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AHS helps make it all add up

AHS graduation speeches

Dr. Thomas McCauley, who teaches mathematics, delivered his address as the faculty speaker at the 2004 Arlington High School commencement. 

Congratulations to you all on graduating from Arlington High School. You have worked hard for four years, through a pandemic, remote school, construction of a new high school and the move into our new building.  I have seen you guys accomplish amazing things.  I have seen Jonah make up his Rainbow Theorem, and then defend it well after he realized it was nonsense.  I have seen eight of you, Jane, Max, Ivy, Noga, Zoe, Grace, Berj, and Lilly tackle differential equations as a committee.  You guys have a remarkable ability to figure things out and you have used it to get a great education.

It’s up to you now to use that education.  My parting wish for you is that you will use it to think critically and always question things.  In particular, I want you to ask this question: “How do you know?”  

How do you know that what you know is true?

A look at some bad answers

This will be an important question your whole life, and you’re guaranteed to find some really bad answers to that question (especially in an election year).  I would like to illustrate a few bad answers from my own daughters.

Let me start with a story about Eliza.  She is 5 years old and excited to start kindergarten in the fall.  She loves puzzles, and she was bragging about doing a 99-piece puzzle.  I thought that was a bit strange – I had never heard of a 99-piece puzzle before – so I asked her how did she know that it was 99 pieces?  She told me that it was supposed to be 100 pieces, but one piece was lost, so it was 99.

I got so excited.  My daughter can do subtraction!  As a dad and a math teacher I was so proud.  I asked her a follow up question: “If you had a 100-piece puzzle, and you lost two pieces, how many pieces would you have?”  And she told me, “98”.  I was overjoyed!  I asked her, “How do you know?”  And she explained, “Because, Dad, I’m WAY more of a math expert than you!”

How Hannah answers

Or maybe you answer the way Hannah does: “How do you know?” Hannah is 3, and her full-time job is not listening.  The other day she asked, “What are we having for dinner?” I explained, “We’re having tacos.”  “No!” She told me, “We’re having noodles!”  I asked her, “How do you know we’re having noodles?”  And she started marching around the house singing “Noodles noodles noodles!” at the top of her lungs. Boy, was she sad to have tacos.

Let me turn the question back to you graduates.  How do you know?  Do you know like Eliza, by asserting your expertise?  Do you know like Hannah, by shouting your opinions over and over and over again?  Or do you know because of evidence?  Because of experience?  Have you considered what both sides of the argument have to say?  And how do you know that your own place in life has allowed you to give both sides a fair hearing?

No easy questions

These are not easy questions, and the funny thing is that it’s a easier to spot a bad answer than to give a good one yourself.  Still, the purpose of your education is to give an honest answer to that question, “How do you know?” My parting wish is that you always ask yourself that question, because I can tell you about a time when asking that question changed my life.

After college, I went to grad school to earn my PhD in math.  I wanted to be a college professor, so I put in five years thinking about one math problem all day, every day, for that one purpose.  Then after five years, my adviser explained to me that I really ought to do a sixth year to be competitive on the job market, and I should consider doing a postdoc in North Carolina, 12 hours away from my wife.  So I asked myself, “How do I know that this is still the path I want?”

You may find yourself in this position, where you have invested so much of your time and energy and your very self into one thing, that you can’t even imagine asking, “How do I know if it’s time to make a change?”  

The right choice for him

For me, the right answer was to make a change to teaching high school, where I got to meet all of you!  And this job has been a lot of things:

  • Exhausting, because everyday students tell me that “This is the right answer because it just has those vibes.”
  • Heartbreaking, because for some reason no one else thinks sinusoids are as cool as I do.
  • Overwhelming, to see how far you all have grown from freshmen year to today.

Congratulations, Class of 2024, we are so proud of you!


This viewpoint was published Sunday, June 2, 2024.

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