This video shows highlights from a lesson in AP Statistics in which a teacher uses a variety of technology tools to support students' learning. Also included is a ...

Hollylynne: Let's watch as an AP Statistics

teacher uses a variety of technologies to

support a lesson on introducing the concept

of sampling distribution.

Mr. Roberts: So tonight I think your homework

is just going to be to look at the PowerPoint

for today and take notes on it, um, because

it's a lot of definitions so I'd rather us

do stuff than go over definitions.

Cause so we're going to talk about it today

but I want you guys to write it down, um,

tonight okay?

Okay, so today we're starting something new,

um.

You guys haven't seen it before it which is

kind of nice um let's do this.

Okay so we have to keep in mind what statistics

is about right.

So the whole point of statistics is that we're

going to take a sample of something, look

at it infer from it okay.

We're going to go from the population we're

going to take a sample out of it okay.

We're going to collect data, um, and then

we're going to infer from it about the population

okay.

So two things that you kind of need to know

right now are these guys right here and we

actually - I need you to write these down

right quick.

A parameter and a statistic.

Well we're going to switch gears okay.

I don't want to look at the population anymore

what we're going to do is that we're going

to find where, when we sample where our sample

lies among other samples.

So what I did is that I recorded a bunch of

people's heights okay.

Specifically I recorded four hundred and thirty,

okay.

I recorded 430 height, okay.

Do you know what's a mean of this is?

No, I don't know what the average of this.

Do you know how much it varies?

No.

Okay you don't know anything about this okay

but what we're going to do is that we're going

to sample from it and see what we can do with

our samples okay.

Um, so what I'm going to do is I'm going to

ask half of you pretty much, I'm going to

number you guys off, I want you guys to take

samples of ten and I'm going to ask you to

record four numbers okay.

I want you to record the range, the mean,

the standard deviation and the median okay.

And then I'm going to the other half of you

guys are going to use a sample size of 20

and do the same exact thing.

Alright so are you telling me that we assigned

and label.

Alright and then what you do?

Randomized selection.

Good.

Where is that in your calculator?

Let's see if you remember where that is real

quick.

Students: Math, probability random?

Mr. Roberts: Okay do we want to do random?

Student: Random integer.

Mr. Roberts: Random integer . We want to do

the random integer.

Okay so when you guys hit rand int it says

lower/upper what does that mean?

Okay so lower is the lowest that you want

to select from the upper is the where?

The highest okay and what does N mean?

Student: The number of, uh, integers you want

to select.

Mr. Roberts: The number that you want to select

okay.

So what happens if you repeat?

Okay if you guys cleared your calculators

let's, um let's seed your calculator real

quick one more time so that you're not getting

the same sample as someone else.

Alright, in your calculator, okay.

The very first thing that you kind of want

to do is that you just want to type in some

random number.

Don't tell your friends!

It's your own number don't look at mine!

Just literally just make up numbers.

Student: (Mumbled question)

Mr. Roberts: Sure it could be one digit, two

digit, three digit, mine's a lot of digits.

Don't look!

Okay so then you're going to hit the store

button which is right here above the on button

okay.

Okay, it's an arrow and then hit math, and

slide over to probability okay?

And you'll see the number right - the first

ones called Rand and you hit enter.

Okay so now hopefully you guys won't get the

same numbers from your algorithms as everybody

else.

Okay because really we can debate this whole

word random right?

With your calculators, but if they're seeded

we all should be getting different numbers.

Hollylynne: Students use large whiteboards

to plot the data from their samples.

Mr. Roberts: Yeah, hey for those that are

waiting to plot, um, I sent you guys through

a remind text, um, I sent you guys a form

for you to fill out, um, it's asking you for

the mean, the range, the standard deviation

and the median of your samples okay.

And next to each question it says the mean

N equals 10, the mean n equals 20.

If you're a 10-person put it in the N equals

10, if you're a 20 sample put it in the N

equals 20 okay?

Cool.

This, when we graph it, I mean this is literally

why we like looking at graphs right?

Why we like looking at histograms and dot

plots because now I can see what the data

is doing correct?

So, when I look at the heights you guys can

tell me about what the range is right?

I did max minus min.

It's about 12.

Okay.

You guys know what the mean is.

It's 67.96.

Okay so when we have software , specifically

when we have a graph you guys can tell me

a lot about it now alright.

And then when we have software that can crunch

big data 'so to speak' like big for us alright.

We can easily pull out some numbers to describe

the height of whatever they're talking about.

I'm going to collect - how many kids are in

here?

30.

Okay let's say that all 30 of you guys did

a sample of ten okay?

So look what I just got here okay.

So this thing just did this okay let me see

if I can pull this guide to the right okay.

So I took out IQR I don't want to do it.

Delete attribute okay.

So what this did, okay, is this literally

represents every single one of you okay?

You pulled ten numbers from your population

you randomly selected right in an SRS okay

with your calculator, some number generator

and then what you guys did is that from every

sample you collected a number correct.

So this was a distribution of what?

Students: (mumbling)

Mr. Roberts: All the population of all the

heights okay it's literally that sheet of

paper right?

It's this thing.

Distribution - this is your population of

heights correct?

What is this guy?

Distribution of your sample okay now from

all the distribution of your samples to every

all 30 of you collected four statistics that

I asked you guys to collect right?

Now the new thing that you guys are going

to learn is this thing called a sampling distribution

okay.

It is literally a distribution of statistics.

D you guys hear the difference?

Did I say heights?

No.

I said of a statistic right?

So I'm going to take all thirty means alright?

I only have like three up there but I'm going

to take every single mean that you guys got

and I'm gonna plot it okay.

This is now a sampling distribution, a very

limited one, but a sampling distribution so

what does this dot right here represent?

Let's just say at 69 what does that dot represent?

What is 69?

Students: (mumbling)

Mr. Roberts: The mean of what?

Of the sample right.

This is like the cool part about this.

Well I think it's cool.

I'm going to do this 500 times okay.

(To do do do) Awesome.

So I took 500 samples out of this population

okay.

Of size what?

Do you remember the size that we did?

10 okay everybody did a sample size of 10.

500 people sampled and all 500 of them filled

out a Google Form and gave it to me.

There it is.

So if I only grabbed 10 of you guys I don't

know as much if I grab 30 of you.

I'm going to take 500 samples of size 30.

We cool with that?

So let's just say that like there's 500 of

ya'll in here, aww man, you know.

Every single one of you took a sample of 30

all right and found these four statistics.

Look at it go.

So every single one of these is a sample right?

Every single one of those is a mean of a sample

okay.

Right okay.

Are we okay with that?

So, okay so let's kind of go through these

questions because this is what I wanted to

hit I don't know if I hit them all or not.

So let's just make sure.

Do we know what a sampling distribution is

that word sampling distribution?

Okay, distribution of samples, okay or distribution

of statistics.

Okay so it's our distribution of means, our

ranges , our medians, our mins our maxes,

our standard deviations okay.

Alright you guys rock.

Thank you.

Hollylynne: Let's hear from the teacher on

how he decided to use technology to support

students' learning.

Mr.Roberts: I think that they did, with the

use of Fathom, I think it did come home pretty

good.

Hollylynne: Uh-huh.

Mr. Roberts: And ultimately like this was

nice I wanted to get them up and moving, but

I really wanted to sample themselves.

Hollylynne: -Right, and I think they had,

they had that experience.

Mr. Roberts: Exactly and they got to use a

number generator to pull numbers and they

got to fight in their heads this idea of what

a sample is versus statistics cause they ask

me like hey doing this and then people go

up and do in the sample themselves helped

out a ton when it came to doing the sampling

distribution in Fathom.

Hollylynne: Em-hmm.

Mr. Roberts: Um, especially when I said this

is all 30 of you and these are all the four

numbers that each of you got, so let's plot

those and then doing - okay well let's say

there's 500 of y'all and plotting those and

seeing that.

Hollylynne: Right, right.

Mr. Roberts: Um, and when they go over that

PowerPoint tonight hopefully they'll connect

things that we do in class with the PowerPoint.

Hollylynne: So you use a lot of different

technology tools today.

Mr. Roberts: Yeah when I think about it I

did, didn't I?

Hollylynne: You did!

So how did you kind of decide and choose-

I mean they were using the graphing calculators,

they, um, you were using Fathom, you use the

Remind app,

Mr. Roberts: Yep

Hollylynne: You know in the Google Form - How

did you kind of think about how to pull that

all together?

Mr. Roberts: Yeah, so I guess it just kind

of went through my head of like what can I

use to model the data.

Um, what can I use to gather information and

when you teach statistics the calculator is

your go to.

I know to use the random integer function,

um, and then through just like using Google

Forms.

I know that I can gather information quickly

and that's what I wanted to do today is gather

information quickly from them.

Hollylynne: Yeah

Mr. Roberts: So just blast it out, fill out

a form, get all the information.

Everything is nice and like I know who did

ten, who did twenty, so I know I can compare

those.

Hollylynne: Fathom.

Mr. Roberts: And then the Fathom like that's

just that's just for me.

I've actually, liked, taken time out to learn

that and so that's just nice just to have

a really quick way to model data which is

awesome because I've used it for some of the

past chapters, especially in descriptive statistics

that's amazing for.

Because you just throw data up on a, on a-

Hollylynne: Em-hmm, em-hmm

Mr. Roberts: Histogram, boxplot, dotplot,

you can, you can go like this (snapping fingers)

and you can really challenge them and say

okay which one is better?

And they have to justify their response.

Or which, what does this give you like, what

information.

So we've done it before using Fathom.

Hollylynne: Em-hmm.

Mr. Roberts: So entering in the sampling distribution

and that's talking about describing sampling

distributions it just kind of flows so.

Hollylynne: Cool.

Mr. Roberts: Yeah.

Preparing to Teach Mathematics with Technology