this video is x-cellent

A little history, a little math, a quick little chat on the origin of the use of the variable "x" in mathematics...

 

teacher appreciation

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This week has been filled with Teacher Appreciation across the country.  I write a quick note to say thank you to all the teachers in my life, past and present, that helped to make me who I am as a student, a teacher, and a person.  Today I also thank all my wonderful colleagues and the dozens of teachers helping me raise my own two sons.   For all of these people, I am so grateful.



I could go on and on, but here is a special hug to these six teachers from my own youth.  Thank you.

• Mrs. Jones, who made me Abigail Adams in the 3rd grade play
• Mr. Oakes, who didn't kill me in 5th grade when I interrupted his lunch for something stupid
• Mr. Hanson, who taught me about the beauty of calculus and later how to own up to my mistakes
• Professor Vessey, my second calculus teacher and academic advisor
• Mr. Arnold, who supervised my student teaching in Taiwan
• Professor Gayle, my thesis advisor

Who were the important teachers from your life?  Feel free to share them in the comments. 

5 things I learned about math from twitter

Sunday night I was on twitter waiting for #Blogchat to start, and I thought I would sift the feed looking for the math hashtag.  Twitter is a public forum (just reminding you to mind what you say there) so I was able to grab some tweets off the feed.  I was curious about what I would find people (mostly students) talking about with regard to math.  Here are five “shocking” revelations.

 

 

 

Some people don’t like math very much.

 

Math can be poetry…  depressing poetry, but still poetic… 

Math is for sale, but I don’t think there’s a living in it.   

Doing math problems is better than some other things.

 

And finally, math is pretty funny...

 

 

2048

2048 is a simple game where players slide pairs of matching numbered tiles together to create new higher numbered tiles and continue this process until they create a tile with the value 2,048.  You can play it on your phone or computer.  Here's a version. 

One of our enterprising students decided to make a new version where the numbers were replaced by pictures of our faculty. Check it out.  We thought it was awesome.  You can make your own version here.

happy

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I'm sitting in our cafeteria, The Grille, during my off period, working on some grading.  Music plays softly through the speakers.  A Great Big World's current hit, "Say Something (I'm Giving Up on You)" featuring Christina Aguilera starts and suddenly three boys working in the corner burst into song.  It's not quiet singing under their breath.  They loudly and happily sing along.  And that's just it.  In that moment, they're happy...  working...  in school...

You know that's the goal, right?      

 

 

senior skip day

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Once upon a time, more that twenty years ago, when my school was much smaller, seniors used to band together and skip a day of school.  I don't know who had this brilliant idea, but on a random day, a day they chose, the entire senior class simply didn't show up.  I can almost hear the wheels turning.  "What are they going to do if everyone skips?"

I had the same conversation with my peers at a swim practice in high school.  We were swimming a  set of 100 yard repeats and a tired someone wondered, "What can Coach do if we ALL swim slow?"  And so we all swam slow.  Coach decided we should do a VERY long set of mile repeats instead.  In our rebellion, we traded discomfort for genuine pain.   We never tried to rebel again. 

My school took a different route.  We simply gave the seniors a Senior Skip Day.  Rather than allow the chaos of student led rebellion, someone must have negotiated a deal where the Monday after prom became Senior Skip Day.  It's now a planned day on our calendar, one senior privilege among several others.  A lot of schools have handled it this way. 

Once in a while I hear a senior say that they should skip another day (never a different day, just an additional day.)  I always give them a stern look and the idea dies a quick death. 

It reminds me how fortunate I am to work at a place where the kids are pretty darn good.

prom

Last Saturday night was Prom, an annual rite of spring in high schools across the nation.  This year's theme was 1920s, a Gatsbyesque celebration of a time long gone.  Students raved about the lovely décor, the delicious food, and the remarkable saxophonist that played so well.  Our students were decked out in their finest gowns and sharp tuxedos.  I don't have permission to post their pictures here, but the costuming was indeed lovely. 

Our school has a no tolerance policy for drugs and alcohol at prom.  Each car is met by chaperones.  Students are expected to arrive and remain sober during the event.  Cars, limos, and party buses are searched as needed. Students are very well supervised.  Any student that leaves the event is not allowed to return.

Post prom parties are another matter.  Some parents believe

that they should host the party and allow drinking in their homes on the grounds that at least the kids are supervised.  Other parents take a no tolerance stance, letting their own children know that underage drinking and drug use are unacceptable under any circumstances. 

What are your thoughts?  How do you think we should handle underage drinking and drug use with our own children and in our culture as a whole?  What are the best means to keep our teens safe?  I welcome your comments below. 

headmaster's day

Photo Credit:  Lane Epps
 

A favorite tradition at our school, Headmaster's Day is called each spring by the headmaster and is an unabashed field day of fun.  Students sleep in, play games, hang out with friends, and enjoy the beautiful weather.  The day begins with a rocket launch and then the games commence.  A dozen competitions follow ranging from relays to ultimate frisbee, balloon tosses to dodge ball. The smell of sweat, the thrill of victory, and the agony of defeat fill the air.  Free Italian ice is available to all morning, cooling sweaty bodies and crushed spirits.  The day concludes with the junior-senior rope pull across our canal.  The juniors get wet swimming across the canal and the seniors almost always win.  School closes at noon and we all head out for an afternoon of rest. 

This is a wonderful day, one that even in the rain remains a tradition worth preserving.  Today we had spectacular weather with a high at noon of 80 degrees.  It never gets better than this. 

squirrel!

I work at a school that is in many ways as idyllic as Disney World.  The weather is lovely and students are able to spend most of their free time outdoors if they choose.  They unceremoniously leave their backpacks, gym bags, and lunches all over campus without concern.  Theft is rare.   Students often say "Someone stole my backpack," when what they really mean is, " I set my backpack down and forgot where I left it." Those of you with a child living at home know that you don't need a 100 acre campus to make this happen.  A child can lose almost anything in a 12 x12 bedroom.

We share this Eden with much wildlife, as many lakes and ponds dot our property.  Wood storks and egrets share the lakes with fish, turtles, and frogs.  Crows battle migrating robins for the grass seed we put down on our lawns, wood peckers pound out a beat while snakes slither into the bushes.  But the kings of our kingdom are definitely the squirrels.  These fat pranksters are bold and unabashed in their pursuit of lunch.  Student lunch bags are gnawed through and Ziplocks and Tupperware are no match for the determined rodent.  Whole sandwiches are dragged across the quad, tins of Pringles devoured.  Our students immortalized our lovely campus with a beautiful mosaic.  Featured on the right side is a gray squirrel digging into a red lunch bag.

Life is good here, for students and squirrels. 

dazed and confused

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Remember the first day of school?  Students were excited to be back, to see friends, share stories, and check out their new schedule, books, and teachers.  There was an air of anticipation, a thought that anything was possible and great things were about to happen.

That was August. 

No such luck on the day after spring break.  Mostly I got that stunned look of a deer in headlights, with no real thoughts other than,

"Why does school start so early?"

I was kind of thinking that myself when the alarm went off.  Then I got up, made some coffee, and got started on another great day at the job I love. 

and we're back...

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The only way to get to summer vacation is to make it through the 4th quarter...  here we go...  29 class days remain with my seniors, 33 with my underclassmen, 25 with my AP students... 

a perfect day

Once a week I have block period with my students, 80 minutes with them to think, to talk, to play.  Each week I try to ask them something about themselves, a question of the day.  It helps me know and understand them better, to make that connection of shared experiences that allows me to try to motivate and inspire them to do better.  This week I asked them to help me build a perfect day.  Each person was able to contribute one thing to our perfect day.  It could be an activity, a thing, an idea, whatever they wished.  We recorded it on the board, a picture of some sixteen year olds' perfect day... 

second opinion, please

I'm trying to decide if I'm a Madame Benevolent Dictator looking out for my students' health and well-being or a permanent Princess Crankypants.  As you know, I can be cranky at times, but I'd like to think I'm basically good.  Here's your chance to give me a grade. 

There's this group of 9th graders that plant themselves in the hallway of my building during lunch.  They talk about teenager stuff and they're not bad kids, but they are loud.  Monday I threw them out the door on the grounds that it was a beautiful day and they were loud enough for me to hear them 3 doors down.  I have no doubt I know what they think of me, but I'd like a second opinion. 

Benevolent Dictator or Princess Crankypants...  What do you think? 

hello monday

princess crankypants speaks...

February may be the shortest month of the year, but I gotta tell you, it's overstayed it's welcome.  I don't know what it is, but even though there's plenty of good that happened this month, I can't say I'm sad to see it end. 

More than anything else, I think that its the cycle of the school year that makes February seem to last forever.  January zips by in the post holiday madness.  March signals the end of 3rd quarter and spring break, and April and May are filled with end-of-year field trips, sporting events, prom, awards assemblies, exams, and graduation. 

Our school's February was jam-packed with Valentine's Day, a long 5-day weekend, and the Sadie Hawkin's Dance.  We had several guests including a visiting alum and helicopter pilot, teachers from a school in Nigeria, and 40 Headmasters in town for the NAIS conference.  I personally took a quick trip down to Key West, watched my children play sports, went to two plays, celebrated two family birthdays, and nursed my whole family through a long bout of lingering viral infections. 

I am sure that you have a similar list of activities and obligations.  I know I ought to be grateful, but mostly I'm just exhausted and looking forward to spring break.  Maybe you are too. 

So long February.  Farewell, Auf Wiedersehen, Goodbye.  Until next year...   

spambots

So a spambot has latched onto one of the posts at this blog and has tried to comment literally hundreds of times.  I am happy to report the spam filter has blocked them all, but I am going to try to shut this down by changing the means by which you can comment at this blog, making it a little more difficult. 

I plan to return the settings to open, anonymous comments on Monday to see if repeated failure caused the bot to move on. 

In the meantime, I hope you all get some rest.  I know my northern readers have had a very snowy, challenging winter.  I have an interesting post planned for Monday, a discussion on why you can't trust political polls.  See you then. 

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5 day weekend

Imagine me dancing.

That is all.

 

sick days...

In case you were missing me ... not sure when I'll be back ... that's literally all I can do...

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putting the "pro" in procrastination

Procrastination:  To put off or defer until a later time

In calculus class our weeks are structured so that the beginning of the week is the presentation of new concepts, the middle of the week is the practicing of these new concepts, and the end of the week is the assessment.  The class is structured in this way for several reasons, but the result is that because we test or quiz on most Fridays, we rarely have weekend homework.

Calculus-free weekends have been a constant this year in the class, something I thought was really valuable for students.  This week was shortened, but we learned a lot of new material, and as a result, we are not quite ready for a Friday quiz or test.  I offered to make the online homework assignment due on Monday morning instead of Friday afternoon, as I had heard several students had a heavy load of work. I figured that most of them would decline, valuing their weekend.

I found the opposite was true.  As soon as I offered to extend their deadline today, many students simply stopped working.  Conversations with neighbors were suddenly about everything but math.  I really can't wait to ask them how they felt about their procrastination on Monday.  The teacher in me senses a really nice "teaching moment." 

I have to wonder how procrastination develops, as most everyone I know does it, adults and teenagers alike.  Is it part of our genetic code, built into our programming, or is it as much learned as calculus, learned like most of what we do in school? 

Other questions:  Does our "just in time" society contribute to the idea of procrastination?  Is it really just a matter of having too much to do?  Are there long-term negative consequences from procrastination?  Does it change our brain chemistry?

If you know anything about procrastination, you know you'd rather comment on this blog post than go back to whatever you "should" be doing, so go ahead and comment.

Do you procrastinate? 

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to infinity and beyond

Infinity has been making the rounds recently, this time in the form of a video that shows that the sum of the whole numbers is -1/12...as in

1 + 2 + 3 + 4 + ... = -1/12 

Now I'm the first to admit that this result is at least counter-intuitive and definitely requires some pretty sophisticated mathematical thinking.  If you'd like a pretty good explanation and have a hankering for some math this morning, you can check out this blog post that includes the original video. 

Infinity is a pretty interesting concept, one I love to use to challenge my students to think a little differently, to think outside the box.  I offer a couple of examples here that may help you understand why infinity is such an interesting concept. 

Zeno's Paradox:  The Archer's Arrow

An archer picks up an arrow, places it against the bowstring,

draws the string back and lets the arrow fly towards the target. It looks like it will be a bulls-eye, but of course we won't know for sure until it hits the target.

Before the arrow reaches the target, it must first travel half of the distance to the target. From there the arrow travels half of the remaining distance to the target. Quickly, the arrow travels half of the distance which remains after that, then half of the distance that is still between it and the target.  In fact, before it can get to the target, the arrow must always first go half of the distance that remains between it and the target.  Does the arrow ever hit the target?

Some Infinities are Bigger than Others 

Consider the counting numbers (called Natural Numbers).  They are infinite.  The first is 1, the second is 2, the fifth is 5, the 100th is 100.  They go on forever, as whatever number you pick, I can add one to it and keep going.  Because I can count them, this kind of infinity is called countably infinite.

Now consider the numbers 0 and 1  How many number lie between them?  Well, there's all the fractions, and I hope you can see that there's an infinite number of those.  I'll mention a few, 1/100, 2/100, 3/100.... 1/1000, 2/1000, 3/1000...  Can you see how there a huge number of these?  There's also a whole lot of other numbers in there called irrational numbers.  They are decimals that neither repeat nor end.  Here's one:  .1234567891011.... Here's another one...  .101001000100001000001....  In fact, there's an infinite number of numbers between any pair of numbers and an infinite number of pairs of numbers between 0 and 1.  In fact, there's an infinite infinities between 0 and 1, in this case called uncountably infinite.  I can't even imagine where to start counting here.  Hence it's name, uncountably infinite.  

Point 9 repeating, .9999.... equals 1.

There's a simple little proof that shows that .9999.... = 1 as shown in the diagram.  The lovely little video explains it and a lot more.  I know, I know...  this whole discussion is also counter-intuitive.  As a student said in my class a few years ago, "I get it, but I just don't buy it."   I just love infinity!   

 

Infinity Credit ,  Arrow Credit, Proof Image Credit, Video Credit