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Teaching power laws


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For some reason ds seems to struggle with understanding power laws in algebra (using aops).  We’ve gone over it a few times and different ways and we seem to get it temporarily and then next time he sees them it’s like a mental blank again.  We’re near the end of the year now and have mostly taken this year off of forward progress to get more solid on the basics but I really want to get moving again next year (8).  

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I get my tutor kids to convert all powers into multiplication.  They do this for numbers and for variables for at least a month while learning the rules. We love to have a giggle about "please let it not be (x^10)^100".  haha.  But I just have them write them all out for how ever long it takes them to realize that powers are just repeated multiplication.  

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I'm also one who uses the definition of exponents to rewrite an expression as multiplication.  As many times as it takes, sometimes months.  I find that it's when the student wants to rush to the answer without thinking that mistakes are made.  

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On 10/20/2019 at 12:16 AM, lewelma said:

I get my tutor kids to convert all powers into multiplication.  They do this for numbers and for variables for at least a month while learning the rules. We love to have a giggle about "please let it not be (x^10)^100".  haha.  But I just have them write them all out for how ever long it takes them to realize that powers are just repeated multiplication.  

 

I do this, too. Also, I like to make posters and create recitations for algorithms. Visual aids and mnemonics help students over those stuck moments. For powers, I would include rules for the basic four operations, for negative numbers and exponents, and for bases and exponents of zero and one.

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I agree with everyone else.  Students have had somewhere between 5 and 8 levels of arithmetic with four operations before hitting exponents, so they just don't feel natural the way the other four operations do (even though, yes, they are just the next step).  

My son has been having ZERO issues with exponents for months now, in chapter 11 of AOPS Algebra.  And then, today, he simplified (x+y)^2 as x^2 +y^2 🤦‍♀️ .  It just happens; the brain hiccups sometimes.  Yesterday, he'd expanded the same binomial all the way out to the 7th power, as a discovery route to Pascal's triangle, and had no issues.  Then today, this.  😩  We went over it, he got it, we moved on.  

I like to remind myself that PreA, Algebra, and puberty all tend to coincide in a sort of perfect storm of frustration for homeschool mothers.  

Every time the brain hiccups, set up a simpler example or have him write it out as a full-on multiplication problem (for things like power to a power means multiply, and base to a power times base to a power means add the powers, etc.)

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