[IAEP] Request for Feedback and Ideas on teaching Algebra

[K. K. Subramaniam]

On Saturday 03 April 2010 11:36:17 am Steve Thomas wrote:
> If you have any ideas for problems I can use and/or suggested lesson
> plans/books/curricullum please let me know.
Having helped my daughter deal with algebra last year, I can share my first-
hand experiences of the 'confusion' that kids face with the subject. It starts 
with the name - 'algebra' - sounds like a magical incantation. Most books on 
algebra begin with notations :-(.

Let me digress a bit here. I have often watched kids struggle with divisions 
dealing with zeroes:
    _______
  3) 6024

If I ask the same kid the following questions (no pen and paper, just head 
math):
 a) How would you split 6000 Rupees equally amongst three friends?
 b) How would you split 24 Rupees amongst the same friends?
 c) How much will each friend get if you distribute both 6000 and 24 Rupees 
amongst the same friends?

Kids who struggle with the former have no trouble answering the latter Qs. 
Once they play this game a few times, they have no trouble solving division 
sums on paper. The rules of the game are understood intuitively. What they see 
on paper is a picture of what they carry in their head. Notation is no longer 
a barrier - 6024, 6000+24, 6000+20+4 are all the same thing in the head.

Back to your question. The origins of algebra lies in the games that kids used 
to play in India with seeds (the subject continues to be known as Seed 
Arithmetic in India). A bag containing different types of seeds constitutes the 
alphabet and arithmetic gives us the rules for composition. Kids get to make 
up different riddles using the alphabet and rules. Algebra is just "Arithmetic 
for Fun".

If a pile with 5 red beans and 10 yellow beans cost 20 pies and another pile 
with 20 more yellow beans cost 40 pies, how much does each bean cost?

Advanced riddles make use of bricks, tiles, blocks, or rope lengths instead of 
seeds but the rules remain the same - simple arithmetic. See Julia Nishijima's 
exercise in page 13 of http://www.vpri.org/pdf/rn2007006a_olpc.pdf

After a few such riddles are solved in the head, the 'reduce and balance' 
algorithm is intuitively grasped by kids. Now the notation can be introduced 
without confusion:

   5r+10y = 20, 5r+10y+20y=40

Introducing notation before thinking leads to all kinds of confusion.

Subbu