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

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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

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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...

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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?   

Friday, April 11, 2014


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

You know that's the goal, right?      

Thursday, April 10, 2014

improving student performance

If you want to change student performance, change teacher expectations. 

This isn't news to a teacher.  As a former psychology teacher I am more than familiar with Rosenthal's 1964 study in which he told teachers that some of their students were very bright.  The catch was that the kids were randomly selected.  The results were that kids identified as bright improved their I.Q. scores more than their unselected peers.  This was incredible work, now routinely called the Pygmalion Effect

A recent story at NPR and a blog post and from Mind/Shift at KQED looks at how a newer study by Robert Pianta took Rosenthal's work to the next level.  The study examines what can be done to get teachers to expect more from kids.  Two plans were attempted, talking and doing.  Some teachers were taught to mentally have higher expectations through discussion.  Others were taught behaviors that indicated that they had higher expectations, regardless of their thoughts.

The outcome, unsurprisingly, was that behaviors worked better.  Teachers that acted like they had high expectations got better results.  Doing trumps saying. 

So the real question is, what are the behaviors that teachers can DO to show kids they have high expectations?  What do you think? 

Wednesday, April 9, 2014

senior skip day

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

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

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

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

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

Tuesday, April 8, 2014


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

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

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

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

Friday, April 4, 2014

headmaster's day

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

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

Thursday, April 3, 2014


So my colleague Jen Baselice is up to her old tricks, trying new technology tools with her students.  This week she shared a document that her students created.  Each student created a slide and recorded an explanation of the work using a simple to use but awesome tool called Vocaroo.  This slide caught my eye. 

Here you see a screen shot of Ava's work.  Click the link here to hear her explanation.

Wednesday, April 2, 2014


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

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

Life is good here, for students and squirrels. 

Tuesday, April 1, 2014

hero worship

Consider a question like, “How many pairs of shoes do you own?”  I am guessing most people in the U.S. would answer somewhere in the neighborhood of two to thirty pairs of shoes.  According to the Daily Mail, the average woman in the U.K. owns nineteen pairs of shoes but wears only seven.  But that’s not important.  What I want to talk about is the woman that owns two hundred pairs of shoes.  She is unusual by almost any standard and statisticians would call her an outlier.  Outliers are pieces of data that alter the outcome in significant ways, so much so that sometimes statisticians throw them out on the grounds that they are not reflective of the general population.  Outliers are impactful.  We can decide how much impact we want them to have.
So there.  You learned a little statistics.
Now consider this movie plot.  An experiment in a lab causes a spider to become infected with a radioactive virus.  The spider then bites a man.  The man dies.  The spider dies.  End of story.  Not much of a story is it?  No one tells this story because it is both predictable and unexceptional.  No one cares about the story where Peter Parker dies.  But we love the story where Peter Parker becomes a super hero.  Spiderman is unusual.  He is an outlier.
Our deep worship of and fascination with the outlier is culturally entrenched.  Everyone loves the story of a person that overcomes incredible odds to excel.  We also watch the fall of our heroes played out in the media with glee. 
So how does this relate to education?

It seems love of the outlier colors our every desire, our every
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decision.  We want our schools to “pull themselves up by their bootstraps” no matter the budget or the challenges of poverty, violence, and health that the children face.  We demand that teachers meet every child’s needs, differentiate every lesson, overcome every setback, because that’s what Jaime Escalante and a few other teachers somehow managed to do.  We envision our schools and our teachers as somehow able to work miracles and fix what has taken decades to break.  And we don’t even apologize for our expectations.

Part of what's hamstringing education today is the demand for outliers.  Heroes do things faster and better, and so do our best schools, teachers, and students.  But this cannot be the expectation.  We can certainly use excellence as a model, to use awesome as inspiration, but in the end, to expect it from everyone is not reasonable.  There's a reason why everyone cannot be an outlier.  Outliers are rare.  Heroes are rare.  Demanding more does not make a hero. 

On the flip side, I think it’s perfectly o.k. to want these things, to hope for a hero. But hope is not a plan.  I am a math teacher.  My job is to teach kids math, assuming they want to learn, and they had breakfast, and they didn’t have a fight with their boyfriend, and they can concentrate for more than a minute, and.. and… and…  If I’m lucky, in the process of teaching math, I might just stumble into some lessons of hard work, compassion, leadership, overcoming adversity, and helping others. 
That’s it folks.  That’s a good day. I’m not a hero.  I’m a teacher.  If you want me or my school or these kids to be heroes, to be outliers, you’re going to have to help.  And by help I don’t mean inventing more hoops for us to jump through, more tests to take.  I mean putting your time, your money, and your wisdom where your mouth is. I mean actually doing something to help schools, teachers, and students.
Does your school have the supplies and computers it needs to be successful?  Do your school’s teachers have the time and training to do the job well?  Do your school’s students have the tutors and one-on-one attention they need to be successful?  No?  So what are YOU going to do about it? 
What if I expected YOU to be an outlier? Hey hero, how does that feel?