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