This is actually a couple of weeks ago, where a topic seemed to take aaages for the students to grok a few important things about Normal Distribution. I’m going to try and highlight the different ways I tried to explain, and get some feedback on how I might approach it differently.
What I wanted them to grok early on:
We did some sketching and some examples of different normal dists after calculating mean and standard dev for some data sets (why does it feel like they ALL need to relearn the graphic calc everytime?) then introduced the standard curve with the areas labelled.
What I feel like they took away from that first lesson:
However, I did not realise this (as they produced for me some nice distributions drawn with appropriate scales) until we tried to do this the next day (excuse the sketch, the sheet is at school and I am not):
So we had to go back over what the area was and what it meant in terms of a probability and how all possible outcomes were under the curve and I felt like I couldn’t explain and they were frustrated by the symmetry and we ran out of time.
So next lesson we went back to the mean and standard deviation and drew some more distributions for things like height sets and weight sets on mini whiteboards so I could see them drawing it. Then We plotted the line for a particular height or weight.
Then we shaded areas and talked about what they represented.
Then we drew some symmetry on the curves and talked about which were the same and how we could work it out (using word-sentence-equations like:
‘Probability of more than 1.55m is the probability of less than 1.55m taken away from 1 (because 1 is everything that could happen’
With symbols becoming more frequent as they went through.
So after that, and a bit of practice reading the normal tables, we could try some standardisation problems; and suddenly it seemed to work. I thought. So I exitslipped them and it seemed alright, and the next day, we built it up again in the first activity: Draw a curve for given mean and SD, shade the area you want, standardise, read the table, find the result and interpret it as a percentage.
WE WERE FREAKING THERE. Time for some problems. YES YES YES.
The two real questions are:
- Why the hell didn’t I think to do it that way right away?
- Will they remember in 2 weeks time
The second will be answered next week…
So my failure here was pretty much a bunch of time where me and the students were frustrated by what we were doing, before I got myself together and figured out a way to redo what I did. So what do people think?
p.s. this wasn’t all fail, one student made me feel much better at the end of the final lesson, having done a TON of exam questions and said ‘I got it on Monday, but I didn’t want to make the others feel bad, so I just helped my table and got on with the work’ THANKS KIDDO!