I am a graduate of Arapahoe High School, the University of Colorado at Boulder with a BS in Aerospace Engineering, and the University of Northern Colorado with a BA in Mathematics Education.
I began my teaching career at the Bollman Occupational Center (now the Bollman Technical Education Center) in 1996.
I have been at Legacy High School since the school opened in 2000.
I have taught every level of high school math from pre-algebra to calculus 3.
I am Legacy's School Improvement Team Data Analyst and statistician for the Lightning Football and Baseball teams.
I am the faculty sponsor of Lightning Robotics - our FIRST Robotics Competition team.
I have been an AP Calculus Exam Reader since 2012
I was honored to be chosen by the Legacy High School Class of 2007 to speak at their graduation. Here is the text of that speech.
Life, Death, and the Heisenberg Uncertainty Principle
June 4 2007 - Coors Events Center, University of Colorado
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I once graduated in this room myself. Only the graduate students, the masters and PhD graduates sat on the floor, the bachelor’s graduates were seated in the stands. Each college was seated in a different section, and the college of engineering was way up there in the back.
What I remember about the ceremony was that at one point, probably during the faculty speaker, someone from the college of business made a paper airplane out of a page from the program, and threw it towards the floor of the arena. Needless to say, from a business school graduate, it was a feeble attempt. Crashed and burned. At this point a noticeable ripple of excitement ran through the engineering graduates. “You call that a paper airplane? Are you kidding?” You see, in the aerospace department, paper airplanes was a required class.
A flurry of activity broke out as everyone started tearing up their programs to make paper airplanes, and soon a flotilla of paper airplanes appeared from the engineer’s section, far superior to those from the business school.
That’s what teachers call an authentic, summative assessment.
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I am happy to be a true geek. The rumors are true, I think about math all the time. When my wife asks me what I am thinking, it is usually math. I have dreams about equations, and I read physics books for fun. Don’t worry; they wouldn’t let me use a whiteboard, so I won’t prove any theorems today. Many years ago I set out to become a calculus teacher. To my astonishment, I actually pulled it off. I like to say that calculus is the mathematical study of change, and that since everything changes, calculus is good for everything.
A student once asked me if calculus is the meaning of life. I said no, the meaning of life is change, and you need calculus to figure that out.
But there is one mathematical idea that I have noticed affecting my life recently that I think is especially appropriate. It’s the Heisenberg Uncertainty Principle.
Now this is a differential equation with position, velocity, Plank’s constant and so on, but what I am interested in is the concept of the Heisenberg Uncertainty Principle. It says that everything affects everything else in ways that you cannot predict. In fact it says that the very act of learning new information about anything changes the way that it behaves. This is as true for people and events as it is for subatomic particles. This is why education is so important. You cannot predict what you will need to know at some point in the future, because between now and then are lots of interactions that will spin off in unpredictable ways. Change is inevitable.
I helped design the Legacy 2000 program at Legacy High School, and a major component of the course is public speaking. I have heard from many students over the years that they are going to be an engineer, so why should they have to practice giving speeches?
There are lots of reasons, of course, but here’s a new one.
Once upon a time I went to engineering school and several years later a bunch of high school seniors voted for me to give a formal public speech in front of thousands of people and here I am. You never know what changes life will throw at you.
This is why the answer to the student’s eternal question “when am I ever going to need to use this?” is “I don’t know. How do you know that you won’t?"
So, what does the Heisenberg Uncertainty Principle have to do with real life? The last few months have given me some lessons.
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My cousin’s daughter Megan died on February 2. She was 12 years old. She had suffered from a rare form of blood cancer since she was 4. She lived in a small town in rural Iowa and 600 people showed up at her funeral. In her short life, she affected all of those people. And the results that those effects will have on all of those people can only be imagined. I realized that I never really knew Megan when she was well. She lived a long way away, I only saw her once a year or so, and in my memories of her, she was always sick, always medicated. She was not herself. At her funeral I heard a lot of stories about her that I had not heard before, and I saw videos of her when she was herself.
I learned a lot about Megan that I did not know. And I realized that I had missed out on knowing her. All of those other people at the funeral knew her better than I did. She showed me that I should pay more attention to the people around me, my family, my friends, my students. And, my reason is selfish. Otherwise I will miss out on something wonderful. And I won’t even know that I missed it.
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About a week after Megan died. Dominic Capra, one of the founders of Legacy High School died. He had suffered from a rare form of blood cancer for several years. He was a long time teacher and coach at Legacy, Horizon, Northglenn, and other schools. Unlike Megan, he had the opportunity to choose a career, work for many years, and decide how he could best affect other people. The number of students and athletes that Coach Capra directly impacted can only be estimated. I will consider myself a success if I can teach half as long and influence half as many students as he did.
One day, during the first week that Legacy High School was open, I was working in the copy room, when Coach Capra and Dr. Binder, Legacy’s first principal, walked in the room.
“We’ve got a job for you” she said.
Now you need to realize, that I was a fairly young teacher, a few days into my dream job; that I had been pursuing for several years, and these are the two most powerful people in the building; living legends would be an appropriate description.
“How would you like to be the statistician for the football team?” Coach Capra said.
Now, I had played football when I was young. I am a football fan. I understand the game. But I had zero experience being a statistician. However, I am not stupid.
“Sure!” I said. “Sounds like fun”.
Now, to be fair, it did sound fun. And this is exactly the sort of thing that I had come to Legacy for; to get involved in the life of the school beyond just teaching a class. But I had no idea what I was getting myself into.
“The bus leaves at 10 AM on Saturday” says Coach Capra.
“I’ll be there” I said.
Since then I have traveled all over the state with the Legacy football team. I have documented every play that they have ever run. I have become a student of football statistics. I get to sit in the press box. I have spent hours developing custom software to keep track of it all. And I published all of the data on an internet page. Doing the football stats got me the job doing wrestling tournaments and baseball stats. I have met lots of interesting people, and I have gotten a bit of recognition for doing it. This has all been tremendously fun and interesting. But I would never have had the chance if Coach Capra had not thrown the job my way.
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I love school. I always have. Since I was 4 years old, I have spent only 18 months of my life not enrolled in or working at a school. When I realized this, I thought a lot about it and reflected on why I am this way.
Well, there was a teacher.
I give full credit to my kindergarten teacher, Consuelo Panos, at Baywood Elementary, San Mateo, California. She first made school the place that I wanted to be, and that has never changed.
Mrs. Panos had been my sister’s kindergarten teacher, and although the school had a policy about siblings not having the same teachers, my mom pulled some strings and got me in her class. At the end of my kindergarten year, Mrs. Panos developed a rare form of pancreatic cancer and took a leave of absence. She came back to school a year later, but kindergarten being stressful, taught 2nd grade instead. My mom pulled some strings and got me in her class.
She also died in February. February 1978. I can only imagine how many students she affected in her career, but she certainly influenced me.
I am a teacher because of her.
Some of you have been students in my class, and if I have managed to have an effect on you, than she has had an effect on you.
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There are people who say that your high school experience is the best of times: “The greatest years of your life”. I think that this is nonsense. Anyone who believes this is fooling themselves. Don’t get me wrong, I think that High School is great, I have after all, devoted my life’s work to it. But there is far more to life than high school. I hope that you all have greater experiences ahead of you.
But I think I know why people say this. When you are in high school you have little responsibility, and our society considers responsibility a burden. Many people consider the lack of responsibility of youth a benefit. I disagree.
The reason that you have had enough of high school is because you have had little freedom. You have been told what to do, where to go and when to be there. Most of your life has not been up to you. That is about to change.
You are about to receive the two greatest gifts there are; freedom and responsibility. Everybody desires freedom, some of you, dramatically so. But many people shy away from responsibility. Don’t. Embrace responsibility. Seek it out. Without it, freedom does not work. It is responsibility that makes your life your own. Your freedom won’t last long without it.
There will be times in your future when you will have the opportunity to accept more responsibility. Given the chance, many people will avoid such responsibility because it is too hard. They are right. Responsibility will require your time, your effort, and your attention. It is supposed to be hard.
But in return, you will earn freedom. If you convince others that you can handle responsibility, you will receive the freedom to choose your own path.
High School should only be the greatest time in your life while you are in high school. Now should always be the greatest time of your life. Now will never come again.
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I have devoted my life to knowledge and education.
It’s what I can do. It is what I have to offer. It is my purpose. I believe that it would be irresponsible for me to not pursue it. I have the capability to do this work, so I believe that I am obligated to fulfill it.
Despite having devoted my life to knowledge and education, there is really only one thing that I am confident that I know for sure.
I know more today than I did yesterday.
I am convinced of this because it has been proven to me repeatedly. On many occasions, I have thought that I knew exactly what was going on, only to find out later that I was wrong. I have been forced to the conclusion that there will always be something I do not know. And the only way to find out what that is, is to keep working and see what happens tomorrow. Therefore, I will know more tomorrow than I do today.
The Heisenberg Uncertainty Principle says that knowledge of one thing changes something else. Consequently, the more that you learn, the more it becomes clear what you still don’t know.
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Megan, Coach Capra, and Mrs. Panos are gone now. But they all left at least one thing behind, their effect on me. I am a changed person because of them.
You have now left Legacy High School. You may not have thought much about what you have left behind. Many of you have forced me to become a better teacher by being demanding students. I have benefited from working with you. Thank you.
Collectively, one thing you have left behind is an expectation of continuous academic improvement. In your four years Legacy’s academic achievement has improved each year in the way that these things are measured. We now expect that improved performance from ourselves and from those will come after you.
Another is a high reputation of artistic quality. We now have a history of good bands, impressive musicals, top choirs and award winning visual artists and performers.
You have set a precedent of competitive success. The Marching Band brought us a team state championship. Individuals won athletic state championships in each season this year. All of them are seniors. The wrestling team has become a regional dynasty. The girl’s basketball team showed how powerful believing in each other can be.
These are all things that you have left behind.
We are not the new school anymore. In many ways that students are probably not aware of, Legacy High School has taken on responsibility for many aggressive programs. As students, you have been the ones who have stepped up to those challenges and succeeded. As a result of your successes, future students, athletes and artists will have more opportunities. The school has been changed because of you.
Everything affects everything else in ways that cannot be predicted. Where will you go next? Who will change you from the person you are now to the person you will become? Who will you change?
One person can have a tremendous effect on another. Two people can change the world.
I wish you all good luck, success, peace, and long life.
You have come far, but you have far to go.
Leave something behind.
Change everything.
The Real Purpose of Education
May 18, 2016
Ladies and Gentlemen, Friends and Families, Guests, and Dignitaries, my esteemed colleagues, and the class of 2016...
I would like to thank the senior class for giving me the opportunity to speak tonight. I got to do this once before, and I thought it was a once in a lifetime experience. But now it's happened again, and I was like, “what am I going to say now?” You see, I pretty much said all I had to say last time, and it's on the Internet so you can all go see it.
But then I realized that was a long time ago. A lifetime in fact. My daughter’s lifetime. Becoming a parent affects your outlook. I am different now. Maybe I've learned something. Maybe I've got something new to say.
It should be no surprise that education is really important to me. Schools and libraries have always been my favorite places. It's my life's work. I literally think about it all of the time. My daughter is in second grade now, and that’s a new perspective.
But whenever I hear people talk about education they always seem to be missing something. Something really important.
Now that you are graduating, I am going to let you in on The Real Purpose of Education.
You see, Our society has the wrong idea about education. We think that it is about job training, future earning potential. return on investment. That's not it at all. Job training and future earnings are very important and necessary, but that's not why you learn.
You learn to become a better person.
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1 - The only way to get really good at anything is to do it repeatedly. The current popular theory is that it takes 10,000 hours of practice to become truly expert at anything. That's 8 hours a day, 40 hours a week, for 5 years. How does anyone do anything for 10,000 hours? You have to really want to do it for 10,000 hours. It is only possible to do something for 10,000 hours if you really love it. If you don't really love it, you will give up long before 10,000 hours.
You can only get that good at something that you think is fun and interesting. So you have to find the thing that you love enough to do it for 10,000 hours.
I used to work for my high school drafting teacher in the summer. He was an architect. Every year he had a project to build an addition on a client’s house. He spent the school year designing it, and the summer building it. He and the shop teacher were in business together. They did most of the skilled work and hired students, like me, to do the grunt work. I dug a lot of foundations. Not with a backhoe, but with a shovel. That's why he hired us, we were cheap. When he needed real craftsmanship, he hired a subcontractor. Like a brick layer. So one week a master bricklayer comes out to do all of the brickwork and it was my job to do whatever he told me. Mostly, carry bricks up a ladder so they were ready when he needed them. You see, master bricklayers don't carry bricks, they lay bricks. Unskilled students carry bricks.
Laying bricks is ridiculously hard. To get them straight, even, level, is soooo hard. But this guy could just knock them down. boom boom boom, all day long. perfect every time. How did he get so good? The trades have a term for this: time on tools. You want to get good at laying bricks, put in time on the tools. Lay a thousand bricks, then lay a thousand more. You will be slightly better than you were before.
This is exactly how I got good at calculus. I did a thousand calculus problems, than a thousand more. The catch is, in order to do something a thousand times, you've got to want to do it a thousand times. It has to be fun for you, and interesting.
This is one of the real purposes of school; for you to try out everything so that you can find the one thing that you want to do a thousand times.
I can really think of nothing that I would rather do than a thousand calculus problems. I have seven that I would rather be working on right now.
One summer I proofread a calculus book. I did every problem in the book. In the summer. I got paid a fee that worked out to about ten cents an hour. It was awesome.
Before he made Alien and Blade Runner, Ridley Scott made 3,000 TV commercials. Can you imagine, 3,000 commercials. The guy is a genius filmmaker, what idiot has him making 30-second TV commercials? No. He is a genius because of the 3,000 commercials. Without making the 3,000 commercials he would not be able to make Blade Runner.
In order to make Blade Runner you have to make 3,000 commercials first.
Our society thinks that genius comes first, that you have to just be a genius then everything will be easy. That's wrong.
Genius comes after a lot of work - Accomplishment is not the result of genius, genius is the result of accomplishment.
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2 - The most important thing that you can learn about in school is yourself.
Now that you have completed 12 years of education, you should know something about yourself. You should have an idea of what you want to do more of, what you never want to do again, what you think is important in the world, and how your brain works.
Are you a procrastinator or an instigator?
Late night or early morning?
Do you learn from Books or from experience?
Do you do your best work in a silent library, or a noisy cafeteria?
Do you like to focus on one thing, or bounce around between different ideas?
Do you like outlines, lists, or web diagrams?
Are you a leader or follower?
Team player or lone wolf?
Good with tools, or a danger to yourself and others?
Audio or Visual?
Star Trek or Star Wars?
You should know all of this by now because now it's time to put it all to use. They call this a commencement ceremony because it's the beginning of your education not the end. Whether you are going to college, into the military, or to work, You are just ready to really get started.
It is absolutely clear that education benefits people. By whatever measure, happiness, life expectancy, income, accomplishment, standard of living… Studies repeatedly show that the more educated you are the better. But exactly why is not clear. In school we make assignments and have learning experiences. We give tests, and do projects. But which ones cause the benefit?
It’s hard to see day to day in a school how all of this activity translates into the clear benefit of education. But I can see it in front of me right now. Today you all are more than you were three and a half years ago when you entered Legacy High School. Some of you, I know it for a fact because I knew you then and I know you now, and you are more. Not just older, not just matured, but more. Some of you I don’t know personally, but I can feel the difference in the halls since you left. The underclassmen don't have it yet. They have work to do.
It's something really hard to measure, likely impossible, although people keep trying,
Which homework assignment was it? Which investigation? Which lecture? Which test?
I don't know, if you do please tell me.
Something existential happens to you when you learn. It's a transformative experience.
Skiing is one of the things I do. It's what my family did together.
My parents met because of skiing.
When I was your age I was confident that life has no questions that can not be answered on a pair of skis. The path to enlightenment is through a mogul field.
I learned to ski at about the same time I learned to walk, and I have put in many hours of practice. But I have no knowledge about how to ski. I can’t teach you. I can just do it.
When I was 13 or 14 I was a perfectionist about pretty much everything, but particularly about skiing. I wanted to ski perfectly. I thought that falling was failure. But eventually skiing taught me something very important. When skiing, if you don’t fall you are not trying hard enough. You are not challenging yourself. The whole point of skiing is to get in over your head, and then see if you can get yourself out.
Without falling, you will never find your limits.
Without finding your limits, you never find out how to overcome them.
So you have to put yourself in situations where you will fall.
We learn from mistakes. The biggest mistake is not making any mistakes.
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3- It is dangerous to attempt to predict what skills and knowledge will be valuable in the future.
When I graduated from high school I went to college, this college, to study aerospace engineering, in part because at the time it was considered a lucrative growth industry. The space program was ascending, and there was a military build up going on. By the time I graduated from college the Cold War was over, the space program was in question, and they were talking about a peace dividend by cutting military spending. I was a space station design specialist, and since you can count on one finger the number of space stations that have been built in the last 25 years, you can see how “useful” that degree was. I had to go back to school to become a teacher.
I get asked all the time if I am sorry that I never ”used” my aerospace degree. Regardless of my job title, I use it every day. I loved every minute I was an engineering student. It's a key part of who I am and how I see the world. I wouldn't trade it for anything.
You want to know what would have been a “useful” skill? Combinatorial Mathematics.
Obviously.
I was in college studying mathematics in the 1990s. I could have become a specialist in combinatorial mathematics. It was right there down the hall. I took a couple of classes in it. That would have been a really “useful” skill. Because it turns out that combinatorial mathematics is exactly what you need to search for information on the Internet. Of course, nobody knew that searching for information on the Internet was important then, but a few years later some guys made a billion dollars using combinatorial mathematics to search the Internet. I could have been one of those guys.
What is the “useful” thing to learn right now? Nobody knows, and anyone who says they know is lying. Except the person who is right. Someone is right, but only because there are so many possibilities. The world is a vast place, changing at an increasing rate, and you can do anything. You can't even know what your options are. Some of them don't exist yet.
You should learn about math, not so you can get a job factoring polynomials all day, but because someday someone will try to sell you an interest only mortgage, and you should understand that's a really bad idea.
You should learn to give a speech not because it pays well, but because someday someone you love will die, and you will want to say something at their funeral.
You should learn about anatomy and physiology not because you are going to medical school but because someday you might find yourself listening to a doctor tell you why your unborn child needs open heart surgery and you will want you understand what they are talking about.
You should be in marching band not because somebody will pay you to walk in a straight line while playing a trumpet but because it's important to be disciplined, to do your job while others are doing their job to produce a whole that is greater than the sum of its parts.
You should learn about eastern religions not because it's on the AP World test, but because the First Truth of the Buddha is absolutely true, all are suffering, so be nice.
You should be part of a sports team not to win championships or to go pro but to learn to have a plan and execute it. To win with grace and lose with dignity.
You should read The Odyssey not because of the lucrative possibilities of being a classics professor, but so that you realize the universal and timeless themes of the human condition. And so that you will recognize them when they show up as the plot of your favorite superhero movie.
You should be on the robotics team not because you want to pursue a career in engineering, but because chicks dig robots.
Learn as much as you can about as much as you can. Be a collector of knowledge and skills.
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4 - Everything is hard
So I went to engineering school, right over there, about a hundred yards from here, and many of you I know are going to spend several years of your life in that building as I did, it's a wonderful place, I was very happy there, and I hope you are too...
Engineering students are elitist about how hard our major is, but that's self indulgent nonsense. Everyone's major is hard. That cliché about easy arts and sciences classes and “underwater basket weaving” …
Do you want to know what's hard? Weaving a basket. Can you weave a basket? I can't, and basket weaving is really important to civilization. If you can't weave baskets, you can't store food. If you can't store food you can't develop a civilization. We would all be living in caves and hunting buffalo if it weren't for basket waving.
I read an article recently in the Wall Street Journal where the writer is apologizing that she and her husband are not good at math, but they are trying to raise their child to like math because society deems it important. They are trying to promote a positive attitude about STEM because its expected, but they are having a really difficult time because math is so hard.
You want to know what’s hard? Becoming a writer for the Wall Street Journal. They don't just hand that job out to everyone. That writer had to do a lot of incredibly hard work for dozens of years to develop the skill that it takes to write for the Wall Street Journal. But she doesn’t think that’s hard. She thinks Math is hard.
I don't care what you decide to do, it will be hard
Everything is hard.
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I have been telling seniors for thirteen years that they are about to receive the two greatest gifts in the world. Freedom and responsibility. The reason that you are sick of high school is because you have no freedom. But freedom demands responsibility. If you are not responsible, others will make decisions for you.
We are lucky to live in a society that allows us freedom and responsibility. It is easy to forget that many people in the world don't have that opportunity. The societies that allow individuals the freedom and responsibility to make mistakes create opportunities to learn. Those that control their populations and restrict their freedoms prohibit learning, that's why they are all stuck in the past. They sabotage their ability to grow and learn and advance in exchange for perceived stability. The same thing will happen to you if you don’t take advantage of the freedom to try things out and find what you want to do a thousand times.
One of the truest things that I have ever heard is a line from the Wes Anderson movie Rushmore.
“What's the secret? Find something you love to do, then do it for the rest of your life.”
I love being a dad. I love being a husband. I love calculus. And I love being a teacher.
What do you love to do? Do you know yet? If so, get to it, your 10,000 hours starts now.
If not, keep looking. Don't stop until you find it.
It has been a privilege to speak to you today. Thank you for the opportunity to be a part of your education. Congratulations on your graduation, and good luck in your future endeavors.