Tuesday, December 17, 2013

a long winter's nap

Sometimes the best part about working hard for a long time is the moment when you take a break and get some rest.

In the first four months of writing this blog, I have been blessed with 10,000+ visits from all of you.  I am so grateful.  Please accept my thanks. 

I am going to take some time to be with my family and friends and indulge in that long winter's nap I so desperately need.  I hope you will find time to do the same. 

Best wishes to you and yours for a restful and relaxing vacation and a joyous and peaceful new year.

Please enjoy this holiday greeting from my Trinity Prep family by clicking here. 

See you in the New Year.  Sweet Dreams. 

Photo Credit

Friday, December 13, 2013

lessons and carols

The Christmas spirit is everywhere on campus these days. Our students are festively sporting Santa hats and Christmas sweaters, Secret Santa exchanges abound, and Thursday was my favorite chapel, our lovely Lessons and Carols service.  Faculty and students tell the story through readings from the gospels, our musicians perform, our choirs sing, and our students join in the carols.  It is a wonderfully beautiful hour. 
You can listen to one of my favorite songs, the annual conclusion to the service.  Christmas in Sarajevo is performed by our Wind Ensemble and directed by my colleague, Brian Beute.  I have included the link is to last year's performance, as this year's is not quite ready yet.  Every year is truly wonderful.  Pour yourself a cup of coffee, sit back, and enjoy a couple of lovely minutes.

Thursday, December 12, 2013

building walls

This week in all of our classes we are reviewing for exams.  I decided to try a free online tool called Padlet that would allow students to collaboratively build review sheets (like posting stuff on a bulletin board or wall) that could contain text, images, links and videos.  The students were assigned to groups and given guidelines as to how many posts, what was expected, and how they were going to be evaluated.  They took to the project like ducks to water and didn't look up for 40 minutes. 

You can see one such wall built  in progress here

Wednesday, December 11, 2013

love and math

This book has been sitting on the left corner of my desk since September, mocking me.  I mentioned that I thought it looked interesting, and our awesome librarian got it for me to read.  I see it every day, but have yet to find time to read even a page or two.  To be honest, I'm afraid to start it for fear that it's really good and I won't be able to put it down.

I used to have the time to read hundreds of books.  When I was single and childless, I really had summers off and could read a book almost every day.  Now I'm working on Nate Silver's, The Signal and the Noise.  I manage about two pages right before falling asleep at night.  I can't remember what I've read from one day to the next, so I've been working on the same two pages for a couple of months. 

I'm hoping that I find time to read over the holiday break, but you know that goes.  My priorities are pretty clear.

Spending time with family and friends
Reclaiming and cleaning my house after the holidays
Sleeping for about a week
Finding my way back to the gym
Preparing for second semester
Reading Love and Math

If you would like to recommend a great book that can hold down the left corner of my desk for second semester, I would love to hear about it! 

Monday, December 9, 2013

monday night blues

In class on Monday we were reviewing for the last test in calculus before we take exams next week.  We started looking at questions on Friday and continued today. Students drew me pictures illustrating the upcoming evening's review process in various ways.  Two are pictured here. 

In case you were wondering what we were working on, the problem is shownbelow.

the neverending story

What if you lived life on a hamster wheel? 

Think about a big project you've worked on in your life, something you sweated over for a long time.  Maybe it's a paper you wrote, the degree you earned, a relationship you developed, a painting completed, a car restored, a job attained, a home built.  What if instead of finishing and knowing how it turned out, you finished and then it disappeared?  You wrote the paper but it was never graded.  You finished your course work, but didn't get a degree.  You dated for years, but you never married.  You completed the painting but it was never hung.  The car was never started, no paycheck ever came, the house stood empty.  How long would you keep working if you never found out if your work mattered? 

This is how teaching works for a lot of us.  Students finish our classes and literally disappear.  Many teachers have no idea whether anything they ever said, did, or taught was useful or meaningful. 

I have been really lucky in that a lot of my students have come back into my life in recent years through the power of social media.  I have been teaching for 27 years and have kept in touch with fewer than ten students from my first five years.  But I have spoken to literally hundreds from the last ten through Facebook. This post isn't a ploy to get you to say nice things to me.  I'm good.  Thank you to every alum that has contacted me over the years.  You are awesome. 

What matters is that we are fast reaching a crisis point in education where new teachers don't last much more than a couple of years before they walk.  There are a lot of reasons for this, but most people will put up with a lot of nonsense if they know that what they are doing matters.  Let's be clear.  Students are the reason we teach. I challenge you to track down a teacher who was meaningful in your life and express your feelings.  You can't change everything that is wrong in a teacher's world, but you just might make today right. 

Thank you. 

You can read about teacher attrition here. 

Photo credit

Friday, December 6, 2013

happy teacher

It's 2:51 on a Thursday.  I have nineteen students in my last class of the day, one that ended at 2:40.  Eight of these students are still here working.

"Is it OK if we stay and finish?"

Yes...  it's definitely OK...   

Photo credit

Thursday, December 5, 2013

toys for tots

In December our school continues to serve our Central Florida community as best we can.  In the middle school, advisory groups adopt children and families from the Orlando Union Rescue Mission, providing Christmas toys, clothes, and gift cards for the homeless.  Our high school students participate in Toys for Tots, donating literally hundreds of toys to help the Marines serve more than 30,000 children in Central Florida alone.  I am always so proud of our students and their families at this time of year. 

I would love to hear about your school's efforts to serve in their communities! 

Happy holidays to all!

rolling the dice

At the start of school a colleague asked me, "Can you use these?" and handed me a box of dice.  They weren't regular 6-sided dice.  They were crazy dice with 8, 10, 12, or 20 sides.  They were a dozen different colors, beautiful and unique.  I spent some time thinking about them and considering whether I could use them to help students learn something about probability.  I asked my students, "How can we figure out if any of these dice are 'loaded?'"  Together we built a project where they rolled the dice many times and attempted to determine whether the dice were loaded, whether a certain number came up more often than was statistically likely. 

Each student chose two different die and calculated the theoretical probability of each roll.  Then they rolled the pair 300 times and calculated the experimental probabilities.  Finally they commented on whether they thought any differences were significant.

In hindsight, I probably should have waited until later in the year when we study how to determine the statistical significance of differences in data, but I am pretty satisfied with how this went.  We got a chance to practice using excel, the students did something they'd never done before, and I got to take advantage of a lucky windfall. 

This is what I love about teaching, the opportunity to take a chance, try new ideas, and evaluate their effectiveness.  I encourage my fellow teachers to go ahead and roll the dice. 

Just for fun, consider a pair of dice, one with 8 sides, one with 12.  If the sides are numbered 1-8 and 1-12, what is the probability that you will roll a lucky 7 on this pair of dice? 

(The probability of rolling a lucky seven on a pair of six-sided dice is about 16.7%)

Wednesday, December 4, 2013

global intelligence

Yesterday the results of an international standardized test were released and surprising to no one, the U.S. did not fair well in the comparison.  You can read a brief summary of the findings here

There are a lot of questions inherent in such tests.

  • How were the students selected?
  • Who wrote the questions?
  • Did the students prepare for the test?
  • Is the sample of students from each country similar?
  • How can we compare ourselves to countries where not all students attend school?
  • Was the test controlled for cultural bias?
  • Does the test actually assess something we care about?

My list can go on and on.  I attempted to research some of these questions, but the website is not as helpful as I would like.  I don't have answers, just more questions.

I think the last question is especially important, so before we once again start beating up on our 15-year-olds, our teachers, and our educational system, why don't we take a look at the problems.  Try them yourself.  There's only 6.  I answered them in about 10 minutes, but I am a math teacher.  Can you do them all?  Presumably everyone older than fifteen should get them correct.  But whether you can or you cannot, I think we'd better start asking the right questions.

  • What is it that we actually want our children to learn? 
  • What kind of problems should they be able to solve? 
  • What are our goals?
  • How will we know if we've met them? 
  • What are the best means to reach these goals?
  • What do we need to be successful?
  • Are we willing to do whatever it takes to educate every child in America? 

I welcome your thoughts. 

You can find some additional commentary here

Monday, December 2, 2013

fear factor

"This is the first time I can remember that I have not been terrified about my math exam." ~student in College Algebra

I teach College Algebra.  It is populated by juniors and seniors that have struggled with math in the past.  For some, math is intellectually challenging.  They work hard, but they just don't get it.  For others, math is not interesting and so they don't do the work they need to do to get it.

The purpose of College Algebra is to give students another chance.  The goal is two-fold.  First reinforce the essential algebra skills required to move forward in a college level study of mathematics.  Second, change hearts and minds.

I think we have to ask some hard questions about how we teach math as a society.  I work in a school with 'good' students.  They want to do well.  They do their work most days.  They take notes, they ask questions, they engage.  But still they are kids.  They get distracted by football games and parties.  Say the word "cake" right before lunch and they're probably lost because they're always hungry.   

Yet in my best case scenario, we still have students who are not only struggling, but afraid.  How can you learn when you are afraid?  In our effort educate them all, we have obviously lost some.  In my school, like in most schools, we went on before they were ready, either in terms of intellectual functioning or maturity.  And as a result, they fell down, they failed.  Maybe they've been failing a long time.  And nowhere along the way did they get up.  We just left them there.

The Atlantic recently published an article discussing the myth of "I'm Bad at Math." It's an interesting read on how kids get caught in a spiral of failure.  I think it's easy to be hard-core, to come to the conclusion that kids that fail are lazy or deserve it.  But it's not about fault.  The world is already a hard place.  Schools are under no obligation to model this.  Instead we must consider our intended goals.  Education on our timetable fails some kids.  Why can't the timetable change?  As parents and educators, we need to start asking questions that don't end with a standardized test.  That's the job. 

I'm not suggesting we just pass students along by lowering our standards.  I am suggesting that we try something different.  As always, we stand on the edge of educational change.  Technology has placed the world's knowledge at our fingertips and open access sites like Khan Academy and Udacity have made tutoring and a world class education available for free.  But all of this doesn't change the need for personalization and attention to individual needs.  Kids are not cans of peas.  One size does not fit all.

Education is not a gift, it's an interaction and a responsibility.  Interaction that leads to fear is failure. 

Interestingly enough, everyone fails.  What we do next says everything about us.

Photo Credit

the world needs more hugs

A student at our school thought the world needed more hugs, so he developed a website that allows you to send people hugs.  In the spirit of the holidays, this seems like a pretty good idea.  I hope y'all send his google analytics through the roof today...  happy Monday...  send a few hugs...   


Friday, November 29, 2013

giving thanks

This is my 51st post since I started this adventure.  Mostly I'm stunned.  This blog has had more than 7000 hits in the past 2+ months. 

I know there are regular readers, students, teachers, friends, alums of my school.  I am deeply grateful for all of you. 

There've also been drive-by readers, people who popped in to make a comment or got lured in by a silly title.  Some of these folks came back over and over.  They are awesome new friends. 

And a few people came by the disagree with me.  I love this!  Those conversations are priceless.  Missing have been spammers and trolls.  I'm grateful for that too. 

I'll be off for the next couple days, on a vacation to recover from the feasting.  When I return it will be a sprint to exams and then a longer vacation. 

I wish you a restful weekend and the peace that comes from being with those you love, your bellies and hearts overflowing. 

Thank you for supporting my first 50...  Get some rest.


P.S.  On another note, if you're on twitter and want to check out students writing tweets from the turkey's perspective, follow @BirdofThanks ...  simply adorable! 

Photo Credit

Tuesday, November 26, 2013


Each year our school collects cans for the Second Harvest Food Bank.  Central Florida was hit hard by the downturn in the economy and our recovery has been slow.  There are still so many folks who are hungry.  Last year we collected more than 13,000 items, weighing more than 6 tons.  We're still totaling up this year's haul, but no matter the numbers, I am proud of our school and our students.  As part of the program, we build sculptures with the cans.  You can see some of them here.



Monday, November 25, 2013

cow...cow... COW!

A colleague posted this silly website on her Facebook page, and I showed it to some students.  I have been hearing it all week...  make sure your volume is on. 

Sometimes you just need to play...

Friday, November 22, 2013

student worries

Student:  Is today a work day?

Me:  Yes.  You can work on the online assignment.  I will need 10 minutes to talk about the quiz.

Student:  I love work days.

Me:  Why?

Student:  There's no pressure.  You can just work on stuff until you get it.  There's no stress to keep up.

Me:  I understand when there's stress on test days.  Is there stress on days when we learn new things?

Student:  Yes.  I'm worried I will fall behind. 

Me:  Do you fall behind?

Student:  No, but I'm worried I will.

Wednesday, November 20, 2013

perfection is overrated

On a mediocre day, teaching math is about showing students how to solve problems.  If it's a decent problem, the students might care, but mostly they'd like me to teach them a rubric so that they can easily do the homework.

On a good day, I manage to not only teach students how to solve a problem, but also why a particular technique works so that they might have a tool to solve a different, but conceptually similar problem later.

On a great day, we have a problem and they figure out the how and why for themselves. 

This week we are working on figuring out how to graph complex functions using calculus techniques.  This lesson was on how we might find the concavity of a graph along with a review on the procedures for finding asymptotes. 

My lecture was perfect.  It started with a good question.  I remembered to emphasize the big ideas.  I modeled the correct techniques and justifications.  I asked them a few questions to be sure they were with me and they answered each one correctly.  And I ended just in time without rushing.   They asked me nothing.  As I was saving the day's notes to post online, I thought, maybe I should use them again later in the day because they were just right.

The hard thing is, because class was perfect for me means it wasn't that great for the students.  The best learning doesn't happen when I do everything right.  It happens when things go a little wrong.  The act of wrestling with the material, struggling to understand, solidifies the learning.  Asking questions about things they don't understand means they are thinking about the ideas, poking holes in the explanation. 

When I deliver a perfect lecture, it means they didn't do any intellectual work.  It means they didn't process.  It means they are going to struggle with the homework.  And it's better to struggle together in class than alone at home. 

I had, at best, a mediocre day. 

Tuesday, November 19, 2013

take me to the river

Humanity hates word problems.  But the reality is, once you know how to do a particular type of problem, it becomes easy.  This particular problem caused a real stir in my classes.  Post your solutions in the comments and I'll follow up with an answer...

A power boat and a raft both left dock A on a river and headed downstream.  The raft drifted at the speed of the river current.  The power boat maintained a constant speed with respect to the river.  The power boat reached dock B downriver, then immediately turned and traveled back upriver.  It eventually met the raft on the river 9 hours after leaving dock A.  How many hours did it take the power boat to go from dock A to dock B. 

Monday, November 18, 2013

what are you afraid of?

A few weeks ago I asked my students two questions. 

What are you proud of? 

What are you working on?

Here are their responses, side by side.

What are you proud of?
What are you working on?
Math test grade
Being a better blocker
Being outgoing
Being more focused and studious
Able to connect with people
Fantasy football team
Not stressing about college
Snow skiing
Math skills
Positive outlook
Work ethic
Crew skills
Getting more work done
Getting even more work done
Improved focus
Musical ability
Books read
Sight reading
Not stressing out
Study habits
Bought own car
Ice hockey
Commitment to one thing

Grammar aside, I can tell you which question my students found most difficult.  All of them had something they were working on, but they weren't allowed to tell me until they first listed something they were proud of. 

It was almost painful to watch.  They were embarrassed.  Some of them gave me nothing important, unwilling to open themselves up to anything worthy of scrutiny.  Others were ready to share, confident in the safety of the environment, sure of themselves.

This blog is read by students, friends, alums, teachers, strangers.  It's your turn. 

What are you proud of?  What are you working on? 

Come on, tell me.  What are you afraid of? 

generation gap

Before class I was telling my students a story about how you never know how you will feel about the people you know in high school.  I am 30 years out of high school and two friends from back in the day, each having raised their own families and then divorced, have recently reconnected and kindled a romance after all these years.  It has been pretty amazing to watch, a testament to the fact that life is long, we often get second chances, and love is a powerful and wonderful thing.

One student's response:  "I wonder if I'll be alive in 30 years."

Friday, November 15, 2013

anyone home?

In our school, the students in grades 8-12 all have their own laptops.  They carry them around with them and use them as appropriate in every class.  This means that when they have a question, they can ask it via email at any moment during the day.

I love that they can do this and will reply as soon as I am able.  Sometimes I am teaching, and can't answer right away.  Other times I respond in seconds because I am online working anyway. 

What strikes me is that although they think to send the email, they rarely think to check to see if I answered.  Every day a student will stand in my doorway and casually ask, did you get my email?

My response is always the same, "Yes.  Did you get my response?"

I have never been more connected, more accessible to my students...  and still we are disconnected. 

Photo credit

Thursday, November 14, 2013

fair warning: this post includes a picture of a cricket

My fabulous colleague Jon Gray teaches 6th grade science and AP Environmental science.  Although it would be fun to comment on what has to be a day of multiple personalities, that's not what I wanted to talk about.

I stepped out of my building to find him being trailed by a gaggle of 6th grade goslings, his six foot frame towering over them.  Jonathan loves to encourage students and adults alike to see the world, to explore the wonders in our beautiful Florida habitat.  He stopped to show me what they had found, a mole cricket. 

I know that insects are large and fierce in our temperate zone, but I still like to look at them and wonder at their beauty and complexity.  I'm also the resident cockroach squasher, so there are limits to my interest.  According to our 6th graders, stereotypes about my curiosity remain.  As I marveled at the cricket's amazing earth moving claws and sturdy jumper legs, the student cradling it in her sweatshirt asked me, "Are you a science teacher?"

Photo Credit

Wednesday, November 13, 2013

this key doesn't fit

Some people think Monday mornings are tough.  I actually think Tuesdays are tougher, and Wednesdays...  whew...

Today I stood in front of my classroom door repeatedly clicking the unlock button on my car keys. 

Just for the record, it didn't work.

Tuesday, November 12, 2013

do you mu?

Some days everything goes right. Last Tuesday was the Mu Alpha Theta initiation ceremony.  Mu Alpha Theta is a mathematical honor society for high achieving high school and junior college math students.  In our chapter, the focus is on service.  All of our members act as tutors in our community, assisting their peers as needed.  They also participate in math competitions and plan and execute a school-wide celebration of Pi Day on March 14.  Each week we hope to select a mathlete that has performed well in a competition, served exceptionally as a tutor, or was nominated by a teacher for excellent work in class. 

Today's initiation ceremony was planned and executed by the officers of the club and included a celebration of our 36 new members.  We all learned a small part of the history of mathematics and afterward enjoyed a buffet lunch donated and served by parents of the students in our society.  The food was delicious, the ceremony well-attended, and the club thriving with 80 members. 

I encourage you to find out more about Mu Alpha Theta and consider a chapter at your school.  It is a great way to foster interest and excellence in service and mathematics.  You can learn more about Mu Alpha Theta here

Photo credit

Monday, November 11, 2013

play ball

Friday's FCIS Keynote speaker was Harvard Physics Professor Eric Mazur.  His talk, entitled "Confessions of a Converted Lecturer" was in line with the current thinking on the flipped classroom.  His thoughts are that education is not simply a transfer of information, but that students must actually assimilate this information in order to both retain and use it effectively.  The flipped classroom is one idea that allows students to transfer the information at home by watching lectures, but then assimilate it in the classroom through problem solving, debate, discussion, and a wide variety of other learning tools. 

In the talk he outlined a 6 - step process by which teachers might effectively get students to assimilate information.  He suggested that teachers

1.  Ask students a question
2.  Give them time to think
3.  Take a poll of student answers
4.  Allow the students to discuss their answers
5.  Repoll the students
6.  Explain the solution or have a student explain

This is not the first time I have heard about this technique.  At another conference, the speaker used it with the question below.  It is a favorite in my calculus classes and in my summer training sessions for calculus teachers.  It stumps my students quite a bit, and many teachers as well, but then we discuss it and you can literally see lightbulb go on.  We cannot follow Mazur's model very easily here, but the method and the question are worthy of discussion. 

Think about a ball you have thrown into the air and consider the ball at the exact moment that it reaches it's greatest height.  At that exact moment, which of the following statements is true?   

A.  The velocity and the acceleration are the same.
B.  The velocity is greater than the acceleration.
C.  The acceleration is greater than the velocity.
D.  There is not enough information to know the answer. 

What do you think?

  • Can you explain your answer in a mathematical way?
  • Can you explain your answer so that a middle school student can understand?
  • What do you think of this model for the classroom?
  • Have you used it and if so, could you share your questions?

I will post the answer at the end of the day if the discussion does not reveal it.

You can learn more about Eric Mazur and his work here

Photo Credit

Friday, November 8, 2013


When my own children were little, I hated teacher workdays.  The school being closed meant that I had to find a place for them or take off work, and being a teacher myself, it drove me crazy.  I can understand why parents hate teacher workdays.

Teacher workdays fall into a bunch of categories.  Some of them truly are work days in which I sit at my desk and plan, grade papers, and handle the mountain of paperwork, both literal and virtual, that comes with the job.  Other workdays are a series of meetings where we set policy, learn computer programs, strategize on student issues, and meet with parents. 

Today we have a teacher workday and this time most of my colleagues and I will be attending the Florida Council of Independent School Conference here in Orlando.  There we will hear a series of talks that are some combination inspiration, educational philosophy, and pragmatic lesson plan ideas.  If this goes well I will have had some deep thoughts about what I am doing as a teacher, and what my school and department are doing to make the education we provide better.  I hope to gather some tips to convey content more effectively or consider some interesting games or lessons to inspire students to learn more. 

I have been fortunate to attend conferences where I had a transformative day.  Afterward I could not wait to return to my classroom and share and implement what I had learned. I have also attended conferences when the information simply reinforced what I was doing.  There was nothing new, but at least I knew I wasn't doing it completely wrong.   

Days like this remind me how fortunate I am to work at an amazing school with great students.  This may be a reaffirming or a transformative day, but either way, I'll be back at my desk on Monday ready to rock.  There's no place like home. 

Photo Credit

Thursday, November 7, 2013

fashion statement

A few times a year we have a "dress up day."  We ask our gentlemen to wear pants, dress shoes, dress shirts, and ties.  Our ladies are asked to dress modestly and nicely in skirts, dresses, or dress pants.  The students look wonderful.  Wednesday was one of those days.

On Tuesday I had the following conversation with two seniors:

Senior 1:  I hate dress up day.

Me:  But why? 

Senior 2:  It's so much effort.

Me:  But both of you are wearing lovely dresses right now.  You need do nothing more than you are already doing.

Senior 1:  Yeah, but it's dress up day, so I feel like I need to do more, to look REALLY nice.

Me:  But you both already look wonderful. 

Senior 2:  Tomorrow we'll look AMAZING.

Photo Credit

Wednesday, November 6, 2013

the long and winding road

Yesterday we were looking at problems like the one pictured in College Algebra.  In most cases, the students were able to clearly explain what to do, but could not actually solve the problem correctly without making little mistakes. I have some questions about these types of problems and welcome your thoughts.

1.  What is their purpose?
2.  Does their length and detail oriented nature do more to discourage students than help them?
3.  Are there other ways to assess these concepts?
4.  What does the inability to complete such a problem tell us about a student? 

The solutions shown are correct, but there are several mistakes in the intermediate steps that make the student's work incorrect.  You are welcome to offer corrections in addition to your thoughts in the comment section.