Thursday, January 30, 2014


This week in professional development one of our technology gurus, Jen Baselice, led a lunch and learn session on using Powtoons.  This program allows you to create videos pretty quickly and effectively.  It may be a little tricky to learn at first, but in no time at all, you are up and running.  I am posting my first Powtoon here and invite you to try it.  This one took me about 40 minutes, and it's far from perfect, but it sure is a fun alternative for content delivery. I'll bet students can make some great Powtoons too!  There's a lot more cool features that I didn't use here and I can't wait to get started.  I know the next one will be better and faster!  Did I mention the best part?  It's free! 

Feel free to post questions in the comments below, and I'll do my best to answer them. 

does money matter? (student edition)

So yesterday I posted an article suggesting that simply paying teachers more might improve schools and student performance.  Today I'd like to talk about student earnings, post graduation.

A new website,, looks at the salaries of recent grads with various degrees at colleges and universities in Florida.  The idea is to help students think about the job market and how their choice of major might impact their future.  The site is a little confusing, but I suggest you click the explore data tab at the top of the home page.

An article in the Orlando Sentinel last weekend suggested some additional impacts to knowing this data.  For example, "Earlier this month, the Board of Governors of Florida's university system said it will start considering the wages of bachelor's degree holders when it decides which schools get performance funding." and "President Barack Obama has directed the U.S. Department of Education to develop a system of rating colleges based on factors such as graduates' earnings and their loan-default rates." You can read the full text of the article here

There's a lot for students to think about in this data.  Pragmatically, if you are a student or the parent of a student today, would knowing the average salaries for graduates of various schools and degrees help you choose a college or a major? 

I'd also like to consider the cultural impact of this data on traditionally low-paying careers and majors.  Will sculptors switch to engineering, just for the money?  Will writers abandon their novels for a degree in computer programming?  What impact will this have on the arts, on literature, on all the non STEM fields?  These are important questions, not just for individuals, but for our society as a whole. 

Photo credit

Tuesday, January 28, 2014

does money matter? (teacher's edition)

Today's post is part one of a two part discussion on the impact of money on teachers and students in education. 
What if we simply paid teachers more?  What if we offered teachers incentives for improving their skills and learning more?  What if we offered incentives to teachers if their students did better?  What if we let teachers decide how to make improvements happen?
It's an interesting proposition, one that was implemented in the 1990s in North Carolina and is again being suggested by former NC Governor, Jim Hunt.  You can read about what North Carolina did, their results, a Jim Hunt's current proposal here.

I think we need to ask important questions here, because the answers matter.  Why did this seem to work in North Carolina?  Why did North Carolina stop?  Will it work again?  Is it worth it to try? 

What do you think? 

seeing the forest for the trees

Today in calculus we were discussing differential equations, an important topic in the AP curriculum.  I have posted a sample of a question here.  There is a similar question on the test almost every year, and you can see all kinds of questions here.

What makes this question so important is that students are asked to apply the Fundamental Theorem of Calculus.  As it's name implies, it is the fundamental centerpiece of my AB Calculus curriculum and describes the relationship between two seemingly disparate processes, differentiation and integration. 

In the last minute of class, I asked my students why we were solving problems of this type.  I am sad to report that most of them did not know.  They had not yet made the connection between today's work and a theorem we learned last semester.  In the context of education, I think helping students make such connections is one of the most important things teachers do.  In every curriculum, there are big, hairy ideas and tiny details.  Differentiating between them is vital to a comprehensive understanding of mathematics at every level. 

When kids are learning, every single day is a tree.  As a result there are seemingly 100+ identical trees.  But that's not really true.  There are mighty oaks, sweeping willows, and scrawny weeds.  The best students are terrific gardeners.  I'm suggesting you ask your students why what you are studying this week is important and report back on the results.  I'm betting many of them don't really know.  If they don't, maybe you can take them up in the helicopter so they can see the entire forest once in a while. 

Question Credit

Sunday, January 26, 2014

two roads diverged in a yellow wood

Our society seems to think that there is a best way for a school, a teacher, or a community to educate children.  There is apparently only one way, a standardized test, to measure the progress that children make.  I disagree at every step of this discussion.  This link is the story of how one school and community has chosen to educate their children.  It's working well, but it is not the only road to success.  We all need to remember there are many roads to where we are going. I would love to hear about innovative programs in your school that help students work to their potential.  Please share! 

Photo Credit
Visit for breaking news, world news, and news about the economy

Friday, January 24, 2014

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? 

Image credit


Thursday, January 23, 2014

what makes a teacher great?

Over the past few months I have been engaged in activities at our school that have made me ask the question, what makes a teacher great?  If you have a moment, please think about the best teacher you ever had in school.  (Your favorite teacher might not have been your best teacher.  I am looking for the qualities of a great teacher, not a popular one.)  In the comments, list the qualities that made that teacher great, the things you remember that helped you learn effectively or love a particular discipline.  Thank you so much for your help. 

Photo Credit

Wednesday, January 22, 2014

answer, please...

Have you ever wanted to ask a math teacher a question?  My students do it all day long.  Here's your chance. For the next 8 hours, I'll answer any and all math questions.  There's no question too silly.  There are questions that are too hard, but if I don't know and can't find out, I'll be happy to tell you that too.  Is there something you've always wondered about?  Is there a puzzle you've always struggled with?  Now's your chance.

And hey, if you know the answer to someone else's question, answer it...  be a math guru, a math nerd...  Now's your chance.  Ask...  or answer...  a question! 

Photo Credit

Tuesday, January 21, 2014

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/ 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!   


Monday, January 20, 2014


We are not in school today, but please enjoy this fabulous video honoring the vision of an incredible man.

You can read more about the group that made this video at

Thank you to our chaplain, Ken Vinal, for sharing this message with our school. 

Photo Credit

Friday, January 17, 2014

a proof of mathematicians

This week a friend sent me this wonderful blog post about how we name groups of mathematicians.  Turns out we have creative ways of naming lots of groups!  Reading it and perusing the accompanying website just made my nerdy heart sing.  I hope you enjoy.   Happy Friday! 

Photo Credit

Scientific American Post

All-Sorts Website

Thursday, January 16, 2014

quit picking on math

This cartoon has been emailed to me, posted on my Facebook page, and left in my mailbox numerous times.  Surely word problems are not the most confusing, difficult thing ever?  COME ON. There must be analogous cartoons for other disciplines with similar titles.   
How about, how I see particle physics, or how I see Shakespearean histories?  Maybe there should be one titled, I just don't understand you. How I see languages I don't speak. 
Surely there are other things in life that people don't understand... aren't there?

Why does everybody hate math so much?

Photo Credit

Wednesday, January 15, 2014

why did you get this wrong?

Yesterday we gave a school-wide test to many of our high school students.  It was part of a monthly, statewide voluntary "fun" competition called the Florida Math League.  There are always six questions and they range from pretty simple to pretty tough.  Perfect scores are rare.  My calculus students usually average about 3 correct, although there is no calculus on the test.

One question caught my eye.  Many, many of our bright students got it wrong, but it's a common type of word problem.  What do you think?  Would you get this one right?

In a 10-km race, First Runner beat second runner by 2 km, and First Runner beat Third Runner by 4 km.  If all 3 runners always ran at constant rates, by how many km did Second Runner beat Third Runner. 

The answer will be posted below in the comments.  If you're a math teacher teaching Algebra II or above, ask your own students and let me know how well they do.

Why do you think so many people get this kind of problem wrong? 

Photo Credit

Tuesday, January 14, 2014

what if you're doing it wrong?

I've always hated "list" posts.  They tell you the 5 best of this or the 8 worst of that.  They often claim to solve problems from how to lose weight to how to save a marriage to how to ask for a raise.  I usually find they over-simplify or generalize to the point of being useless.

With that rather negative introduction, I ask you to consider the following post, Six of the best: the traits your child needs to succeed.

In it the author proceeds to list and describe the six qualities that children need to be successful in school. 

1. Joie de vivre
2. Resilience
3. Self-discipline
4. Honesty

5. Courage
6. Kindness

Hillary Wilce concludes the post with the following: 
"Our children badly need us to help them develop stronger, more flexible backbones, and all the qualities that contribute to a strong inner core can be actively fostered and encouraged by parents (parents and schools working together is even better). Just as muscles grow stronger with regular exercise, so character traits are strengthened by thoughtful encouragement and reinforcement."

I'm trying to set aside the fact that there is no discussion of the relationship that these traits have with success in school.  Do these traits cause kids to be successful?  Does success in school provide the exercise to strengthen these traits?  Or do these traits and success in school happen together, both enhanced by any number of additional, unexplored factors ranging from genetics to family income to who knows what?

What I really want to know is what you think about the very idea of fostering traits in children.  Do you think it is even possible to "build" a child with these traits?  What role do parents and schools play in creating these "super" children?

I ask because as a parent of two sons who could not be more different, I have to wonder what I did that made them so.  As a teacher of literally thousands of students whose accomplishments range from incredible success to dismal failure, I have to ask what I and their parents did to foster the disparate range of traits that resulted. 

It's not that I don't think there's a level of responsibility inherent in teaching or in parenting.  There is tremendous responsibility in both jobs and the article is happy to list those things parents believe are the schools' and teachers' jobs, items like "well-run lessons, skilled teachers, a creative curriculum, high expectations."  But as I watch parents beat themselves up because they're too tired to make every meal perfectly nutritious and teachers give up in despair because their students can't pass the state exams, I think we need to ask ourselves if articles like this aren't really just a set up. 

Do parents (and teachers) really have the ability to create kids that possess joie de vivre, resilience, self-discipline, honesty, courage, and kindness?  Are there really parents (or teachers) out there actively discouraging these traits? 

If we are to believe articles like this and take a look at the children of the world, we are forced to come to the conclusion that most kids do not have all these traits.  And if your own children, wonderful as they are, are among those that do not exhibit these traits, then this means that someone, everyone, or perhaps just you, are doing "it" wrong. 

Monday, January 13, 2014

the final countdown

Senioritis:  A crippling disease that strikes high school seniors. Symptoms include: laziness, an over-excessive wearing of track pants, old athletic shirts, sweatpants, athletic shorts, and sweatshirts. Also features a lack of studying, repeated absences, and a generally dismissive attitude. The only known cure is a phenomenon known as Graduation. ~Urban Dictionary

My seniors come back from Christmas break wishing it was over.  They hear from colleges and start to make plans for the rest of their lives, lives that rarely include high school.  They need it to end. 

As a teacher I used to wear myself out letting the seniors' attitudes drive me crazy.  But now in my later years, I've come to know it's not about me.  Second semester doesn't signify the end of anything for me.  I plan to be back next year.  After 27 years of teaching, this is just another semester.

I plan to keep going.  I will teach every day, assign homework, give tests and quizzes, create projects and novel activities.  What the seniors do does not change my plans or my attitude.  They will not turn in homework sometimes. They will do poorly on tests and quizzes.  Their grades will drop.  I will try to encourage them and attempt to remind them that it's the finish that counts.  Some will hear me.  Some will ignore me.  I do not control the behavior of others.

We are on a modified block schedule, and I have about 60 days of classes left with my seniors.  That's 60 days to teach them about math and about life.  There's 60 days to enjoy their company and their teenagerness.  On any given day I'm never sure if they will laugh or cry. 

60 days is an eternity for my seniors, but for me, it's not enough.  These days will crawl in their minds and fly by in mine.  They can't wait to be gone.  I long for them to stay. 

I always tell them it's not over until I say it's over. It's not over yet.  But it is the final countdown. 

Friday, January 10, 2014

welcome home

Wednesday was an exceptionally busy day for our school.  In addition to the visiting a cappella group, the Yale Alley Cats, the city of Winter Park put on a parade for one our alums, Charles Nadd.  A member of the Trinity Prep class of 2007, Chuck attended West Point '11 and now, at age 24, is a helicopter pilot.  His positive, can-do attitude was evident when he was in high school, and we all knew he was going places.  He is not our first alum to serve overseas, but his safe return from Afghanistan and continuous zest for life make us so proud.  As Chuck would say, "Life is Beautiful."

video platformvideo managementvideo solutionsvideo player

Photo Credit:  Ashley Johnston
Video Credit

Thursday, January 9, 2014

no accompaniment required

On Wednesday we were treated to a concert from the Yale Alley Cats.  Yearly visits from an a cappella group are definitely a favorite at our school, and sometimes they even feature an alum, a special treat.  You can listen to a song from this fantastically talented group here.  Enjoy! 

Find out more about the Yale Alley Cats here.

Wednesday, January 8, 2014

snow days

So it got cold in Orlando, a brisk 35 degrees on Tuesday morning.  Then we all blinked, and it was mostly over.  It'll be 80 degrees by Friday.  But my friends up north were not so lucky.  As the temperatures dropped below zero with dangerously cold wind chills, schools all over the north and even those as far south as Atlanta closed their doors.  This wasn't a just a snow day, although there was plenty of snow.  Millions of parents sighed in dismay as snow days turned their homes into prisons.

You'd think snow days would be awesome, but most of these kids have been home for two or more weeks. With the excitement of Christmas and New Year's over, these snow days stunk.  Kids were bored.  It's tough to entertain 7-year old Sally for days on end when she's trapped inside.  She needs exercise and interaction with other kids, something that's not possible when you're snowed in and it's literally too cold to play outside. Tough too, occupying her brother, 9-year-old Billy, a child not so excited about reading or doing puzzles.  He'd much rather fight with his sister, watch cartoons, or play video games for hours on end, much to his mother's dismay.

The cold will end and all the children will head back to school.  A collective and silent parental cheer of relief will erupt nationwide.  But school is not always such a great place for kids.  Teachers across the country will embrace these restless little souls, not just one or two at a time, but in packs of thirty, all confined to a twenty by twenty foot room. You'd think there'd be science experiments and games, theatre performances complete with costumes and learning as play.  Study after study has shown us this is how to best teach kids, but we no longer have time to do these things   Instead we continually cut back on rich experiences in favor of more and more seat work.  The richness is confined to "specials" like physical education, computers, art, or music a couple times a week.  We all know that kids only have pent up energy on Mondays and Thursdays right before lunch.  Their musical and artistic creativity can be adequately expressed from 9:30-10:00 on alternate Wednesdays.  And frankly, what's the point of teaching them about computers.  In twenty years we'll all have a chip in our heads anyway. 

This is the modern school.  Children are forced to sit too quietly for hours on end, preparing for standardized tests and five-paragraph essays.  There will be plenty of math worksheets but little physical release.  There's always another spelling test but no money or time for music, for art, for beauty.  And teachers will do the job of somehow entertaining and educating these children, a job that many parents are tired of doing after a week or two. 

Teachers do their best, but let's all be honest.  The only thing that matters is the standardized test.  The test is the measure the student, the teacher, and the school.  Unfortunately that means that for a lot of kids, once they get to school, every day is a really bad, totally boring snow day. 

Photo Credit

Tuesday, January 7, 2014

a hard look at the SAT

This weekend I was working with one of my own children on SAT questions.  We were looking at questions he had either missed or omitted.  I offer a pair of such questions for your consideration. 

Chose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

The director's __________ anything outside the cocooned world of her film's protagonist is evident in the __________ of the few stilted scenes depicting unrelated events in the lives of other characters.

a) apathy toward ... raptness
b) infatuation with ... timorousness
c) veneration of ... adroitness
d) impatience with ... desultoriness
e) honesty about ... disingenuousness

Solve the problem and choose the correct answer.

If j is a positive integer and the remainder when j is divided by 11 is 5, what is the remainder when 3j+2 is divided by 11?

a)  3
b)  5
c)  6
d)  8
e)  9

So I have some questions about these two examples, both rated "hard" by the SAT folks.

  • Which question was harder for you?
  • What is the purpose of each question in the context of English or math?
  • What does the ability to answer either of these questions tell you about a person?
  • Would the ability to answer these questions help you be more successful in college?  If so, how?

Genuine discussion requested here... 

(I know many of you are wont to wander back over to my Facebook page to discuss, but I am hoping you'll do it here.  I've made commenting easier at this site, and you can even be anonymous if you like.) 

P.S.  The answers to the above questions are d and c. 

Photo Credit

Monday, January 6, 2014

calculus: a drama

Today I decided to spend a few minutes checking out a google tool called Story Builder.  (Again compliments of our amazing professional development and technology folks) With absolutely no training I simply started writing a story.  When I finished I added music and here it is.  It took me 10 minutes, mostly because I had to correct my silly typos.

This is an amazingly simple, free tool that can be used in every discipline.  I can think of dozens of stories students could tell.

  • Envision and create a conversation between Grant and Lee.
  • Tell the stories of Greek mythology in modern language.
  • What would Watson say to Crick about an issue such as human cloning?
  • Explain how to solve a math problem through text messages.
  • Conjugate verbs in Spanish.
  • Rewrite the last scenes from "Hamlet" so that the story ends well. 

Check it out, or better yet, let your students check it out and show you what stories they can tell! 

What would you do with Story Builder

it's time

It's been a wonderful couple of weeks.  I saw a bunch of movies, spent time with family and friends, slept as much as I could, started working out again, and read a book.  Mostly I got to slow down, to sit and think, to do nothing for a while. 

Here's what I noticed about Sunday, my last day of vacation.  I woke up at 8:30 and started structuring my day.  CBS Sunday morning was on from 9:00-10:30 and my husband and I watch it over breakfast every weekend.  From 10:30-11:30 I needed to do some laundry and the dishes, prepare the marinade for dinner, and take a shower.  At 11:30 I left to pick up one of my cubs from a friend's house.  That took an hour.  When I got home, I worked with him on some SAT questions for an hour and then spent the next two grading the last of my exams.  For about thirty minutes I answered emails and for thirty more I sat thinking about how my time is structured and writing this post.  After I finish writing, I'll jump on my elliptical for a bit, finish the laundry, and make dinner. 

What makes this day different than a regular school day is really about how I structure time.  Today I will finish about ten things ranging from the mundane of laundry folding to the "intellectual challenge" of the SAT.  On a regular school day, I will do maybe fifty things, most of which I have no way to anticipate and will always be about people.  Students will have questions.  Colleagues will share stories.  Meetings will appear from the ether.  Phone calls and emails will need answering.  And in the midst of all this will be the teaching, grading, and planning that every teacher must do every single day. 

Don't get me wrong.  I'm not complaining.  I absolutely love teaching.  But maybe what makes me able to handle the unexpected and uncontrolled on a regular school day is this long, leisurely break where I do half as much work in twice as much time.  There is nothing more relaxing than thinking about something or nothing without guilt or consequence. 

People give teachers grief sometimes because we get so much vacation time. I actually did a fair amount of work on this break, although nothing close to what I would do normally.  But that's not really the point.  I concede that maybe it's not fair. I've never done any other job, so I can't speak for the rest of the world.  I do know that I am anxious to get back to my students.  I have some things I need to teach them.  I really hope that's what people want from their children's teachers, people anxious to teach.  

I'm ready to go back now, my heart light, my head clear. I 've got a new watch to help keep me on track.  I found my patience for the mundane and my humor in the ridiculous.  They were hiding under a big pile of exams I finally finished grading.

It's time.