## Saturday, April 11, 2015

### The Gods of Irony Smile Upon Us

Five of our school's math teachers decided not to attend the last 3 hours of the unconscious bias training a few weeks ago, so this past Thursday we met for an hour to review the statistics standards that are imbedded in the Common Core Integrated Math 1, 2, and 3 courses that our district is switching to next year.  Believe it or not, standard deviation is mentioned in the Integrated 1 standards--freshman math!  To be honest, we're not sure exactly what level of detail we're supposed to address in these standards, but it's best anyway if teachers know significantly more about a subject than merely what they're supposed to teach, so we spent our first hour (two more to go!) reviewing introductory statistics.

One of the foundational concepts in inferential statistics is the difference between a population and a sample.  If you want to learn something about a population, you take a sample from it and infer about the population from that sample.  The formulas for calculating the standard deviations of a population and a sample are slightly different; if we were to use the "population" formula for a "sample", that sample would always underestimate the true standard deviation.  Therefore the formula has to be tweaked a little bit, the value inflated, so that the sample standard deviation becomes a good predictor of the population standard deviation.

This tweaking makes the sample standard deviation what is known as an unbiased estimator for the population standard deviation.

maxutils said...

First, I have a meeting with the Assistant Superintendent on Tuesday in my continuing quest to undo this abomination ...

But my gut reaction, if you have to do this, is that at a mat 1 level, you don't need to be using formulas at all. I would just introduce the concept of a normal curve, mean, standard deviation, and how to read a table and do it completely graphically -- you can mention that there are ways to calculate the std deviation that they will learn later; I think broad stroke would be all that is necessary, and all that might be tested.

PeggyU said...

I don't find it ironic. Part of the reason they switched to an "integrated" approach was so that kids would get some exposure to statistics. I want to know how they "integrate" it though. How do they tie it to other concepts learned in algebra and geometry? And how much depth is there? In my experience with what I have seen in this state (early adopters of integrated math), the way in which they present topics seems really disjointed and haphazard. I don't know how this would be better than just sticking with a more traditional approach and reserving time at the end of the course to provide supplementary lectures that cover topics which have been underrepresented.

Darren said...

It's not "integrated", it's "hodgepodge". There's a world of difference.

And the irony is in missing unconscious bias training in order to learn about unbiased estimators. I guess it's not that funny if I have to explain it!

maxutils said...

I got it. Very funny, in a very sad way ...

PeggyU said...

Nope ... people have to explain humor to me all the time. ;)