## Saturday, September 6, 2008

### Index laws and the lower ability group

It always surprises me what will work with a low ability group and what will not. Generally you have to hit the ability level spot on for the whole group for them to be able to grasp a concept (even if only momentarily).

Take indices. On one day grasping 3x3 = 3 squared = 9 was impossible, not to mention any attempts at 3^2 x 3^3 = 3^5. We went through a number of examples and by the end of the lesson I had 10 bored students and had lost half of my hair.

The next day I took a different investigative approach. This might be obvious to an experienced teacher but was fairly radical to me.

Sequence (imagine that ^3 is written as 3 superscripted):
a) Discuss nomenclature with notes (base, index, indicies, power, factor and power form)
b) Use calculator to evaluate single term powers - eg. 3^3 = ...
c) Add multiplying powers to the board (with positive index) - eg. 3^3 x 3^5 = ...
e) Look for a pattern in the numbers - supply the base after a few minutes.
f) Explain how multiplying powers works and supply notes including general forms
g) Rub off the answers, write as index addition - eg. 3^3 x 3^5 = 3^...+... = 3^8 = 6561
h) Add dividing powers to the board where answers are positive > 0 - eg. 3^5 ÷ 3^2 = ...
i) Look for a pattern in the numbers - supply the base after a few minutes.
j) Explain dividing powers, supply notes including general form (as ÷ and fraction)
k) Rub off the answers, write as index subtraction - eg. 3^5 ÷ 3^3 = 3^...-... = 3^2 = 9
l) Supply mixed problems

About 40 mins. I don't think I could have done this investigating factored form with these students as regrouping and cancelling bored them silly the previous day (I will revisit it later though). Using calculators to do the sum and examine the sum backwards worked far better. Special note was made from e) onwards about checking for same base, superscripting properly, neatness, identifying operator used in original sum and always referring back to general form to make sure the correct index operation is being done. By the end of class all 5 students were engaged and had grasped the concepts involved. yay!

Now some may ask 'why do index laws with a low ability group in yr 10?'. I suppose it is a philosophy problem put in place at uni. Students shouldn't have impoverished courses 'entertainment based/childcare oriented' purely because they are in a low ability group. If they could master simple algebra earlier in the year and ratios later in the year, I consider index laws and other more 'pure' maths well within their grasp even with behaviour difficulties. These students too should have the pleasure of mastering something that looks quite cool on paper, harder than they believe possible to learn and not feel inferior to peers when they walk into an upper school maths class.

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