Friday Five - 1.20.17

“Son, anything can happen to anyone," my father told me, "but it usually doesn't.” 
― Philip Roth


Canada National Parks Pass 

Today no doubt has many of you dreaming of moving to Canada. If you can't make the move, you can at least make a visit. Canada is super beautiful, and did you know that this year - as a part of Canada’s National Parks 150th anniversary celebration - they are giving away National Parks Passes for free?! Well - they are! You have to order the pass here - but everything is free. The pass will get you in to any of Canada’s 38 National Parks all year. I ordered mine a few weeks ago and I’m sure there is a huge demand so get yours today! And plan a trip to Canada :) 

Get yours here!


This week I watched a video from the National Women’s Law Center’s #letherlearn campaign and couldn't help but cry. The Let Her Learn campaign's aim is to help stop school pushout of black girls. Black girls are more than five times as likely to be suspended from school for minor offenses than white girls - despite no evidence of them actually being worse behaved. This is a subject very close to my heart and something I have seen first hand - so I knew I had to share this with anyone and everyone. 

In the book Pushout: The Criminalization of Black Girls In Schools, author Monique Morris addresses Pushout, “the structural racism and the cultural barriers that push Black girls out of the classroom and to the outer brinks of society. Black girls are suspended at six times the rate of white girls, and they make up only 17 percent of girls in public schools but almost half of school related arrests.” 

This is a disgrace. We have to do better. Watch the video. Read the book. Share. 

Read more here and here. Watch the video here:

Folk Numeracy and the Monty Hall Problem

I recently read about a super interesting new (to me) term - folk numeracy. Coined by Michael Shermer, folk numeracy is “our natural tendency to misperceive and miscalculate probabilities - to think anecdotally instead of statistically and focus on short term trends” 

Basically, this explains those people on Facebook who make some joke about global warming not being real every time it’s cold for a few days in a row. They look at a situation that they experienced and use it to extrapolate (false) data. 

Probability is always hard for people to understand - the language is so specific and technical, and it’s hard to wrap our heads around. Take the Monty Hall Problem - imagine you are on a game show and there are three doors. Behind one door is a car and behind the other two are goats. You choose a door - let's say 2 - and then the host opens one of the other doors with a goat behind it - let's say 3 - and gives you the option to switch your original guess. What would you do? Many people - the overwhelming majority in fact - would say that it doesn't matter because you now have a fifty-fifty chance at choosing the car. The problem is that the majority of people are wrong. 

Probability - and years of mathematical models - tell us that you have a 2/3 chance of choosing correctly if you switch your original guess. You see - originally you had a 1/3 chance of guessing correctly and a 2/3 chance that the car was behind one of the doors you didn't choose. Because the host opens a door that was not your initial guess - you still have a 2/3 chance that the car is behind the other door you did not pick. 

This has perplexed people (even mathematicians) for years. It is a veridical paradox - a paradox that is so counterintuitive it seems absurd. But it's been proven over and over. Try it with a friend - each person plays 10 rounds as the host and 10 rounds as the guest. Switch 5 times and stay 5 times as contestant and see what happens. 

Ahhhh math :) 

Read more here and here.

Birthday Paradox

Have you ever heard the birthday paradox? I heard it for the first time a few years ago at a Saturday morning math teaching conference (that believe it or not I went to willingly and even paid for myself). It posits that if you are in a room with 22 other people there is an over 50% chance that at least two people will have the same birthday. Really. 

When someone - usually a math professor, natch - introduces the question, those in the room are always asked to guess what the probability/percent chance will be that two people share a birthday and, without fail, participants always guess a super low percent. 

The problem is our context is off. When we are asked the question - most people think of it in terms of “what are the chances someone else in the room has the same birthday as me” which indeed does have a much lower probability. The context is that any two people in the entire room will have the same birthday - but that isn’t our natural thought. Like the Monty Hall Problem - humans just don't have a good grasp on probability. 

Richard Dawkins surmised that our probability problem is evolutionary - that humans exist in "middle world" where we can only understand medium sized things. Probability is just too big. What do you think? 

Read more here and here. Or watch this video:

Does randomness exist?

One of the things I hate most as a teacher is when students say they “just guessed and got it right”. I always tell them that there is no such thing as guessing - their subconscious has knowledge of the problem and influenced their choice whether they realize it or not. I say this in part to give them back the power over their learning they are trying to give away, but also because I really believe it. Can anything ever really be random?

This is definitely a question too big for this blog post but, I like to think about it. Mathematicians have coined a term for situations that technically pass statistical tests for randomness but where the number is still determined - “psuedo-randomness” Take rolling a dice. It seems random, but if we knew all of the variables and physics behind the dice, who is throwing them, the speed, the angles, the ground that it is being rolled on etc.. then it is not random at all - we could determine what would be rolled. 

Free will vs. determinism is, again, way too big to cover here but another interesting topic when thinking about randomness. Between the two schools of thought I think I stand closer to a soft determinism. Soft determinism says that determinism - all behavior is caused by preceding factors - can coexist with free will - self-determination. Maybe it’s the mathematician in me but, probability can explain almost everything. Even supposed “miracles” will happen eventually after enough trials. 

So what do you think, is there anything truly random? Are you ever really just "guessing"? Hmm. 

Read more here and here

Happy Friday :)