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 :)

Friday Five - 12.9.16

“Prime numbers are what is left when you have taken all the patterns away. I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spent all your time thinking about them.”

― Mark Haddon, The Curious Incident of the Dog in the Night-Time

This week has been a strange one. It's my last solid week as a 30 year old, it's colder in Denver than it has been in 2 years, it's the week before finals, and it snowed! It's been the sort of week that somehow feels long and short at the same time. A week where I have been happy and sad and everywhere in between for reasons I mostly can't even remember now. So, just like this scattered week, here is a scattered list of five things that have gotten my attention:

Emotional Relationships to Numbers (aka thank goodness I'm a prime number again)

In three short days I will be turning 31! Like many others, I am excited to leave this year behind. - not just 2016 but 30. It wasn't all bad - in fact, it was mostly really great - but the number 31 itself is exciting for me.

Why is 31 so interesting? Well, I am a math teacher, so I'm sure it's not surprising that I love reading about numbers. But my fascination is not just with numbers in a mathematical sense, but the emotions and relationships we have with numbers. I - like a lot of people - have always been obsessed with the number 3. I count out everything into groups of three. Three (and any multiple of three) feels calming to me. I'm also really interested in prime numbers - the lack of pattern and divisibility make them unique. I also like that 3 and 1 are both odd, that 3 divided by 1 is 3 and that the difference between the two are equal to the digits of the number. So.. maybe the fascination is mostly sort of mathematical (and strange). 

While I am excited about 31, my favorite numbers are actually 11 and 3. There are so many interesting studies about favorite numbers and number relationships. Even numbers are seen to be good or calm, while odd numbers are seen as bad. Evens are said to be feminine while odds are masculine and more difficult to process. Despite the seemingly negative connotations, odd numbers are far more likely to be someone's "favorite number"

The number 7 is - by far - the most common favorite number in the world. It is arithmetically unique and seems mystical in some way. It's the only one digit number that isn't a part of another single digit fact family (nothing under 10 can be divided into/multiplied etc to make 7). Three feels that way for me. It's odd, it's prime, it's curvy, and it's everywhere in art. Eleven is odd, prime, but still has even characteristics (add up to an even, first two digits of the Fibonacci sequence, etc..) 

If you want to learn more about favorite numbers and the emotional relationship we have with them, listen to this episode of Radiolab (embedded below) or read this, this, or this

Petrified Forest National Park

Today marks the 54th anniversary of the establishment of Petrified Forest National Park. I visited the vast park in the middle of nowhere nearly two years ago now. 

Interesting part of the parks history: at one point the park said it was losing 1 ton of petrified wood a month to visitors illegally smuggling it out. The park took several punitive steps to curb the theft but found that it actually seemed to increase with the attention placed on it.

I recommend a great, short, Criminal podcast (embedded below the pictures) about the wood theft. It talks about the bad luck people claim to experience after they've stolen wood from the park and the subsequent letters they send back (with the wood) in the hopes of their luck being reversed. The so called "conscience letters" used to be on display at the park - now they are trying to step away from that narrative - but the letters are still available on the website "Bad Luck, Hot Rocks" and book of the same name. Here are a couple of my favorites: 

Read more here and here

Creators vs. Consumers

Last weekend I spent Saturday night getting (much needed) drinks with a friend and catching each other up on our creative projects. Through the night - as we got a few more drinks and a little more honest in our venting - the refrain "at least I'm doing something" came up more than once. It can be frustrating and lonely to try to make something new. To put yourself out there for judgment. But at least I'm creating. At least I'm trying. At least I'm sharing. At least I am doing something. 

While "sharing" online seems to be constant, most people are not actively creating content. Consider the 1% rule of the internet - the theory that 1% of users actively create new content and that 99% generally "lurk" on most platforms . The 1-9-90 Principal is similar - that 1% of users are creators, 9% are synthesizers (Blooms Taxonomy woo) and 90% are just consumers. The Pareto Principle is also very similar and theorizes that 80% of content is created by 20% of users. 

Any way you look at it it's a very small percentage of people creating and the overwhelming majority of people are simply consuming. Here are some interesting stats I found:

0.2% of Wikipedia users ever contribute new content

44% of twitter users have never even tweeted (lurkers) and only 3% tweet daily

< 0.1% of YouTube users are creating any content

1-3% of Reddit users are contributing

< 1% of people who buy books on Amazon leave reviews

I don't know about you but I'd rather be a creator. I may not always create the best content but at least I am creating it. Creating gives you power - the only cultural influencers are creators. Consumers are passive. They believe they have limited options and work within a framework that's already been decided. Boring. And the more you create the better it gets! 

Read more about creating vs consuming here, here, and here


Psychology of Holiday Decor

One of the best parts of the holidays for me is the opportunity to decorate! I especially love Christmas decorating and despite living in a small one bedroom apartment, I have managed to fit in 7 Christmas trees of various sizes, shapes, and colors. 

 Generally I am the only person to ever see the 7 trees but I know that decorating is important to me and my mood. I wanted to know more so I did some digging into the psychology of decor. I ran into several articles talking about "neuroarchitecture"- the study of the link between neuroscience and the physical built environment. (i.e. how light affects mood)

Some interesting takeaways:

Clutter can sometimes be a good thing! It's been found that some clutter can be beneficial in a home and that being surrounded by evidence of who you are has a grounding effect. 

"Soft Geometry"or the idea that curved surfaces activate more emotional centers of our brain and cause us to relax. Conversely, a Harvard Medical School study found that sharp objects produced a negative feeling and conveyed a sense of danger. 

Plants reduce stress! Even just a picture of a landscape can improve concentration and lower stress. 

Rearranging can lift your moods! Just like the hedonic adaptation I talked about here, your physical environment can benefit from novelty. When you make changes in your environment, dopamine kicks in and motivates us. Easy way to rearrange: Holiday decor :) 

Read more here, here, and here

Math Stained Glass - Math/Art Connection

This week my classes all finished one of my favorite activities of the year - Math Stained Glass! They have to graph linear equations into a stained glass pattern then color them in and we put them on the window - instant fancy. 

The math art connection is so important to me. Every year kids complain that this "isn't art class" and I have to tell them it is. Math is art. They are inextricably linked. Here is some proof/things to ponder:

Maryam Mirzakhani, a mathematician who became the first woman and Iranian to win the Fields Medal (most prestigious award in math) works almost entirely visually. She sketches out everything on large paper and says that "The process of drawing something helps you somehow to stay connected”. This is math in the real world. It is open, creative, and outside the box. It is the direct antithesis of school math - math that is generally closed and absurd. School math poses very few interesting questions, and assumes a general algorithm can be used to find a tidy answer. That is not math.

Math is more than numbers and computation. The most powerful learning occurs when we use different areas of the brain. There are different pathways for drawing/visualizing and numbers and symbols and achievement has shown to improve when subjects are taught in a way that uses both of these pathways. Brain crossings are the definition of creativity - making connections between seemingly unrelated things and finding hidden patterns. The world is a pattern and math is all - guess what - patterns! 

Another creativity block in (boring) school math is the idea of "learning styles" that has permeated education and other fields despite there being no scientific evidence or brain research that supports the idea. Instead, many of the same styles and modalities apply to most people and EVERYONE is a visual learner! 

Visualization and visual representations are key in math. Students who use more visualizing in their curriculum achieve higher. Not just in math class, but students who are in more arts courses have been shown to score higher on SAT's and other standardized measures, as well as have more confidence, better motor skills, better decision making and problem solving skills. 

I could go on. And on. But if this is interesting to you read more here, here or here. (Or just bring it up with me over a glass of wine. But be prepared.)


Happy Friday :) 



"Take chances, make mistakes, get messy." - Ms. Frizzle

I love celebrating. Every day in my classroom we celebrate one of those weird National Days (today is National Food Day btw) and I have holiday decor for all seasons in my apartment down to cocktail napkins. So it's no surprise that I have made up my own weekly holiday - Jess Day Tuesday. More commonly known as #jessdaytuesday. I've gotten a lot of questions about what the heck this is, why and what I am celebrating etc. So here is the history and background of this great day.

I've always loved to theme dress. I frequently think of my outfits as "looks" (others think of them as "getup's" yikes)  and try to dress for the occasion at hand. My first foray into whimsical work dresses came with this math print dress: 

I'm a math teacher so this was an obvious purchase. But the interesting part of the dress isn't the dress - it's the feeling I get when I am wearing it. 

A lot of research has been done on the affect of clothing on our lives and self-perception. I've always known that when I look better I feel better, but there is some serious science to back it up. According to a study cited in the Wall Street Journal article "Why Dressing for Success Leads to Success" wearing nicer clothes than required raises confidence levels, affects how others perceive you, and boosts levels of abstract thinking - which is the thinking of successful leaders and executives. 

Another interesting study came from the Journal of Experimental Psychology and found that clothing affects our performance through "enclothed cognition" - a type of embodied cognition that basically means that the clothing you wear affects your cognitive process and your behaviors mirror your expectations of how someone wearing that clothing would behave. In one of the experiments,

"subjects who donned white coats that they thought belonged to doctors performed better on tests than those who wore street clothes, or those who thought the coats were associated with artists. Their heightened focus was evident only when subjects actually put on the coat in question (not merely when they were in the same room)."

So what does all this have to do with whimsical dresses on Tuesday? Well, the math dress made me take on the role of the most important teacher in history of course: Ms. Frizzle! Ms. Frizzle is the teacher in the Magic School Bus series and according to Wikipedia (and me) she is,

"eccentric and a bit strange, The Friz is intelligent, kind, resourceful, happy, funny, supportive, loving and somewhat motherly. She loves making jokes revolving around the lesson she teaches, even if she is the only one laughing. A redhead, she wears wacky clothing that reflects the subject of each adventure and earrings that glow before a field trip begins." 

If I had to be described as a teacher (or just as a person really), that is pretty much word for word what I would want to be said. And according to the enclothed cognition phenomena (and my own anecdotal evidence) the dresses help! 

So why isn't the holiday Ms. Frizzle Tuesday? Well you see that doesn't rhyme and things like that matter to me. :) Also, another fictional whimsical dressing teacher I admire is Jess Day - a character on New Girl - and since New Girl is on Tuesdays (and it all rhymes) a holiday was born! What started as a funny hashtag has turned into a vital and important part of my week.

So here is my challenge to you: think about the way your clothes make you feel and dress the way that makes you feel great/powerful/confident whatever. Maybe create your own day!! Post a selfie without shame. It's not frivolous and it's not shallow - it's fun! And it's science :)

And let me know how it goes :)