From: Kristina (for Teacher2Teacher Service)
Date: Nov 03, 2000 at 10:42:32
Subject: Re: Teaching algebra in middle school

Hi Alice,

Here's another response for you about teaching algebra at the middle school
level. It focuses more on how to appropriately introduce algebra regardless
of the age of the student.

 -Kristina, for the T2T service


J.D. wrote:

Teaching Algebra to beginning algebra students (5th grade to adults) should 
not be formal.  The problem with teaching Algebra to beginning students is 
that we made it too abstract.  I have talked to a lot of adults who say they 
never understood Algebra. What a shame.
  Let's stop trying to scare students who are starting to learn algebra and 
get real.  Instead of being abstract and talk about the variables x and y 
let's use letters that relate to real measurable objects. Let's make sure that 
students understand that in most cases we use the first letter of words. Why, 
because it is quicker to write the first letter instead of writing the entire 
word.  Instead of writing five tickets we write 5T and if a ticket cost $8 
then 5T is worth $40. The word variable loses its scare factor if we point out
that the value of a T (ticket) depends on what the ticket is for. If the 
ticket is for a pro basketball game then T has a large value. If the ticket is 
for the school play then it wouldn't cost as much. The value of T varies so we 
are going to call T a variable. The value of 5T varies according to what 
tickets we are going to buy.

Let's explain to the students that if we are talking about tickets and we are 
given the value of one ticket (let's say one ticket is worth $5) then we would 
probably be interested in how many tickets we have. So let's use N to mean the 
number of tickets that we have.  In this case N5 would mean that the number of 
tickets times 5 dollar each is the value of all five tickets.  Of course, we 
don't like the way N5 looks so in mathematics we will write N5 as 5N 
(commutative property lets us get away with this).

Let T be the value of one ticket.  What does the following mean?
    3T + 12 = 30
It could mean that we bought 3 tickets (3T is amount of money used to buy 3 
tickets) to a movie and we spent 12 dollars for snacks. The whole thing cost 
us 30 dollars. Question what was the average cost of one ticket?  Note that I 
specified average. It could be that two of the tickets were adult tickets and 
one ticket was for a child.

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