Can you tell which plot above is randomly generated?
Being able to determine if something is “truly” random is not just an investigation carried out by forensic accountants, sociologists, and law enforcement. Rather it is an interesting and complicated mathematical problem. Consider the two plots above. You may look at the on the left and see the clumps, the spacing, and think “That can’t be the random plot.” And yet it is. The plot on the left has been randomly generated, while the plot on the right is a scatter plot of glowworm positions on a ceiling.
So here, the clumps actually help indicate randomness. Try thinking of it in another way: imagine you have two students who were asked to flip a coin 100 times for homework. The first student was diligent and flipped accordingly:
Now while it might seem strange that the first student has long runs, it fits closer to what one would expect if the flip is random. On the other hand, in the second student’s data, there is less than a 0.1% chance that they wouldn’t get a single run longer than four in a row!
The images and coin flip data was found at this article. It takes a closer look at some of these topics and provides some pretty neat historical background.
“Now that we know that math anxiety has a neurobiological profile like that of other anxieties,” he says, “we can use techniques such as progressive exposure and cognitive-behavioral therapy, which have worked with other anxiety-provoking stimuli and phobias, to reduce math anxiety and its…
I have now asked both classes who have had a test to write out their worries. I did not perform a controlled experiment. I am sorry. But I hope they liked it.
I also tried this with my students this month. Some said it helped, while others said that thinking about the anxiety made it worse.
It was so excellent of you to try! I would frame that as unequivocally good, because now you and your students have more data about what works for them, so next time you can say, if this worked for you, do it, if not, doodle a panda.
I can totally see some of my students insisting we can’t start the test yet because their panda isn’t done…
(Obviously I’d start by saying you have two minutes to either write about anxiety or draw a silly picture, but they’d still try for more time.)
Haha me too. Though it’s odd, since they know they have only the period, so you’d think they’d want to make best use of that time.
For people who don’t have time to bathe or access to fresh water, a South African college student has a solution: a shower gel users simply rub onto their skin. One small packet replaces one bath, and users never need any water. Ludwick Marishane’s inspiration was a lazy friend, but his invention will be a boon to people who live in areas where clean water is in short supply.