoint what the cognitive problem is. She has started math > >class with me three times, but hasn't been able to stay with it long > >enough for me to get to try some alternative approaches. > >I look forward to any thoughts you might have on this. > > > >Bonnie Fortini (14-e) I have seen this, as well. I would suggest, however, that the problem is not likely to be "cognitive" in the sense that there are skills or processes missing (or erroneous). The problem often deals with emotional trauma which has been paired up with "algebra" -- which is like a person who can't deal with a certain model of car because of an earlier trauma; it's not a property of algebra, but it is a strong association that is challenging to breakdown. Often, a student with moderate anxiety can be helped just by learning that most people feel math anxiety -- including their teachers. Situations involving more extensive trauma, however, are best passed along to counseling professionals.
Thanks for your attention!
-- <<<<<<<<<<<<<<<<<<<< from >>>>>>>>>>>>>>>>>>>> Jack Rotman phone (517)483-1079 Math Professor ROTMAN@ALPHA.LANSING.CC.MI.US Lansing Community College Lansing, MI "Like all art & science, mathematics surrounds us." <<<<<<<<<<<<<<<< Math Success ! >>>>>>>>>>>>>>>>> dept web page http://www.lansing.cc.mi.us/sas/mathsci