Monday, June 2, 2014

last dance

Saturday morning was graduation for our class of 2014.  The ceremony was packed, with our students' families eager to celebrate this important day.  We heard excellent speeches from our students and an alum, diplomas were received, pictures snapped.  Fifteen minutes after the ceremony, I stuck my head into our auditorium and as you can see, our "Boys in Blue" and cleaning crew were already on the job breaking everything down.  Less than an hour after graduation ended, the lights were off and everyone was on their way home to start the weekend. 

If high school graduation is the end of an important life chapter  and life is the Song of Fire and Ice series, I hope that Saturday was the end of book 1, Game of Thrones, and there are plenty of books and adventures in the future for the class of 2014, though with a lot less blood.  As our salutatorian Paul Reggentin  explained, it's not that life thus far hasn't been important.  High school is an incredibly important part of our lives.  It's just that there's just so much more to do. 

On a personal note, this blog has been an important part of my life in the past year.  It started as an experiment in September.  I wanted to see what I could do.  I tried to explore writing and see what it meant to work in an area that is well outside my comfort zone on a regular basis.  I knew it would take discipline.  I wondered what the hell I had to say.

Fortunately I work at a place and in a profession that gave me plenty to say.  Everyone has an opinion and this forum gave me the chance to express mine.  It also allowed me to share my passion for teaching and mathematics and share some of the stories of life behind the closed doors of a classroom. 

I have loved talking to so many of you on Facebook, here at the blog, and in person.  More than 20,000 page views tells me that somebody out there was reading what I wrote.  I am humbled and exceptionally grateful.  Thank you so much.

I never intended to do this for more than a year.  When I tell people I am going to stop writing, some folks seem surprised.  Others look relieved, perhaps grateful that I will finally shut up.  To be honest, I don't really know what to do.  For now, it's summer, and I have other adventures planned.   Time off will allow me to think, to consider the possibilities, and to choose a path forward.  Maybe this the end.  Maybe this is the beginning.  Maybe I have six more books to go, Game of Thrones style. 

Whatever happens, here's hoping for a lot less blood. 

Wednesday, May 28, 2014

the psychology of exams

In college I discovered that I loved psychology and added several psychology courses to my math major as an undergrad and in graduate school.  One of those courses, History and Systems of Psychology, was a senior level survey course taught by one of my favorite undergraduate professors, Dr. Howard Thorsheim.  The course was designed to cover 100+ years of psychological study and development in detail.  At the end of the course we were to know the details of the many prominent names in psychology, their lives, their theories, their strengths and weaknesses.

I dove into this course and created pages of detailed notes and hundreds of note cards.  I aced every test along the way and was fully confident that I would rock the final exam.  I was actually excited to take the exam, thrilled that I had mastered the material and had developed the techniques and work-ethic required for excellence in a challenging college level course.

About a week before exams I was sitting in class when Dr. Thorsheim threw a wrench in my works.  He asked the class to vote as to whether the course would actually have an exam.  Not surprisingly, the class voted overwhelmingly to skip the final and with that vote, the course was over. 

At the time I felt really disappointed, as if all that work was for nothing.  It took me many years before I realized the value of the learning I had done.  Certainly this deep and thorough understanding of the development of psychology informed my efforts as a teacher of AP Psychology.  It also guided my interactions with colleagues and students and taught me much about myself.

Thirty years later I realize the value of learning for its own sake.  I am an avid reader on many topics and have done much research on topics in psychology and mathematics over the years, not because I needed to, but because I wanted to.  I often wonder how my students would react if I told them there was no exam in my class, or if I made the exam exceptionally easy and unworthy of their efforts. 

I imagine some would feel let down, as if their efforts were not rewarded, their knowledge unrevealed.  The pursuit of knowledge for external rewards requires evaluations like exams for closure, assessments to make the efforts worthwhile.

But what if kids learned for the sake of learning, studied math or science or psychology because it was interesting or useful rather that simply for a grade?  We all know there's some great psychology and a real discussion in that.

If you'd like to find out how schools of the future might be redesigned from the ground up, this article from Education Week might give some insights. 

Tuesday, May 27, 2014

exams... what are we testing??

Most people know what the 2nd amendment is about.  But do you know what the 10th amendment says? The 17th?  I can't recall, but I can find out in under a minute using my phone.  Do you think knowledge of the amendments should be required knowledge for a citizen to vote in this country?  Do you even know how many constitutional amendments there are? 

This week our underclassmen will finish off the year by taking exams.  Each exam is 60-90 minutes long and is meant to assess learning in all of the topics discussed over the last semester.  My own children are in their rooms right now studying.

An interesting study by Larsen, Butler, Roediger from 2009 comparing repeated study of topics to repeated testing on topics demonstrated that repeated testing of students with feedback over time does a better job of improving recall.  Thus it is not enough to simply relearn ideas throughout a semester.  Students will recall information better through repeated testing. 

A 2010 study by Maitreyi Raman demonstrated that several short bursts of instruction were more effective in enhancing long-term recall that a single long session.  Thus four one hour sessions, each a week apart, led to better recall than a single four hour session.  Both of these scenarios suggest that there are a variety of means to deliver content and that all methods are not equal if the goal is improving recall.

But I guess the real question I want to ask is do we actually want to increase recall in our students?  As we think about what it is we want our students to learn, how important is it that they are able to recall civil war battles, elemental qualities from the periodic table, the unit circle in trigonometry, or the characters names from every play they read in English. 

Who were the generals at Gettysburg?  What is the atomic number of potassium?  What is the sine of 135 degrees?  Who was Othello's wife? 

Did you know the answers to these questions?  If so, congratulations!  You should try out for Jeopardy!  But what does it actually mean about you if you know them, or more likely, if you don't? 

Students spend a lot of time cramming such things into their heads, and often forget them within hours or days of exams.  Thus I would ask us to think carefully as educators, as parents, and as leaders about what we are teaching in school.  Is it important that our children be able to recall information that is readily available on the internet? 

Obviously a literate, well-informed population requires shared knowledge, a foundation of information and cultural reference that informs our decision making, advanced studies, and basic conversation.  Dare I call this foundational knowledge our common core?  (Bet you didn't see that coming.)

And while we all debate who should determine this core, what it should be, how it is best taught, and how the students and teachers will be assessed, my students and students across the nation will continue to take the same old exams.  Based on student recall on these exams, we will determine grades and futures for students, teachers, and schools.  

How much does it matter in your life if you remember the 17th amendment?  If you're trying to be a senator, probably a lot.  But for the rest of us, surely there are more important things. 

Friday, May 23, 2014


When I was dating, a long time ago, I learned that I was one of those people that needed closure.  I could never stand a relationship that slowly faded away.  I needed to both say and hear that things were over, that the relationship was done.

I guess a lot of people are like that, and especially schools.  The last few weeks have been a series of movements towards closure.  We have had awards ceremonies for athletics, community service, and academics.  Next week our underclassmen will take exams.  Next weekend our seniors will graduate.  And finally the faculty will have last meetings and say farewell to some colleagues. 

Today is all about closure, the last day of classes for our underclassmen.  Next door in AP Chemistry, I heard them count down the last 10 seconds of class.  There is this need for a formal ending, the desire to hear the click of the door latching behind us. 

Next week high school will be officially over for our seniors and some of them will never look back and never return. But what they don't realize is that the door they heard click behind them when they accepted their diploma isn't actually locked.  When they are ready, they can come home to us, to share their adventures and accomplishments, to introduce their spouses and children. 
Between attending high school and teaching, I have been immersed in the lives of teenagers for more than 30 years.  For me, high school never really ended.  When I see alums, I can never remember whether they graduated two years ago or ten.  They are all part of the ribbon of my life that has stretched almost as far back as I can remember. 

Some doors are closing.  Mine is always open. 

Monday, May 19, 2014

getting to the end of the line

You know when you go to a theme park and you have to wait in line a long time to get to a particularly awesome ride?  Sometimes you wait an hour to ride for only 5 minutes.  But the wait is worth it because the ride is awesome.  It's worth it, right?  Otherwise why would you wait so long?

Friday was the last day of classes for seniors.  For the past week they have been playing out on the lawn during their free periods...  badminton, baseball.  There was a barbeque at 12:30 and a pool party.  It was a fun day final day for our seniors. 

I gave my classes a quiz on Friday morning, a last ditch effort to keep them engaged.  I am "evil" like that, just ask the seniors. 

A few of them have exams next week.  There's a senior luncheon on Wednesday and the unveiling of the yearbook.  They have rehearsal for graduation.  There's a baccalaureate service and the graduation ceremony.  The end of high school looms on the horizon, and they can count the remaining responsibilities on one hand.  Most say they can't wait for it to be over.  They've been waiting for a long time and finally they are reaching the end of line.

But I have to ask, what's on the other side of this line?  Certainly summer.  Some will get jobs, some will start college, some will travel, some will hang around at home restlessly waiting for their next ride to start, but what is it?  What is the new ride?

When I think about college, it was great, but so was high school, and so is adult life  That's just it.  What is great about the next ride shouldn't be just about waiting.  Waiting is boring. Waiting is wasteful.  It is what you are doing while you're waiting that matters.   Because there is no next ride.  It's all one ride, the same ride.  It's your LIFE.

LIFE is great because we work hard, play hard, and take care of the people in our lives.  LIFE is great because we take risks and face challenges and fall down and pick ourselves up again.  LIFE is great when we say yes to new experiences and no to stupidity, when we love and give back and rise to the occasion.  LIFE is great every day that we can go home with a good story to tell.

I watch these seniors, waiting anxiously for high school to end so that they can get on with the next thing.  The funny thing is, I don't think it's the next thing that matters.  I think it's this thing that matters. Today matters.  Every day matters. 

Friday, May 16, 2014

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...


Thursday, May 15, 2014

calculus is beautiful

Last week my AP students took their calculus exam.  After the exam, our seniors are essentially done, but our juniors continue to attend class through the end of the year.  On Monday and Tuesday these juniors worked through the posted free response questions and wrote their solutions on the board.  The problems stay up through the end of classes, a beautiful testament to their hard work all year long.  Seniors stick their heads in to see the solutions and consider how well they might have done. My desk chair faces this board, and it makes me happy to reflect on their progress and the fast approaching end of the year. 

Monday, May 12, 2014

Friday, May 9, 2014

teacher appreciation

Photo Credit

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. 

Wednesday, May 7, 2014

ap calculus

This morning my students will go into a room and give their best on an exam that lasts for 3 hours and 15 minutes and will literally suck their brain out through a pencil.  OK, not literally, but it will feel like it.

I am an AP Calculus teacher and have been for 20 years. I work at a school that gives no yearly standardized test to students in order to measure achievement and progress.  Although most of our students come to us in 6th or 7th grade, the first standardized measure of our success comes from the SAT or ACT.  The second measure comes from AP scores.  Both of these tests are voluntary, although our students are college bound and all end up taking the SAT.  There is no expected standard and salaries are not tied to performance.  There is no one teacher responsible for SAT scores.  And although I teach the AP course, my students' success is not simply of my own making.  My colleagues have all painstakingly taught my students the foundation they need to succeed on this one test.  And they do.

We are very successful as a school, so much so that people pay to attend.  We are selective in that we do not have unlimited space and so can only take as many as we have seats in our classrooms.  We have many children on financial aid, and 1.3 million dollars is devoted to this each year.  Our ability to choose students allows us to follow our mission, to focus on academic and extracurricular excellence, leadership and service, and spiritual growth.  We turn kids away every year because we do not believe that they will succeed in our community.  In many ways it is as perfect as teaching gets, and when I have a hard day, I need only look around for a moment to be reminded that I am truly blessed.

It is standardized test season nationwide, and public and charter schools are administering the various yearly assessments, waiting anxiously for the results, knowing their schools and jobs are on the line.  I will go and help to grade the 350,000+ AP Calculus exams in June, and I too will wait anxiously for the results, not because my livelihood depends on it, but because I am deeply invested in the success of my students.  Many will have graduated before I get the results, but I remain hopeful that their hard work will pay off with a good result and college credit. 

I know that I do not face the challenges of a public school teacher.  I do not teach children of widely differing intellectual abilities or interests.  I do not fear violence in my school.  There are no gangs, few if any drugs, and little disrespect.  The most common student referrals are for tardies, gum, and dress code violations.  The parents are deeply invested, and my colleagues are passionate, hard-working, and positive.  I cannot imagine teaching in a school without these advantages, all the while being forced to spend my days preparing for a standardized test as well.  It feels overwhelming.  I sometimes wonder why anyone would do it.

People might ask how we know if we're doing things right.  First we put our trust in experts.  We use educators to make decisions about curriculum rather than politicians.  We collaborate and discuss.  We watch each other teach and offer feedback.  We are on a steady diet of professional development and curriculum revision.  We have strong leaders who make decisions based on a clearly defined mission.  We remediate when needed, offer support when required, and sometimes, when necessary, remove teachers who do not act in keeping with our own standards. 

And finally, after years of efforts, our kids take a standardized tests, not because we demand it, but because colleges do. We do not need such measures to know we are doing things well.  Most of our students go to college, graduate, get jobs and become good citizens.  That's what has happened thousands of times since our founding in 1967.  This is how we measure success.  It is the only thing that matters.

I know that every school is different and our model will not serve all, but that's the point.  Every school is different, and every child.  This long-winded rant is just one more effort to highlight the struggles and challenges in education.  And one more attempt to point out, it doesn't have to be this way in so many of our public schools.  There is another way. There are a lot of other ways. 

Monday, May 5, 2014

the myth of the hero teacher

Photo Credit
Yesterday a colleague shared an INCREDIBLE post on Facebook entitled "The Myth of the Hero Teacher" by Allison Ricket.  You need to pause and read this right now!

If you have been reading along with me this year, you know in April I also wrote about the idea of teachers as heroes in this post.  I am thrilled that Ricket's article so clearly explains the fallacy of thinking about teachers as heroes. 

Her final two paragraphs are a call to action that brilliantly points to a path for genuine improvement in American education.  I hope you will take her words to heart.

We need to draw more attention not to how individual teachers overcome immeasurable odds, but to ways in which we can reduce those odds to begin with. If teachers need to be creative and honest in the classroom—if that’s what makes a teacher a “hero”—then we need to dismantle the obstacles to creativity and free speech on a wide scale so that those teachers become the rule, not the exception. We need to promote teacher creativity by reducing the amount of standardized testing and the resulting fear of poor results and loss of funding. If being authentic were really a quality valued in great teachers, we would celebrate inclusive, empowering teachers regardless of race, ethnicity, gender, sexual orientation or ability. 
The dramatic light the hero myth casts on teachers is one I think we—as teachers—should wholeheartedly work to avoid. The example of a few isolated individuals working alone in red capes makes for an inspiring narrative, but it won’t transform our troubled educational system. We need a new narrative for teaching, one that we write together, one that unites us as educators and honors our students.
You can read more from Allison Ricket here.

come on... make my day...

Blast from the past...  I was 21 ...  It's hard to know which one is the teacher
For the most part teaching is a one year gig.  We start in August, we end in June.  There's two months of summer and then we begin again, from scratch.  There's a cycle to the year of getting to know students, teaching them stuff, and sending them on to the next adventure.  There are students that mark us, wiggle their way into our hearts and memories, but in many ways, the years start to run together as the cycle is repeated over and over throughout our careers.  Each year is slightly different, some very hard, others more joyful, but always there is this opportunity to begin again after a couple of months of doing something else. 
It used to be true that the students largely disappeared from our lives after they graduated, became memories.  All of the students in this picture have disappeared... Now through the power of social media, I am far more connected to students from that past decade.  This month I have had the pleasure of watching many graduate from college, the high school class of 2010 becoming college graduates.  It is incredibly gratifying to know they have continued their education and pursued their dreams.  They are off on new adventures now, finding jobs, going to grad school.  I feel a sense of gratitude that I was able to be a part of their lives for a few months, that I have shared this same journey with hundreds of students over the past 28 years. 
This week I received a letter from a former student.  It was just a brief note, but it made my week.  The text of the note is below.  
  • "A few years ago in your Calc AB class you showed us the problem of the "Seven Bridges of Konigsberg". You tried to make our class solve it. You said if we ever took "Discreet Math" we would know. Well, I never solved it.

    Just so happens, 2 years later, I'm in a Discreet Math class. Studying for finals I came across that problem again. I am now aware of the devious trick you pulled on us. Props.

    Haha, anyway hope all is well! You and the rest of the math department do a great job of preparing students for college math. Give everyone there my regards and pat yourselves on the back! Hope AP exams go well and have a great summer!"

It turns out, I did the same thing to this year's class that I did to his a few years ago.  Some things never change I guess.  I wrote about it earlier this year.  You can read that post here.  

I challenge each of you to think about a teacher that made a difference in your life.  If they are still teaching, you can email them a brief note simply by accessing the school website.  Contact information for teachers is usually found there.  If they are retired, you might have to work a little harder, but hearing from you makes a huge difference in a teacher's life.

Friday, May 2, 2014


Photo Credit

My colleague, Jeff Wilson, sent me this awesome performance from Clayton Cameron on the intersection of music and math.  A perfect start to your day!  Enjoy! 

Check out his website here

Wednesday, April 30, 2014

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...

Sunday, April 27, 2014

education is creating a million cans of peas

Image credit
There is a proverb that says, "The road to hell is paved with good intentions."  This weekend, this letter was posted in the Washington Post from a school in New York.  Read the letter and then come back here, and we'll talk. 

Without saying too much about the ridiculousness of cancelling a kindergarten show in favor of college prep, I believe that education is on that road to hell.  The profession is stuffed to the brim with well-meaning people.  Teachers, administrators, parents, and politicians are all acting in what they believe is "the best interest of children."  But in the end, all these well-intentioned folks are acting in concert, but they're on the wrong road.  Their well-intentioned march has left education, and our children, completely lost. 

Let's start at the "top."  Politicians set broad federal or state policies that attempt to serve the dual goals of educational excellence and accountability.  Administrators set school policies that attempt to serve the parallel goals of educational excellence and school rankings.  Teachers set classroom policies to serve both the goals of educational excellence and their own performance rating.  Involved parents set home policies that attempt to serve the twin goals of educational excellence and high test scores. 

You can see there's a common goal here, that of educational excellence, and if this were the only goal, perhaps something great might be happening in education.  But each constituency has a second goal, one that qualifies the first, one that compromises the integrity of the process and of those involved. 

Here's what I mean. 

Politicians want excellence, but all excellence must be measurable by a standardized test or some other objective criteria.  As a result, they value only those things that can be measured in this way.

Administrators want excellence but only excellence that comes from high scores on whatever process has been developed to measure and grade the school.  Therefore they value the criteria that improves the school's grade.  Standardized test scores, enrollment and performance in AP and IB courses, student attendance, graduation rates, and continuous demands for improvement have all been or continue to be factors in school ratings and are therefore valued by administrators.

Teachers want excellence but only the excellence that advances their students and by extension, their own careers.  For example, in Florida, if students do not perform as expected on the FCAT, then the teacher's rating and salary suffers. 

And finally, of course parents want excellence as well, but only the excellence that results in a strong performance on these same standardized tests along with high grades.  

The reason that our educational system has become so compromised is because the phrase "Educational Excellence" is now defined as "high test scores."  We have turned schools into test prep factories. 

The irony in all this testing is that our schools might well have met this goal, they might have had high scoring test-takers, if they had been given the time, resources, and training to actually achieve the goal.  Instead the curriculum, tests, and expectations change every two or three years and the whole system must begin again from scratch.  Impatience destroys even the best laid plans. 

So I am suggesting we change how we think about education.  What if we defined "Educational Excellence" as "helping children reach their individual potentials and creating an informed citizenry, compassionate and responsible, physically healthy, and having a deep appreciation of the arts and humanities."   Don't we want a generation of children like this as our legacy? 

As long as we think about schools like factories and children as cans of peas, education will continue to fail.  The last thing we need is a million more cans of peas.  Let's be honest.  Does anyone really like canned peas? 

Thursday, April 24, 2014

the results are in...

This week we had our students fill out the annual feedback forms, their opportunity to tell their teachers what is going well, what is not, and how we can become better.  The results are anonymous and to be honest, one or two really angry students with hurtful comments can ruin a teacher's day and maybe more.  I treat the process as an opportunity to get things right and find ways to get better.  Even so, my fingers are always crossed and as usual, my students gave me some things to think about.  When I got to my final course, Statistics, I opened the response file, and it was blank.  Something had gone wrong, and the student responses were not collected.

The next day I came into class and asked them to fill out the online form again.  I figured they'd be kind of annoyed to have to redo this work.  The class is populated with second semester seniors, ready to head out into the world, restless, desperately wishing high school was over.  If anyone was going to be critical of my work, it was this group.

But in the end, they left me the most positive and constructive comments of all.  These seniors, these almost adult, still teenager, straining to escape, fearful of jumping into the world young men and women actually ended up making my day. 

And at the exact moment I was wrapping up this blog post, a colleague shared this Slate article on professor evaluations.  It posits that evaluations are worthless and the solution is that they should not be anonymous.  Read it and let me know what you think.

Every day of the last months of school I never know if my seniors are going to hug me, mouth off, or burst into tears.  About to face the uncertain future, afraid to leave their family and friends, anxious to escape the confines of childhood, worried about adult responsibilities, these students ride an emotional roller coaster of incredible twists and turns.  It is my privilege to help them finish the ride without puking, and this week they gave me a great big hug. 

I am enormously grateful, but still bracing for whatever comes next week. I'm well stocked with tissues and barf bags.   

here's what I really think about #blogchat

Image Credit
Blogchat is a weekly conversation about blogging held at 8pm Central on Twitter and hosted by Mack Collier.  Each week the group discusses different blog-related topics and last night they reviewed four very different blogs in an hour, offering the authors positive comments and suggestions for improvement.  I have always found reading these reviews really helpful, for it helped me think about ways I could improve my own blog. 

I never much cared for the group chats on twitter.  They are incredibly challenging as the group is like the worst cocktail party ever, everyone able to simultaneously yell about anything and everything.  These comments come at the reader in a fire hose of information.  If you even think about pausing to respond to one comment, a dozen more have already passed you by.  Most of the time I just read.  Some folks are great an adding 140 character pithy comments and responding effectively.  I end up scrolling through the feed later reviewing what I read and what I missed, collecting my thoughts. 

But my personal opinions don't change the fact that conversations like Blogchat are an incredibly effective method of opening up a conversation, providing a huge amount of information in a short period of time, and fostering future connections.  I'd like to thank the folks at Blogchat for their time and expertise.  You gave me a lot to think about and I'd like to share a few of my many takeaways.

  • Many of the comments were focused on my need to be more present in the blog.  My father always told me that people should let their work speak for itself, that who you are to others is based on what you do.  I was surprised by these comments, but understand that strangers might want to know they are reading from a credible source.
  • There were many suggestions about moving this "about me" information and a lot of other things around to make sharing, following, and contacting me easier.  This is easy and I thank you for your suggestions.  (As any blogger knows, if you really want to contact me, comment on a post.)
  • Some mixed messages about the background, header, title, tagline, and description leave me with the ability to tweak some things and see what happens.  All blogs need a little refreshing.
  • I am embarrassed to say that I had to look up SEO to even understand what people were asking me to do, but the reality is that I currently don't know how Blogger supports the use of keywords.  In the beginning, I started out just wanting to write.  This whole year has been an exercise in learning about technology as well.  If I can't figure it out, I'll probably have to switch to a more robust platform.  I am sure readers have suggestions for me there too.
  • Finally, Shane Arthur (@shanearthur) left me with a suggestion to try doing podcasts or videos, to try to "coolify" math.  I am intrigued, but will have to think on that.  It would definitely be a summer project, but in the meantime, the teacher in me wants to share that there are lots REALLY cool videos about math made by Vi Hart.  Check this one out!

My thanks to all the folks at Blogchat for their insights, to Mack Collier for choosing my blog, and to all of you for reading this far. 
You can find the transcript of the Blogchat here.
You can find the Storify summary of the comments on my blog here.  

And come back soon to see the changes! 

Friday, April 18, 2014


Humans have this need to find order in chaos, to find patterns in the fire hose of data that comes at us every day.  We see faces in our burnt toast, apocalyptic messages in our calendar. I pulled this image off the WJTX4 Facebook page, but it's been wandering around all week.  Yes, this week's dates, if written in this way, are palindromes...  AND??

Scientific American points out the there are biological reasons why recognizing patterns could be advantageous for survival.  You can read more about it here.   

Apophenia is defined as "the experience of seeing patterns or connections in random or meaningless data."   

In fact, we have lots of other words describing our finding of patterns in the randomness of our lives.  Try karma on for size, or fate, deja vu, coincidence, or faith. 

But not all of the patterns we find are actually important.  This week's palindromes are actually a human construct, a pattern created solely by our own calendar and the way in which we choose to represent the information.  April 17, 2014 is not a palindrome, nor is 04-17-2014.  The date written as 4-17-14 is a palindrome, but so what.  Numbers are cool, but in this context, not particularly meaningful.

As we consider the patterns in our lives, it is important to remember the intersection of our need to create them and the complexity of our environment.  The structures of leaves, the spirals of shells, these are patterns that are not human constructs but are inherent in the fabric of our universe.  Similarities found in architecture are human constructs that mimic these patterns inherent in nature.  We have found that the structures of nature are often far sturdier that the ones we create ourselves. 

A long time ago Disney created a lovely video that explored the intersection of patterns, both natural and human.  If you have a half an hour, you can watch it.  Donald Duck in MathMagic Land is one of my all-time favorites.  Enjoy. 

Wednesday, April 16, 2014

the most desirable job in the world

And the Most

Desirable Job

in the World Is…

 UCF Mathematics Professor Barry Griffiths sent me a summary of a Time Magazine article claiming math is the most desirable job in the world and explaining why.  I post the summary below.  You can read the full text of the article here.  You can contact Professsor  Griffiths here.

For a new study ranking the best jobs of 2014, jobs website did some number-crunching and found — perhaps not surprisingly — that crunching numbers is a pretty good gig.
With a median income of $101,360 and a 23% projected job growth rate by 2022, mathematician topped the site’s roundup of the most desirable jobs. CareerCast points to the “exponentially growing popularity of mathematics” in everything from healthcare and technology to sports and politics.
“Mathematicians are employed in every sector of the economy… from Wall Street brokerages to energy exploration companies to IT R&D labs to university classrooms,” CareerCast publisher Tony Lee tells BusinessInsider.
Companies and government agencies rely more heavily on analytics to make all sorts of decisions today, so employers need people who can generate and parse this data, CareerCast says in its overview. “Mathematical analyses of trends are used to gauge many activities, ranging from internet-user tendencies to airport traffic control.”
Companies looking for all these math whizzes are going to have a tough time, though: As a nation, our math skills stink. A survey of 5,000 Americans between the ages of 16 and 65 last year found that our mathematical abilities are better than those of people in just two other countries — Italy and Spain — and behind the other 18 surveyed by the Organization for Economic Cooperation and Development. “Explanations for the relatively weak performance of the United States include failings in initial schooling, lack of improvement in educational attainment over time, and poor skills in some subpopulations,” the OECD said in a report examining the U.S.’s poor academic showing.
Unfortunately, our kids aren’t any better at math than we are. In fact, when the Program for International Student Assessment evaluated the math skills of teenagers from 65 countries, it found that math scores dropped among U.S. teens. Their math abilities trail not only those of kids from countries like Japan and South Korea, but also Ireland and Poland, whose scores rose about the U.S. in the most recent test.
That’s too bad, because half of CareerCast’s top 10 jobs are in the so-called STEM fields: science, technology, engineering and mathematics. After “tenured university professor” at number two, the next two jobs are statistician and actuary (last year’s top job in CareerCast’s ranking), with median incomes of $75,560 and $93,680, respectively.


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.

Tuesday, April 15, 2014

OK, but wrong...

Image Credit
So a quick question for my mathy friends.  I often hear from students these words. 

"I got it wrong, but I know how to do the problem." 

The student has mastered the procedure or understands what is being asked, but makes a mistake or several in the process and the result is an incorrect answer.

This is very common in my advanced classes where students are asked to understand and solve complex, multistep questions.  They often know the solution in theory, but cannot execute the later, simpler algebra or arithmetic of the problem accurately.  My response is to circle the error and write, "OK, but wrong."

As we think about the teaching, learning, and using of mathematics, is it enough to know how to do the problem, even if you can't get the right answer?

Where is the line between understanding in principle and correct solutions? What do you think?