Math on Quora

quora iconI may not have been very active on my blog recently (sorry for the three-month hiatus), but it’s not because I haven’t been actively doing math. And in fact, I’ve also found other outlets to share about math.

Have you used Quora yet?

Quora, at least in principle, is a grown-up version of yahoo answers. It’s like stackoverflow, but more philosophical and less technical. You’ll (usually) find thoughtful questions and thoughtful answers. Like most question-answer sites, you can ‘up-vote’ an answer, so the best answers generally appear at the top of the feed.

The best part about Quora is that it somehow attracts really high quality respondents, including: Ashton Kutcher, Jimmy Wales, Jermey Lin, and even Barack Obama. Many other mayors, famous athletes, CEOs, and the like, seem to darken the halls of Quora. For a list of famous folks on Quora, check out this Quora question (how meta!).

Also contributing quality answers is none other than me. It’s still a new space for me, but I’ve made my foray into Quora in a few small ways. Check out the following questions for which I’ve contributed answers, and give me some up-votes, or start a comment battle with me or something :-).

And here are a few posts where my comments appear:

USA Science and Engineering Festival

If you’re local, you should go check out the USA Science and Engineering Festival this weekend. It’s on the mall in DC and everything is free.

USA-Science-and Engineering-Festival LogoThey will have tons of booths, free stuff, demonstrations, presentations, and performances. Go check it out!

For my report on the fest from two years ago, see this post. The USA Science and Engineering Festival is also responsible for bringing to our school, free of charge, the amazing James Tanton!

One thing that makes my class unique

Photo from Flickr.com, credit Alan Cleaver, under Creative Commons License.

What’s one thing that makes my class unique?

We play Two Truths and a Lie.

Let me explain. I teach 150+ kids each semester (which means I get new ones in January). I used to think that my job was to teach the material, and the kids didn’t need to like me for that mission to be accomplished. It doesn’t matter what they think of me. That’s not my job, so I reasoned. But thanks to reading awesome books like The Essential 55, The Excellent 11 (both by Ron Clark), and most important, Teaching with Love and Logic (Jim Fay and David Funk), I now know that’s completely and totally false. Here’s the truth: You can’t teach students until they like you.

Getting to know my students has become a major part of what teaching means to me now. The Mr. Chase of eight years ago would never have done a get-to-know you activity at all, since it takes valuable instructional time.

The trouble is, it’s super hard to get to know 150 students in one semester. Even learning their names is a monumental task. The cursory get-to-know-you activity on the first day is cool, and better than nothing, but can you really get to know 150 students in ONE DAY? I still do a little mini, fun first-day activity. But here’s an additional, deeper activity that I’ve come to love.

On the first day of class I hand out index cards. I don’t ask students for their information anymore. I can get their parents names, email addresses, phone numbers, address, and more, through our school’s database, just as you probably can. So asking for that information is a waste of time as far as I’m concerned–it’s just busy work for them. Instead, on their index card, I ask them to write their name and Two Truths and a Lie. They can give it to me after the 45 minute period is over. I tell them they can work on it while I’m going over the syllabus, if they find me boring :-). They can even turn it in the next day if they really want to craft an excellent set of statements that will fool their classmates.

Have you ever played this game? Here’s how it works: You write down three statements about yourself, two of which are true and one of which is false. Then people try to guess which statement is the false statement. Students share things that are interesting and unusual–things their closest friends in the class might not even know.

“I speak four languages”

“I have two dogs and a turtle.”

“My grandmother lives in Portugal.”

“I’ve never broken a bone.”

“I’ve been to five continents.”

“I’m a black-belt in Jujitsu.”

“I don’t like chocolate.”

“My dog’s name is Bubbles.”

When you play this at parties, it takes a while–a minute or two for each person. And of course you want to discuss the results afterward. “What languages do you speak??” “Okay, your dog’s name isn’t Bubbles. But do you have a dog? What kind is it? What is its name?”

So if it takes a while, and you want to take your time, how do you fit it into class time? Well, I have a stack of them at the front of the room and whenever we have extra time, throughout the first month or two of school, we pull a random card (or a few) and meet that student. I say “Today we’re going to meet Robert…everyone say hi Robert!” and everyone says “HI ROBERT!!” (way less corny when it actually happens; don’t worry they love it!). Then we read Robert’s card, and on the second reading everyone is required to raise their hand upon hearing the statement they think is false. Great fun. And afterward we ask Robert some follow-up questions.

It’s a fun activity and lets us genuinely get to know one another and learn very unique things about each other. I give them my own Two Truths and a Lie on the first day of class as an example:

1. I’ve done tricks on a flying trapeze.

2. I lived in Peru for a year.

3. My parents have chickens in their backyard.

(Feel free to make guesses as to which of my statements is a lie.)

This was a unique idea to my class, but some of my other teacher friends have adopted it now, so perhaps it doesn’t qualify anymore :-).

This blog post was in response to the prompt, “What is one thing that happens in your classroom that makes it distinctly yours?” which I was encouraged to answer as I participate in the Exploring the MathTwitterBlogosphere challenge. More challenges to come! (And more blog posts, I’m sure!)

Happy Metric Day, by the way!

Mindset List for incoming High School class of 2017

Flickr, Creative Commons License

Happy first day of school! For us, today marks the first day of the school year and we’re welcoming students into our midst. What are the new kids (the freshmen) going to be like?

Each year Beloit College describes the incoming college freshmen class with its now famous “Mindset List.” I looked around and couldn’t find a high-school equivalent. So here’s one I came up with. This is a description of the incoming high school freshmen class (class of 2017). Note that all of descriptions on Beloit’s college freshmen mindset list apply also to high school freshmen. So here’s my own “high school class of 2017 mindset list.” Enjoy!

  1. The Euro has always existed. So has Sponge Bob Square Pants. And Google, Inc. And the iMac. And Viagra.
  2. Bill Gates has always been worth over $100 billion.
  3. You can talk to them about the Sandy Hook shooting or the Virginia Tech massacre, but they won’t remember anything about Columbine, which happened the year they were born.
  4. Star Wars Episode 1: The Phantom Menace is as much of an ‘old-school’ classic as any of the original Star Wars movies. The movies Fight ClubThe MatrixAmerican PieSaving Private RyanArmageddon, and The Sixth Sense also came out in the years they were born.
  5. East Timor has always been a sovereign nation.
  6. George W. Bush and Barack Obama are the only presidents that they really know. Clinton left office when they were just 2.
  7. Exxon and Mobil have always been the same company.
  8. Movies have always been reviewed by Ebert & Roeper .(Gene Siskel died the year they were born; Roger Ebert just died this past April.)
  9. They won’t have any memories of John F. Kennedy Jr, Dr. Spock, Frank Sinatra, Roy Rogers, or Alan Shepherd, all of whom died just as they were being born.
  10. They have always had their music in mp3 format and used mp3 players (invented in 1998). CD players? SO passé.
  11. Seinfeld closed up shop before they were born.

——–

For more events that happened in 1998 and 1999, visit the wikipedia articles. Please feel free to correct any of my above information or suggest additions!

Arithmetic/Geometric Hybrid Sequences

Here’s a question that the folks who run the NCTM facebook page posed this week:

Find the next three terms of the sequence 2, 8, 4, 10, 5, 11, 5.5, …

Feel free to work it out. I’ll give you a minute.

Done?

still need more time?

..

give up?

Okay. The answer is 11.5, 5.75, 11.75.

The pattern is interesting. Informally, we might say “add 6, divide by 2.” This is an atypical kind of sequence, in which it seems as though we have two different rules at work in the same sequence. Let’s call this an Arithmetic/Geometric Hybrid Sequence. (Does anyone have a better name for these kinds of sequences?)

But a deeper question came out in the comments: Someone asked for the explicit rule. After a little work, I came up with one. I’ll give you my explicit rule, but you’ll have to figure out where it came from yourself:

a_n=\begin{cases}6-4\left(\frac{1}{2}\right)^{\frac{n-1}{2}}, & n \text{ odd} \\ 12-4\left(\frac{1}{2}\right)^{\frac{n-2}{2}}, & n \text{ even}\end{cases}

More generally, if we have a sequence in which we add d, then multiply by r repeatedly, beginning with a_1, the explicit rule is

a_n=\begin{cases}\frac{rd}{1-r}+\left(a_1-\frac{rd}{1-r}\right)r^{\frac{n-1}{2}}, & n \text{ odd} \\ \frac{d}{1-r}+\left(a_1-\frac{rd}{1-r}\right)r^{\frac{n-2}{2}}, & n \text{ even}\end{cases}.

And if instead we multiply first and then add, we have the following similar rule.

a_n=\begin{cases}\frac{d}{1-r}+\left(a_1-d-\frac{rd}{1-r}\right)r^{\frac{n-1}{2}}, & n \text{ odd} \\ \frac{rd}{1-r}+\left(a_1-d-\frac{rd}{1-r}\right)r^{\frac{n}{2}}, & n \text{ even}\end{cases}.

And there you have it! The explicit formulas for an Arithmetic/Geometric Hybrid Sequence:-).

(Perhaps another day I’ll show my work. For now, I leave it the reader to verify these formulas.)