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. 

Tuesday, November 5, 2013

be careful what you wish for

Today in calculus we were practicing substitution, a procedure by we which we are able to convert seemingly complex functions into simple ones in order to do integration.  If you haven't studied calculus for a long time, or ever, I just spewed out a bunch of gibberish, but no matter.  I have included a problem here for your perusal. Whether you understand it or not, this problem and others like it often result in the need for fractions. 

A student commented, "I hate fractions.  Why doesn't math only use whole numbers."  It was good that my back was to him as he said this, or he would have seen my fiendish smile. 

"But there is such a math," I replied.  "It's called discrete math.  Would you like to try a problem?" 

Of course he agreed and so I promised to post it online and offered a little prize to the first student to solve it.  You may recognise it. 

There once was a city through which flowed a river.  At the center of the river were islands.  The citizens had built 7 bridges so that they could cross these rivers and move from one part of the city to another.  The map shows the layout of the city, the river and the bridges.  The land is green, the river blue, and the bridges gold.  The problem was to find a walk through the city that would cross each bridge once and only once. The islands could not be reached by any route other than the bridges, and every bridge must have been crossed completely every time; one could not walk halfway onto the bridge and then turn around and later cross the other half from the other side. The walk need not start and end at the same spot.  Can you find this path? 

Be careful what you wish for...   

substitution photo credit
7 bridges photo credit

Monday, November 4, 2013


Homecoming week ended with a bang up weekend.  Friday was a school-wide lunch on the lawn followed by a pep rally.  That evening we had a carnival for our alums and their families complete with bounce houses and face painting for the kids, snacks and drinks, and free admission to the game.  Our football team played well and won 21-7.  The next day was the homecoming dance and by all accounts, the kids stayed and danced right to the end.  As far as I know, everyone got home safely.

I work at an Episcopal school.  Part of our mission is to foster spiritual growth in all of our students, regardless of faith.  As a result, we have a diverse population of not just Christians, but also Muslims, Jews, Hindus, Buddhists, Atheists, and a host of other faiths and plenty of kids still trying to figure everything out.  Every week we have chapel, and we say a prayer at the start of each assembly, but there are very few other times where we pray, and we certainly are not in the business of conversion.  I like that about our school, our willing acceptance of all members of our community, no matter their faith. 

Not all teams are the same, but at the end of each football game, our head coach says a prayer over the team, win or lose.  As the parent of a player who has suffered broken bones and strained tendons due to the sport, I'd like to think they give thanks for the opportunity to play and the safe conclusion of the game. 

This past week was an eventful homecoming.  I loved watching the joy it gave the students, the memories it built, and the safe return of my scholars on Monday. 

That's not really a prayer.  Just my gratitude. 

Sunday, November 3, 2013

moving mountains

Yesterday I assigned 10 problems to my College Algebra class and gave them a class period to work on them.  Anything that was unfinished became homework.  Each problem had 5 parts and the section they cover ties up a bunch of ideas that we have been focused on for months.  It was good cumulative work that cemented some important ideas for my students, and these students have struggled with algebra for a long time.

For a few, you'd have thought I asked them to move a mountain one stone at a time.  Such whining...  such complaining...  finally some of their friends told them to pipe down. 

I could be mad about this, but I just have to laugh.  These students that cannot bear 45 minutes of math work are the same ones that can play a mindless game like Flappy Birds for hours. Focusing on homework for hours on end is destined to be a part of their future should they want to succeed in college.  Sometimes I think I should give them more work, just to get them ready for the future, but I don't think endless assignments are productive or useful.  Instead we do a little bit of work most days.

It's interesting.  I actually am asking them to move a mountain, a mountain of algebra.  We do it one day, one small stone at a time. It takes all year.

Friday, November 1, 2013

nana, nana, nana, nana

Day 4 of Spirit Week was Super Hero Day.  Always a favorite, lots and lots of students joined in the fun by simply wearing a t-shirt, but some students went all out in full costume.  Choices ranged from Flash to mild mannered Clark Kent, full out Superman in tights and a cape to Bubble Girls, the Fearsome Foursome, and of course a host of characters I never knew about. 

The most common character was Batman, as the popularity of the movies has spawned a dozen different t-shirts from old school purple to true dark knight.  A couple hundred wore just the shirt, myself included, but a few donned masks and utility belts.  Our school became the poster child for Hollywood marketing.  I concluded that Batman's super power must actually be cloning himself, thus creating the hundreds of Batmans walking our campus today.

But then my colleague Jeff Wilson reminded me of the facebook meme that has been so popular and explains the many Batmans.

We took this advice.
We were all Batman.