# I to the What Power???

Posted on March 12, 2013

A student helped me see a connection to help teaching students how to figure out what i to the big number power is.   The procedural “divide by four, use the remainder, and then choose from these four  memorized  possibilities” is pretty danged taxing on the working memory.

The student in question understood about odd and even multiples of negative numbers… that every pair of negative numbers gave a positive answer…

We discussed and decided that i was taking that negative idea into another dimension so that now it would take *four* of these even more negative negatives to [turn into one and] CANCEL.   So you take out the ones that cancel… and with what’s left… (and you still might memorize those possibilities — but you do already know that i to the fourth is one, and i to the first is plain i… so you’re left with the middle two to figure out…)

Then there’s that problem with figuring out decimal places.  My student just easily nailed changing 0.093 to a fraction and I’m making yet another note to self… Just like figuring out big place value, she started with “ones,” with that nice little zero.   Ones, tenths, hundredths, thousandths… done.

Yet another clue about just how procedural the student processing is, though, is the challenge that graphing the temperatures through the course of a day is.   Most have to be talked through why Excel didn’t graph things right when they put 11:00, 12:00, 1:00, tho’ the directions clearly stated “use the hours after midnight, not the real time.”   It’s all about that ZPD — that Vygotsky thing with the  zone of proximal development, .   I can say that they *should* already know that, pretend they do and wonder why they’re just memorizing procedures for more complicated stuff…  or I can recognize the reality and make sure they learn it.   (News flash:  understanding working with time is more useful than factoring IRL.)