High School Student Understanding of Randomness

>>8458937

in thinking fast of slow theres examples similar to this. the author, daniel kahneman, did studies on people testing their intuitive understanding of statistics and i think some of the examples are in the book.

>>8459044
Thanks for the heads up.

Found a pdf. I'll see if I can't find anything.

File: kahneman 1.jpg (144KB, 825x687px) Image search: [Google]

144KB, 825x687px

>>8459118
>>8459044
I think I will use the example with kids instead of coins because I think that students may not consider the gender of a child as being random.

The next chapter in this book was about anchoring. I think that would be an interesting topic to explore with my students.

Thanks so much for the recommendation!!! So many good ideas in that book.

>>8459143
I'm thinking outloud, but do you think if students are made aware of the anchoring effect, that they will then be more immune to being manipulated by it?

I think I'm going to throw the question on my survey about:

Are there less than 50 countries in the world?
How many are there?

Vs.

Are there more than 150 countries?
How many are there?

In my two classes to see if there is a deal of variation due to the anchoring effect.

>>8458937
>1. What does it mean for something to be random?

what's the answer to this?

>>8459168

im not sure, i havent read the book in a while so i dont remember too much specifically on anchoring. i think he mentions something about that in the book though, being aware of it when making choices.

there was one quite interesting probability one which was like asking if it was more probably for some woman to be a bank teller or a feminist bank teller. thats probably not it but its a question about probability that most/alot of people get wrong on first try.

theres actually a whole bunch of interesting unintuitive tests related to probability and stuff across the other pages.

>>8459899

i think its to do with predictability.

>>8460277
Yeah I saw that and decided to ask my question this one. It's about Linda being a feminist bank teller just a bank teller based on the scenario.


Yeah I'm gonna be picking up that book sometime. There was a lot of good stuff in there. Thanks dude.

>>8459899
I would be looking for students to say that it is unpredictable. That question I'm more so curious to what students say. Not necessarily a wrong or right answer.

>>8458937
mmm I would follow up number 4 with something along the lines of

John just lost at roulette after betting on black 3 times in a row. If John bets on red the next time is he blah blah blah, etc..

For the first question maybe even go more general, as that specific question is a little daunting. Something like what does random mean. Or give me an example of randomness.

Umm maybe something relating to expected value. Like would you rather play a game where you win on every even dice roll from a single die or every heads flip on a single dice. Equally maybe compare things with different expected values.

oooo or even something along the lines of: What is the difference between flipping a single coin twice or two coins at once. Kind of what you were alluding to here in a sense with 3

Or mabye propose a certain probability scenario like: John and Billy are playing a game. They both flip a coin. If the coins match or Billy gets a heads he automatically wins. Every other case John wins, is this a fair game?
This is like super introductory level yeah?

>>8458937
For that last one you might want to pick a game where the hands are independent.

>>8458937
Is it more about probability in general or randomness specifically.

What level are you teaching?

I am assuming highschool but general or AP?

>>8460563

Seems like general. AP students probably already have a firm grasp on the notion of randomness and basic probability.

>>8458937
>What does it mean for something to be random?

Pretty tough question desu. How would you answer this?

>>8460621
I think the point he was getting at was a general consensus. There is not really true answer to this that any highschooler would be expected to state.

But if i were to answer i would say:

Given that a particular something has a set of possible states,values,events. It is equally probable for each state,value,event to occur given a particular operation on the something. All of the probabilities of each individual value,event,state add up to 1, and are all equal to one another.