[IAEP] Request for Feedback and Ideas on teaching Algebra

[Caryl Bigenho]

Right On!  Make it fun. Don't just learn the processes, understand the concepts first.
Caryl

> From: subbukk at gmail.com
> To: iaep at lists.sugarlabs.org
> Date: Sun, 4 Apr 2010 15:39:19 +0530
> CC: sthomas1 at gosargon.com
> Subject: Re: [IAEP] Request for Feedback and Ideas on teaching Algebra
> 
> 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
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