So, I’m going to Europe tomorrow…

I’ve only traveled out of the country once in my life. I got the wonderful opportunity to visit Guatemala for a week with the Highland Support Project while in high school, and I’ve been to a number of places in the states, but this is going to be travel on a whole new level for me.

Although I’ve barely traveled, I have a passion for the world. In my Ph.D. program, two-thirds of our students are international. I haven’t been to India or Lebanon or China, but I’ve gotten to know their cultures through my graduate school friends over the past several years.

This trip feels like I’m finally living a dream.

Amy Hermundstad and I will be traveling to Iceland and Germany before heading to Zurich to meet the rest of the Global Perspectives Program crew for the official school trip. Driving on I-81 today, puffin tour on Sunday. I still don’t believe this is real life.


As we visit universities and meet faculty and students, my research question for the trip will focus on the role of a faculty member as a mentor to students. I want to learn the differences in the way that faculty view their jobs through different countries in order to be the best mentor I can be in my career.

I have no idea what to expect, but I know that I’m excited to be there.


There’s more to life than what you read in books

Maybe it’s the caffeine or the sunshine, but I don’t know if an article has ever energized me as much as the one I just read.

I started by watching Seth Godin’s TEDx Talk in which he posed the question:

“What is school for?”

Then I read Dan Edelstein’s article, about the purpose and the indirect impacts of education in the humanities.

However, as incredible as those were, it was Parker Palmer’s article that has me so excited. Maybe the first two set the stage for this one. Maybe it’s just the ideas that he mentions or the incredible examples he used.

If higher education is to serve humane purposes, we who educate must insist that knowing is not enough, that we are not fully human until we recognize what we know and take responsibility for it.

Palmer’s article really drove home the point that education is for more than just content knowledge. One of the key topics he discusses is the interaction of an individual with the institutions of which they are a part. I believe that this knowledge of institutional relationships is something a lot of folks struggle with these days. Often the narrative of “I have a problem with this organization. I’ll find something else to do” defeats the harder narrative of “I have a problem with this organization. However, I believe in it and will work to make it better.” Too often we believe that institutions are untouchable.

Palmer gets into a deep discussion of how to navigate our own feelings and let them speak to us in the workplace and in academia, which my commentary cannot do justice. I’ll let him speak for himself here.

So we have precious little experience and even less competence at extracting work-related information from our feelings. […] “So what?” might be a reasonable response to that observation—until we realize that a capacity to translate private feelings into knowledge and then public action, when warranted, has been an engine of every movement for social change.

Palmer is asserting, and I agree, that education is for more than just teaching people the “stuff” they learn in school. It’s more than solving equations and memorizing anatomy. Our educational institutions provide settings that could be used for so much more. So what are some things that I believe school is for? I’ll tell you.

School is for

  • Self-discovery
  • Gaining inspiration from those who have gone before us
  • Learning how to make connections between seemingly unrelated topics
  • Building and making and creating
  • Figuring out how our feelings relate to what we do
  • Learning how to work with other people to accomplish a goal
  • Seeing the value in people different than us
  • Learning how to work hard even when you don’t want to
  • Empowerment and Freedom (via Renu)
  • Developing one’s view of the world and their perceived place in it (via Ken)
  • Discovering one’s passions and skills (via Sarah)
  • Learning how to use context for discernment (via Kristen)

School is a playground to discover who we are and how we want to interact with the world around us. My good friend Jeff wrote a blog post sharing college advice he had recently given to a high school senior. His first point really stuck with me:

You will learn about your degree in class.  You have the potential to learn about yourself every single moment.

This is the point I want to end with. Too often our educational system downplays this idea, but it should be sung in every classroom:

The most important thing we can learn is who we are.


What bullet points would you add to the list? How have you learned who you are through interactions inside or outside the classroom?

Why conversations about diversity are necessary

Diversity is something that has been important to me for a long time. Through so many conversations with friends, my worldview has grown in so many ways and continues to grow daily. My life has been made better because of diversity.

One particular quote from Brian Arao and Kristi Clemens article “From safe spaces to brave spaces” really stuck out to me as I think about diversity.

Was it the activity that had made our students unsafe, or did this sense of danger originate somewhere else?

This sentiment really supports their idea that safe spaces are impossible when talking about diversity of any kind in academic settings or really any setting. The concepts of privilege and inequality are necessarily uncomfortable, and to discuss them and bring some sort of resolution, we will have to make ourselves uncomfortable.

This reminds me of one of my favorite quotes. It is in Dr. King’s Letter from Birmingham Jail. It is a letter written to fellow clergymen imploring them to support his movement and when I read it, I feel like it was written to me. There is one part in particular that I find incredibly convicting. Here, he calls out the “white moderate.” I’d like to share it here (emphasis mine):

First, I must confess that over the past few years I have been gravely disappointed with the white moderate. I have almost reached the regrettable conclusion that the Negro’s great stumbling block in his stride toward freedom is not the White Citizen’s Counciler or the Ku Klux Klanner, but the white moderate, who is more devoted to “order” than to justice; who prefers a negative peace which is the absence of tension to a positive peace which is the presence of justice; who constantly says: “I agree with you in the goal you seek, but I cannot agree with your methods of direct action”; who paternalistically believes he can set the timetable for another man’s freedom; who lives by a mythical concept of time and who constantly advises the Negro to wait for a “more convenient season.” Shallow understanding from people of good will is more frustrating than absolute misunderstanding from people of ill will. Lukewarm acceptance is much more bewildering than outright rejection.

I had hoped that the white moderate would understand that law and order exist for the purpose of establishing justice and that when they fail in this purpose they become the dangerously structured dams that block the flow of social progress. I had hoped that the white moderate would understand that the present tension in the South is a necessary phase of the transition from an obnoxious negative peace, in which the Negro passively accepted his unjust plight, to a substantive and positive peace, in which all men will respect the dignity and worth of human personality. Actually, we who engage in nonviolent direct action are not the creators of tension. We merely bring to the surface the hidden tension that is already alive. We bring it out in the open, where it can be seen and dealt with. Like a boil that can never be cured so long as it is covered up but must be opened with all its ugliness to the natural medicines of air and light, injustice must be exposed, with all the tension its exposure creates, to the light of human conscience and the air of national opinion before it can be cured.

This letter is incredibly relevant to the issues that remain present today. There exist in this country so many injustices that are hidden under the surface. We need to bring these issues to the surface. They will make us uncomfortable. We will likely feel bad or guilty or hopeless at times. Whether we talk about them or not, they persist.

In the engineering classes I’ve taken and those I hope to teach in the near future, most of the students are heterosexual white males, and therefore ours is the loudest opinion. That means that people of color and women already hear our opinion whether they want to or not. It is absolutely essential to the human experience to be aware of the way that others experience it. Therefore, we, as members of the majority, have to take special care to hear other worldviews.

We cannot discredit another human’s experience because it’s different than ours. When people of color are insisting that there is a race issue in this country, we cannot say that there isn’t one. When females in engineering say that the culture in the classroom is too hostile, we cannot say that they are just being too sensitive. We must learn from others. We must grow as people. That is why diversity matters.

Teaching to the choir

Although much of the reason that I am in graduate school is for an eventual career teaching college students, I have not had many opportunities to teach courses yet. Therefore, for a teaching reflection, I will be reflecting on other opportunities I have had to speak and the one or two opportunities I have had to give a guest lecture.

For the purposes of this blog, I will consider two different experience I’ve had related to teaching: (1) in the fall, when I gave a guest lecture for my advisor in a sophomore-level dynamics course, and (2) yesterday, when I got the opportunity to preach the sermon at my church, Fieldstone UMC. There are actually a surprising amount of similarities between the two experiences. Note: my faith is very important to me, but this is a blog about teaching.

In reflecting on these two experiences, I’ve noticed some things about my teaching style.

Examples are very important to me

Examples help illustrate concepts and help us connect ideas to things we can already wrap our heads around. Maybe its the engineer in me, but I think that examples make incredibly powerful teaching tools.

In the dynamics course, I was teaching about the impulse-momentum equation

J \equiv \int_{t_1}^{t_2} Fdt = mv_2-mv_1

Which says that there’s this thing called the impulse, J, that is equal to the change in momentum. It is a useful formula for studying things like the dynamics of billiards and car accidents. To introduce the topic to my class, though, I didn’t just give them that equation, because equations are scary. I showed a video of a golf ball deforming and talked about how the impulse represents the total effect of that deformation and restoration. Therefore, we don’t have to know the details of that deformation. All we need to know is the change in velocity of the club head in order to determine the velocity that the ball.

In the sermon, I was discussing how small actions can have a profound impact, and I shared a TED talk by Drew Dudley entitled Everyday Leadership. He shares the amazing story about a time that he gave a lollipop to a girl and it utterly changed her life. Thinking about how this moment where he had so profoundly impacted somebody without even remembering it, we can see how we may all be able to impact those around us through small actions.

Examples people something tangible to hold onto when discussions become abstract.

I like to make people move

As we’ve discussed in class, lectures can get boring and people don’t have the attention span. I like to make people move around the room if possible to get the blood flowing and to help them engage.

In the dynamics course, I used a sort of think-pair-share to get the students to try to apply the knowledge in small groups and then discuss with the class in order to make sure that students were engaging with the material rather than just listening to me drone on. In a boring class talking about a derivation, I had the students try it first. Then, they would have something to go from when we talked about the material in class.

During the sermon, I was trying to encourage people to be more conscious of creating a welcoming environment. In the middle of the sermon, I asked everyone to stand up and learn the name of one other person in the room. The room was immediately filled with energy and the rest of the sermon flowed from that energy.

Getting people physically moving during a lecture helps them be involved.

It’s important to keep people engaged

Engagement is hard to describe when giving a presentation of any kind, but it is the most important thing. I think that engagement is just something you can feel. It’s in eye contact and facial expressions, but it’s really just something that you can feel.

I felt it while performing in musicals in high school. I felt it I spent my first couple years of graduate school giving presentations to prospective students and their parents. I felt it yesterday while preaching, and I felt it from some of the students when I taught the dynamics class.

I don’t yet know how to improve that engagement in the classroom. I think that is something that I’ll be working at throughout my career as a teacher.

What do you think? Do you have any fun examples to share? Do you have fun ideas to get people moving in the classroom? Do you know what it feels like when the audience is engaged? Why is it so much harder to be an engaging speaker in a classroom environment?

Ignorance is bliss?

I don’t know anything about Thermodynamics.

It’s true. I got an A- in Thermodynamics, but I don’t know anything about Thermodynamics.

In that class, I had a very personal experience with Alfie Kohn’s assertion:

“Grades create a preference for the easiest possible task”

When I took Thermo, 5% of the course grade was homework. After two weeks of class, I found that I was spending 3-5 hours to do each homework, and they were due 3 times a week. I was getting bogged down in those assignments and I made a choice. I decided that I wasn’t going to do homework for that class. It turned out that I was missing something that would’ve made the homework a lot easier, but I had a preference for the easiest possible task. And I chose to take a 5 point hit on my final grade to spend my time better elsewhere.

I was doing very poorly in the class, but I can test like a pro. I crammed so hard for the final and actually got a 99. The professor curved the class like crazy and now I don’t know anything about Thermo but my undergrad GPA is okay.

And I was so proud of this at the time. Nowadays, I value homework so highly. It is the place where you have to try to wrestle with the material from class and actually learn things. Homework is where you put into practice all of the crazy things your professor talks about during the lecture.

I missed out on learning something because I was thinking about grades. Have you ever done that?

The pendulum swings

I think that Michael Wesch hits the nail on the head in his article Anti-Teaching: Confronting the Crisis of Significance when he states in the first two sentences that,

The most significant problem with education today is the problem of significance itself. Students – our most important critics – are struggling to find meaning and significance in their education.


A dominant problem in our educational system is that we lose the student by silencing their voice. We do not make the education relevant to their lives, and therefore they do not engage.

It is my opinion, though, that as we discuss solutions to this, we go too far. We, as people, have a tendency to rebel against one extreme by running to the other. When it’s cold outside, my mother cranks the heat in the car until I’m sweating. When all pop music sounded the same, we ended up with such levels of individuality that some music became hardly musical.

I think this can happen in education too. Today, Christine Ortiz, the Dean of the Graduate School at MIT announced that she is taking a leave to start a new university with “no majors, no lectures, and no classrooms.”

Too often we ignore the input of the student crying “This isn’t relevant to me!” But we need not run so far that we ignore wisdom of the faculty member saying “I know it’s a stretch for you, but this is really important for you to learn.” How do we provide a meaningful and significant experience for the student without losing the direction of their education?

The nice thing about the car heater is that it usually ends up at a comfortable temperature after a little bit of sweating. And thanks to those that have continually pushed the boundaries of music, we’ve ended up with so many original masterpieces.

We need people like Dr. Ortiz to help us push the pendulum in a new direction. I can’t wait to see where we end up.

Why is education significant to you?
What do you think of Dr. Ortiz’s new university?
Where do you think education is headed?

Did curiosity kill the cat?

In my first blog post for this course, I see it only fit to reference my favorite blog on education: Math With Bad Drawings by Ben Orlin. (I expect I will reference it a number of times in this course.)


Unfortunate Metaphors for Teaching

If our current educational system is dry food, connected learning proposes to be cat nip.

Connected learning, as I understand from the videos we watched in class, is characterized by a deep curiosity that is encouraged and explored in the classroom, in discussions with friends and mentors, and in free time on the internet and in books.

Learning driven by curiosity can be addictive. In fact, it can drive us wild. It led me to read about the Estevez/Sheen family tree while watching West Wing last week. It led me to take a math class that was way over my head last semester. It’s also what has driven me to this point in my education and it continues to lead me on my path toward a career in academia.

I hope that most of us graduate students have felt this curiosity at some point. I hope that we can improve our educational systems to emphasize curiosity and connection. I hope that we as teachers can put away the dry food and find the cat nip.

How do we engage that curiosity? When was a time when you experienced unbridled curiosity? What helped it and/or killed it?

More than just ethics

For a course that I took this semester, we were asked to investigate a professional organization’s Code of Ethics for a blog post. Here goes:

I am currently only a member of one professional organization: the American Physical Society, and their guidelines for professional conduct is pretty standard and are mostly about authorship.

In researching this topic, however, I found a professional society whose Code of Ethics I’d much rather discuss: the Society for Industrial and Applied Mathematics. The post I’d like to discuss is not the official Code of Ethics (that can be found here), but comes in the form of a blog post on their website, which comes up adjacent to the official statement. The less formal tone of the post proves to be more effective at communicating principles of ethics to the community.

SIAM: Professional Ethics: Taking the High Road by Dianne P. O’Leary

I highly recommend reading the whole post, but I’ll discuss two sections which stuck out to me from the post. The first section is regarding Professional Integrity. She gives straightforward and helpful statements regarding how to conduct oneself in an academic career. Two of these statements particularly stood out to me:

An old labor rallying cry says, “A full day’s work for a full day’s pay.” Every job has its pleasant and unpleasant aspects. (For me, the worst part of professional life is dealing with academic dishonesty.) But in accepting a job, you agree to perform all of its duties, not just the pleasant ones.

The idea that doing the unpleasant parts of one’s job is an ethical responsibility struck me. I think it is just part of growing up, but this is particularly challenging to me. I’ve always been a bit of a dreamer, so I like to imagine the job that I want and the life that I want. Even as a graduate student now, there are parts that are exciting, and parts that are unpleasant. This is not to say that I’m not in the job that I want and the field that I want. It is just to say that life comes with rough edges. To me, growing up means dealing with those.

The physician’s motto—“First, do no harm”—is also relevant to our profession. This means that any product or idea you deliver must be as correct as you can make it, with no known but unannounced defects. Your mathematical model may be used to determine load limits on a building or safeguards on a nuclear stockpile. Your computer program may be used as a module in a hospital’s drug delivery system, or as part of a guidance system in a passenger aircraft. You must do everything you can to ensure that your work, if used as you say it can be, will perform as intended.

The second quote is really quite wonderful. If we oversell our ideas in a scientific paper or aren’t clear about the shortcomings of our code, there could be terrible consequences. Honest presentation of one’s work helps protect from potentially doing harm. It also allows the work to speak for itself.

Dr. O’Leary’s essay on ethics concludes with a section on values. This is the part of the essay that will stay with me for a long time.

“Some people live to work; others work to live.” Whether your job is the greatest joy in your life or just a duty, it is worth reflecting on the broader impact of your work. Maybe your research won’t win a Fields Medal, and maybe you will never be SIAM’s John von Neumann Lecturer, but you can use some of your creative energy to see that your efforts have some positive value. When all is said and done, if you have encouraged an at-risk student, written a clear textbook, helped a staff member or a more junior colleague, or organized a conference that catalyzed new research, you have made contributions that could far outweigh your technical ones. Whatever your values, bring them to work.

I am in graduate school not just to learn to be a researcher, but hopefully to serve college students and help them grow through a critical period of change in their lives. It is refreshing to hear someone raise the fact that our personal interactions can have a greater impact than our scientific contributions. It is so easy to get caught up in the work that we can easily forget this as future faculty.

If we don’t include someone as an author or oversell our own work, we are doing harm. If we take the time to just sit with a colleague or student going through a hard time, we are doing immense good. This gets not at the rules of ethics, but at its heart.

Through all of our work, whether we realize it or not, we are impacting people. Let’s do so for the better.

Communicating Science to, well, Scientists

A few weeks ago, in a course that I’m taking, we did some fantastic and thoroughly entertaining games to practice communication, and had an excellent discussion about why it is important to communicate science with the general public in addition to our fields through journals and conferences.

Communication with our field is vitally important. This is how ideas are shared and science grows.

Communication with the general public is vitally important. It helps the insights gained from our research reach and impact those who can actually do something with it. It also helps Mom understand what we do all the time. And Mom wants to know what we do all the time.

There is a 3rd community with whom we need to be constantly communicating and sharing our work: scientists in other disciplines. There was an article in Scientific American last year discussing just that: ( and another blog post for this course which inspired this blog post (

In our focuses on the first two communities for communication, we need to remember this third community. One of the best methods for scientific advancement comes from applying techniques commonly used in one field to a problem in another discipline. The Lorenz attractor, a canonical problem in chaos and dynamical systems, came from attempts to model atmospheric convection in a meteorology department. There was an article last month entitled “Why mathematical biology is good for mathematics” ( that discusses how science has stimulated many areas of growth in mathematics. By sharing our ideas with scientists in other disciplines, not only do we allow for more uses of our tools, we often find new problems to grow our own field. Interdisciplinary research is not just something that Universities are doing because it gets them funding. Interdisciplinary research is essential for the development of science.

Assume my research provides an interesting tool that you could use on yours. By sharing with you, I gain new applications for my research and you gain new tools to look at problems you’ve been thinking about for a long time. This is the obvious result of interdisciplinary research. However, there is another key impact at play here: by testing the limits of my tools on your research, it allows my research to grow. This is one aspect that Michael Reed’s article discusses: The problem of the planets created the discipline of dynamical systems. The heat, wave, and Maxwell’s equations drove the development of partial differential equations. By drawing the comparison to the way physics has impacted mathematics, he opens our eyes to the potential, and much of the past, of the ways that biology can impact the field of mathematics.

It is essential to share our science, and not just for the sake of getting it out there so that others may hear it. It is essential that we share our science so that, with new perspectives, our science itself may grow.