#FailFriday Normal Distribution

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:

20130129 - Normal Dist probabilities_3a

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:

20130129 - Normal Dist probabilities_4

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):

DSCF0671

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!

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3 Responses to #FailFriday Normal Distribution

  1. Pingback: #FailFriday – Normal Distribution | Productive Struggle

  2. Kate Nowak says:

    Why the hell didn’t I think to do it that way right away?

    Because, that’s how this works. That’s what experience is good for. Sometimes there’s no way to know what is going to work ahead of time.

    I’m wondering, since you didn’t give too much background, if the kids got any experience taking a big-ish set of data and looking at histograms? Contextualization makes all the difference with stats. Here is an example: http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=5026&t=1192&id=11143 I don’t know if you use nspires, and I doubt NBA stats is going to fly with your kids, but, if you can find something like it that will work for your class, I’ve been successful with it.

  3. nik_d_maths says:

    Hi Kate, thanks for the advice – we did some histogram work before normal distribution but we didn’t go into really big data sets – which looking back I should have made time for!

    Hopefully we will be getting a set of Npires and I’m sure I can find a suitable equivalent of relevant statistics. Honestly more than anything the end of this stats unit has made me realise how little experience I had with these topics, and how our current resources do not link or build on the ‘separate’ ares very much at all, and how poor the contexts we use are. Stats are not my favourite area if I am honest, and because of this I don’t find that resources/ideas come as easily to me as they do in other things. Might have to throw that in to a something to work on post.

    Thanks!

    Nik

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