Optical Fibers

One of the great things about graduate studies is the many hats we get to wear.  I've mostly written about my experiences teaching and researching education this year, but I've also had the opportunity to be a student.  I think it is a very helpful thing to be on both sides of the desk at the same time.  

This semester, I enrolled in a quantitative research methods over in the Education Faculty and an electrodynamics course here in physics.  The courses couldn't have been more different from each other, and I'd say I quite enjoyed both courses for different reasons.  Last year when I was in teacher's college, I blogged a bit about how much I missed a really challenging physics problem (this post: http://birefringencemms.blogspot.ca/2011/01/reminiscing.html).  Education classes can sometimes feel a bit like chocolate - they're sweet, fun, and can be very well taught.  But it seems that there's not a great deal of education classes which you could really classify as 'hard' or 'challenging'.  For me, I find that physics classes are more like steak - the content can be a bit dense for me to understand, but you finish the course feeling very satisfied - like you really learned something challenging and interesting.  

My electrodynamics course this semester was exactly what I needed.  Problem sets were typically only 3 or 4 questions, but working out the solution would take sometimes 60 pages.  When you jump through that many algebra manipulations and integrals and you finally arrive at an answer, it can be a real thrill.  There is something just fabulous about stretching your brain for hours, and then suddenly on the horizon, seeing a promising solution like an oasis in the dessert (and hoping it's not a mirage!)  Perhaps this explains why physics can be so addictive? 

The electrodynamics professor taught his course in a fairly traditional manner, but for our final assessment, he kindly agreed to let us do a project instead of an exam! I was so pleased.  The only sad part of this assignment was handing in the essay, completing my presentation, and realizing that I had no one to share all my pretty physics with.  But I have a solution to this sadness!  I am sharing the physics-love with you my dear friends :)  

Therefore, the following is the non-physicsy edition of my essay on optical fibers.  If you enjoy the read, and would like to read the physicsy-edition, just leave a comment for me, and I would love to explain the "why?" behind everything here or even send you my real report if you are interested. 

Optical Fibers: 

You talk to a friend across the ocean over skype with almost no delay in the conversation. Militaries send confidential data around the globe in fractions of a second. You watch a youtube video of a really cute puppy.  You turn on your sweet 90's fiber optic lamp for 'mood lighting'.   How are all these technologies possible?  Optical fibers of course! With the exception of the 90's mood lighting and some other light delivery applications, optical fibers are mostly used to connect our world by allowing almost instantaneous hard-to-intercept sharing of huge amounts of data. Under the ocean, we have many submarine cables which can send data around the world encrypted in pulses of light. Here's a map of where these cables were 5 years ago:

How does light actually travel along these optical fibers? Well, we can get a pretty good sense of what's going on using a ray optics model. Whenever a ray of light hits an interface between two different clear mediums, the light ray changes direction (or refracts). If you hit this interface at the right angle (called the critical angle), the ray will change direction so much that it will end up just travelling right along the fiber. The light is trapped! So our message will stay stuck in the fiber, and will therefore arrive wherever we want to send it. This is called total internal reflection, and here is a sketch of it:

We can use this "ray model" to describe light propagation in big fibers ('big' refering to fibers around 0.0001m in diameter and bigger). An example of a really big optical fiber is a stream of water. Water is not a very practical material for a real optical fiber (especially in the ocean...), but I think it is a rather pretty demo. You can guide a ray of light inside a stream of water using total internal reflection. Here's a picture of this demo in my kitchen:

Kinda looks like the diagram above, eh? A little? To do this at home, you just need a bottle with a hole in the side near the bottom, a laser pointer, some water, and an anneke to ramble on about how beautiful the total internal reflection is.

Unfortunately, if we send data down big fibers we run into all sorts of problems. Pulses of light spread out in time and smear on top of each other so much that by the time they've traveled a long distance (eg. under the ocean), they are completely unintelligible. So instead, we like to make really tiny fibers to get rid of this problem (by tiny, I mean a fiber with a diameter of around 0.00001m and smaller). The trouble is that with a fiber this small, the diameter of the fiber is not much bigger than the wavelength of light, and our ray approximation doesn't work anymore.

What do we do when an approximation lets us down? Do we throw up our hands? No! It's time for us to travel...

Yes Maxwell, not the future. But equally awesome. This is in fact one of the things I find particularly beautiful about physics: its complex simplicity. An incredibly complex system can be described by the smallest fundamental concepts. The fundamentals which describe light propagation are Maxwell's equations. Physics folks like to represent Maxwell's equations like this:

I know this might look a little weird if you're not familiar with the "nabla" symbol (it's actually nothing fancy - just a slope in three spatial directions). But definitely do take a minute to revel in the amazing complex simplicity: those four little unassuming equations just explained every x-ray machine, MRI, computer, light bulb, stove, lightning bolt, sunny day... and the list could go on for literally days of typing! Maxwell's equations describe pretty much anything and everything about electromagnetism. I think this is pretty awesome.

Now you might not feel quite so enthusiastic about these four equations, and this is okay. So for the non-equation-lovers out there, here are Maxwell's equations in words:

i) You can make electricity just by having a changing magnetic field (eg. moving a magnet around).  If you've take a first year physics course, you can connect this to what you've learned: this Maxwell equation leads to a fun little law you might remember by Mr. Faraday.

ii) You can create little magnetic field loops if you have either a current or a changing electric field or both. Take the 'steady-state' case where the electric field isn't changing - what does this give you? Ampere's Law!

iii) Electric charges can be single, or they can find the love of their life and become a dipole (the physics word for happily married couple). If you know where charges are, then you can figure out the electric field they create. This is useful for predicting how the relationship will progress - who will feel forces of attraction? Who won't? 

iv) So far, no one has ever seen a north pole all alone without a south pole companion. Even if a magnet is really big (eg. the earth) and the poles seem far far away from each other, they're always connected by magnetic field lines. It's actually a pretty adorable romance. 

Okay, so now you know all about Maxwell's equations and how pretty they are. But why did we go back to Max in the first place? Remember we wanted to find out how light propagates in a tiny fiber (the kind that they actually use to send data under the ocean).  So next, we do a bunch of mathy cartwheels which combine Maxwell's equations, then we shake things up a bit, and something called the "wave equations" will appear.  Once you've got wave equations, you should be a very happy camper because now all you have to do is solve the wave equations and you can describe exactly how electric and magnetic waves (that's just a fancy way of saying 'light') travel down the fiber.

Unfortunately, when we do our mathy cartwheels, we end up with what's called "coupled wave equations" (quiver in fear). Physically, this means that the electric field wave is influencing the magnetic field wave and vice versa. Practically, this means we have two really beastly equations to solve. We're saved by some approximations though! Most tiny fibers are "weakly guiding" - this means that 'critical angle' we talked about is really small, so the light is pretty much going straight down the fiber. This lets us 'decouple' our wave equations, so we can solve them! When we do this, we get pretty pictures of the electric and magnetic fields. There's a lot of different possibilities (called 'modes') for what you can get - here are two:

This picture is a cross section of the fiber (the dark purple part is the main core where the light mostly travels). And the electric field is represented by the red lines (longer line = stronger electric field). Imagine this as a cross section of a wave which is bopping up and down, while moving directly towards you. Here's another way to draw the second picture: 

In the picture above, I'm representing a strong magnetic field as a bigger height on the 3D graph. The electric field gets small as you go out to the edges, and follows this pretty cosine as you go around the circle. 

That is a snapshot in time of one of the electric field waves, which is travelling down an optical fiber right now to send this blog post to you! There's also a magnetic field wave - I didn't mention him because he's not too hard to find once you know the electric field. He's always just 90 degrees to his buddy, the electric field.  

And that's it - a brief intro to sending data in light pulses inside optical fibers! Now you can dream of total internal reflection and pretty wave patterns the next time you send an email or make an overseas phone call :)  I hope you enjoyed the read!  If you'd like to see the actual math behind light travelling in optical fibers, just leave me a note in the comments and I'd be happy to share!

When I Grow Up - Part 2

I can hardly believe classes are over. I have been so blessed by fifty-two talented and interested students this year. Some moments I'll remember from this year: the amazing weather this spring when we could bring our whiteboards outside and learn physics in the sunshine, the ridiculous errors I made and the comfortable atmosphere we had where we could laugh about them, far too many velociraptor problems, and watching friendships grow between students as they learned together.

The experience certainly convinced me that I would like to make teaching a big part of my career. As described in part 1 of this post, the question of what I want to be when I grow up is mostly answered. So the question of this blog post is: what sort of teacher do I want to be when I grow up? Now I don't have the foggiest idea if I want to be a high school teacher or a prof, a physics teacher or a special education teacher, etc. I do know, however, as every teacher does, that I want to be a great teacher. But when I think of great teachers I've met, they're all so different - so what is it that makes a teacher great?

Well, maybe it starts with not thinking so much about "being a great teacher", but rather focusing on helping my students get where they need to go. As someone who thinks far too much about things, it's easy for me to focus on my teaching rather than on my students' learning. And I think that's an unfortunate place to go - this is how we make teachers who spend hours preparing the most beautiful derivations to write on the black board, but are unaware that their class is actually just having a nap.

Alright, by now you must be thinking - is she actually just going to spend an entire blog post just rephrasing a question without ever really answering it? Yes. That is exactly what I'm doing. The fact is, I just don't know the answer. But...

There are at least some things I am pretty sure of. For example, one of the things I've been researching is what motivates students to go on into second year physics. For my male students, strong conceptual understanding and high grades were highly correlated with choosing a physics major. Makes sense. But for my female students, who have the experience of being a minority in the class, the only two variables I found which correlated with retention were a) their physics self-efficacy (aka confidence in doing physics) and b) the extent to which they felt that the prof and TAs cared about them. This is great because I certainly want to be the sort of teacher who shows my students that I care about them - not just because this could reduce the gender gap, but because I think it is simply a human way to live life. We were created to care about others and to be cared about - it only makes sense for this to happen in the classroom, in discussions about future career plans in the foyer, etc.

Feeling cared about is important to students, particularly the female students in my class, but we can't stop there. Students obviously need the opportunity to build an understanding of the physical world if they're going to be successful in physics. I'm currently really interested in the research suggesting that social environments can be very successful in doing this - that we can build understanding better with others than we can alone. If this is the case, "good teaching" involves less of the traditional download of information through a lecture, and more questions, more stepping back and assisting students as they form new knowledge problem solving together. Practically, this has been a really fun strategy to work on and tweak this year in tutorial.

Alright then, so far we can be fairly comfortable saying that students certainly need to know they are valued and cared about, and they certainly need to learn to do good physics. But this still doesn't seem like a very complete picture of good teaching. I have bigger goals for my students than that they merely be great physicists - I want them to be great people. I want them to care about each other and about the world, and I want them to be inspired to act on that love in selfless, genuine, and thoughtful ways. This is a challenging goal. So let me diverge to look at some examples of this through an analogy to film - I promise that this really will tie back into teaching, so do bear with me.

So I went to see Hunger Games the other day. And I really appreciated the themes the story brought to light. First, the idea of impacting change by acting together: At one point, the main character says, referring to a televised game in which children are forced to kill each other, "What if they all just stopped watching? There would be no Hunger Games." She is of course reminded that this will never happen. Though few people would intentionally kill an innocent child, the public continues to fund these atrocities with their choice of viewing material. The public collectively has the ability to end the games, but no one believes they hold this power - it's the thought process of, "The games will probably occur anyway, so what could be the harm in my watching it?"

The Hunger Games may be set in a post-apocalyptic world, but this theme certainly strikes a chord with our present day. Few pornography viewers would intentionally abuse women, yet every click directly funds this abuse. Few shoppers believe in inhumane working conditions or child labour, but how often do I look into the origin of my new blouse or gadget before I buy it? We could end the porn industry and drastically improve working conditions for employees in other countries. Yet we choose not to, because it's just too tempting to view the small difference our decisions make as being zero difference. (A physics aside: dx may be infinitesimally small, but it's not zero. And in fact when we integrate up all the little dx's we can get something actually quite big.) On top of this, we know these issues are complex, and solutions are not easy to come by. But knowing the complexities involved in finding actual solutions can't simply remove our personal responsibility for our choices to fund abuse.

This brings to mind a second theme in the Hunger Games: the power of the media in inspiring people to act cohesively without necessarily taking thoughtful consideration. At the start of the games, the public is told through video and speeches that the games are a wonderful thing. The children are bringing "honour" to their district, and the games are promoting "peace" by keeping the districts under the rule of the capitol. Of course, many of those directly involved know that this is not true, as evidenced when the father of one of the murdered children sparks a riot. But the crowds, who aren't personally involved, roar with applause at these statements of supposed honour and peace.

A more current example would of course be the Kony 2012 campaign. Many of us saw the emotionally charged video which encouraged us to support Invisible Children in bringing a very horrible man to justice. Watching the video, I think most people would agree that it just felt like such a great campaign - especially from our perspective as people who aren't personally involved. But fortunately, the same technology, which quickly spread the Kony 2012 campaign, also shared with us the responses of Ugandans to the film, such as this one: http://www.youtube.com/watch?v=KLVY5jBnD-E.  In her response, this speaker describes the devaluing consequences of reducing horrific events to a "just catch the bad guy" black and white issue, while intentionally ignoring the complexities of the situation. Facebook postings about Kony 2012 soon came down as we started to consider what our support meant and the impact it had. We asked hard questions such as: "How can we actually go about bringing Kony to justice without many innocent deaths - particularly of the children we hoped to protect?"  Of great importance, we took a tough look at our personal motivations: were we truly concerned and willing to make genuine sacrifices for our fellow human beings? Or in promoting Kony 2012, were we simply boosting our already ridiculous western Saviour complex, at the expense of Ugandans?

I could probably just ramble on all day about these things. But this is a teaching blog after all, and I promised that this does indeed have everything to do with answering the question of what kind of teacher I want to be.  So let's try to get to some semblance of a "point".

I want to teach more than physics. I want to first inspire in my students an understanding that they have the ability to effect enormous change, especially when they act cohesively. But second, I want to teach them to use this very carefully - to think deeply about how the decisions they make effect others, and to act accordingly. We first need to recognize that we can do something about the abuse in the porn industry, the deplorable working conditions in some factories, the atrocities committed against child soldiers, and the many other issues facing our world - we need to realize that our individual choices do make a difference in these situations and can be used for great good. But we also need to recognize that our choices can also be used negatively, and that in acting cohesively without thinking deeply about the complexities in these issues, we can actually make things quite a bit worse. We work through physics problems in tutorial, but I want my students to find thoughtful solutions to the problems that I don't know the answer to. And want them to be inspired to act on these solutions.

The challenge is that I have no idea how to be this sort of teacher. Seriously, no idea. I don't even know if this is entirely the kind of teacher I should be aiming to be - there's likely many important aspects of good teaching which I'm not yet even aware of.

But maybe the question of "what kind of teacher do I want to be when I grow up?" is a false one (if I could have just one more rephrasing of the question). I like to think that I'll always be "growing up" as a teacher, but never really arriving at some perfect understanding of what a great teacher is, or how to be this great teacher. Maybe the only "bad" teacher is a teacher who has stopped learning. And if that's true, then I'm okay with the fact that I have no idea how to be the teacher I want to be right now. It simply means that I have lots of time to learn from my students, from fellow teachers and from you - lots of time before I have to worry about running out of things to learn about teaching :)

When I Grow Up - Part 1

What do you want to be when you grow up? The answer was so simple when I was four years old - I would become a train man, an airplane man, or a nurse in a hospital. I have since decided that I should probably give up on the original plan of becoming a "man". And while I like trains, airplanes and helping people, it turns out that there are many other possible careers that I could also enjoy.

Right now, I'm in the very broad categories of "student" and "teacher" (which interestingly enough, does tend to involve train or airplane relative motion diagrams and a good deal of helping people). The past few weeks, I discovered some things I wouldn't have guessed about myself and my feelings towards teaching and learning; this has led me to feel quite certain that teaching (along with the related learning that teachers do) is a career that I can love. So I thought I'd share.

Life outside of teaching has been downright difficult lately. As I've been working through the ending of a relationship which mattered a lot to me, I've struggled to say goodbye to the hopes and dreams I had with someone whose dreams have changed. It has been challenging for me to redefine my value - not in a man's definition of my worth, but in God's, to strive to keep loving with my whole heart rather than building walls around it, to learn from the things I did wrong which contributed to this ending, but still forgive myself for the ways in which I wasn't the girlfriend I should have been, and to walk everyday with God. These things are easy to write down, but I'm finding they are much much more challenging to live. I've never experienced a broken relationship before, and God has a lot to teach me about love, grace and life. As I've been working through these things, I've felt a lot more sadness than I'm used to. So after our last weekend together, I was very worried that I wouldn't be able to teach well - that on top of everything, I would let my students down.

But an amazing thing happened last Monday. I walked into class with my bowl of gummies for our gummy bear circuit, my students said hi, and I just felt so much joy  (even more joy than I would feel if I had a bowl of gummies on a regular good day!) As the class went on, and I bopped around from group to group, I realized more and more just how much I love teaching. It actually almost made me cry, and I'm not a very leaky person.  It just hit me how blessed I am to be part of my students lives right now, as they're discovering who they are in their world - a blessing which is too easy for me to take for granted. It continues to surprise the socks off me: when I'm with my students, it's as if all of my concerns and sadness slip away. Of course, the things I need to work through are still there - that can't be avoided. But it has been a wonderful surprise to learn that teaching (especially with my students who are honestly such a dream class) really is a safe haven for me.

My science side can't help but look at this as a bit of a self-experiment. Somehow teaching continues to bring me joy even when my other work feels heavy and requires extra effort to complete. I think this suggests at least one good answer to the question of what I should be when I grow up. My dad, true to his funny engineer self, suggested (among other very loving encouragements) that I "re-calibrate" now that I'm on my own.  I won't dive too much into my relationship-recalibration thoughts on this blog, but so far my career-recalibration thoughts have been reaffirming the path I'm on. I truly do love teaching. I love seeing those beautiful aha moments when the student starts to piece everything together. I love being part of positive change, and teaching is all about growth and change - change in my students and change in myself. It's terribly nerdy, but as my poor friends who put up with endless demo's know, there is so much physics-happiness to be shared, and I just love sharing it.  And now I've learned that teaching brings me joy even when life is not easy. I really do have one of the best jobs a person could ever ask for.

The question of what I want to be when I grow up isn't fully answered yet, however.  The next aspect of this question is of course, "What kind of teacher do I plan to be?" I have a feeling, however, that this second question will require more words than the first, so I'll save it for another day.

Bicycle under a street light

Fun physics showed up on my bike ride home today! Did you know that you can pedal at the right speed to match the frequency of the street lights' flickering, so that the wheel appears to be not moving?

What's happening here? The streetlights are like very quickly flickering strobe lights - they "freeze" a moving object in time by taking many quick snap-shots. If the bicycle wheel is spinning too slowly, these fast snap-shots just tell the story of a rotating bicycle wheel - not very exciting. But if the bicycle wheel is spinning at just the right speed, the tread will have rotated exactly the right amount to appear to be in exactly the same position when the next "snap-shot" is taken by the street strobe light. Notice that this doesn't need to be a full 360 rotation of the wheel: the wheel just has to spin far enough so that the tread, say, one centimeter behind has now exactly taken the place of the tread ahead at the moment the street light flickers. 

These frozen "snap-shots" are really close together in time: the street light was flickering at a frequency so fast that the light just looked like it was continually shining to my eyes. So when I look down at my bicycle wheel, the series of snap-shots are put together smoothly, and my bicycle wheel appears to be still!

Here's an example of the same effect using a strobe light and a fan: http://www.youtube.com/watch?v=_3Fk5avi6kA. The key is just to match the frequency that the strobe is flashing to the angular frequency at which the fan blade is spinning, so that the fan blade is in the same location when each snap shot is taken.

For love and groceries

All you need is love... and groceries and rent and utilities and...

When it comes to physics and education, I have more than enough love. Indeed, friends, who endure my random "fun physics moments", might rather I restrain my physics love a little more. I'm currently trying to decide if I should pursue a PhD in physics education research or simply do a masters. I have no doubt that I would thoroughly enjoy the experience - I love the learning environment of the university, I love the research and I love the teaching opportunities. It would most definitely be a lot of fun to work on a PhD.

But I have to admit, love isn't the only factor in my decision. Tuition is higher and funding is lower than I'd planned for, and my practical brain can't help but wonder if a PhD would really be a financially sound decision.

So this semester will be an experiment. I just finished making advertising posters (using my sketch of the learning student, pictured to the left) for my physics tutoring services. I very much enjoy tutoring, so if I find it possible to break even this semester with some additional funds from tutoring, then I expect I'll be confident in diving into a PhD.

The key will be finding students who want regular weekly tutoring, not just cramming before the exam. I will try to be fairly strict about this anti-cramming policy. It's nearly impossible to learn physics in a short period of time just before the exam - it's like learning to play the piano - a student needs to work at it regularly and consistently throughout the semester in order to be successful. It would be terribly unethical for me to charge for tutoring if I didn't have sufficient time with the student to tutor effectively and consistently. As an aside, I do wish companies such as "CourseCram" felt the same way.

Now I know you're probably thinking, "Fabulous! As long as we don't hire her as a tutor, Anneke will finally stop inflicting her physics demonstrations with accompanying jazzy-hands on us." But you should know, I couldn't stop teaching physics to innocent bystanders if I tried. No one is safe from a fun physics moment! I'll try to differentiate between random free physics teaching and paid tutoring though through the degree of planning/preparation, building of ideas upon ideas and of course the direct connection to course material. Here's to hoping I have the heart to request pay to do a job that I enjoy perhaps even more than the customer...

Singing Palestrina & Learning to Teach

There are many aspects of learning about teaching which I love; one of these is the relatedness of life experiences and teaching. An example: in choral ensemble this fall, we learned a piece by Palestrina called Cantabo Domino. It's an absolutely beautiful piece when it comes together, but it was written back in the days before time signatures were a big deal, so it's quite challenging to sing. During practice, it wasn't uncommon for us to be completely off track in within just a few measures of starting the piece. When this happened, I expected our conductor to stop us and have us return to the beginning to find our notes, but he didn't. He kept conducting a mostly silent choir! I tried to come back in, "in vita mea-" no, wait, I wasn't in time with the sopranos. I listened anxiously for someone to give me a prominant phrase so I could find my place in the intertwining melodies of the piece.  Then there it was, the 2nd sopranos singing "delectabor in Domino" - I was back in. And I even got to feel a little bit useful: after the piece was done, one of the other 1st altos beside me thanked me for helping her find her part when she was off track.

Of particular note in this practice was our conductor's unwillingness to give up, even when we had no idea where we were. The atmosphere in the alto section was much less hopeful - we were all ready to throw in the towel. But our conductor just wasn't willing to give up on us; no matter how off track our singing was, he knew that if we took a moment to listen to the singers around us, we would find our way back into the music, and he was right.

I think teaching is very much like singing Palestrina. It is beautiful and thrilling when it comes together, but it is also very challenging to do well. And much like our conductor, teaching does not stop when we make mistakes. I will always be learning how to teach: making mistakes, reflecting on them, and trying to teach better. And though I want so much to be a perfect teacher - always inspiring all my students - I'm not, and those mistakes are part of the process. Bad teaching days aren't fun, but they are no reason to give up - just reason to reflect, listen to feedback from others like a singer does, and come back in.

I feel an invisible pressure (mostly from myself) that every lesson must go off without a hitch, which is heightened through being "that physics pedagogy researcher" in my department. Needless to say, my teaching this semester didn't meet these invisible standards of perfection.  For example, during one of our weekly quizzes, a student asked me about the quiz problem and I second guessed myself. In a non-flustered state after the quiz, I double checked the problem, and it turned out that my physics had been fine, but I felt really silly in the moment floundering and not sure how to respond. In another lesson, I wanted to talk to my students about mental illness in such a way as to normalize it and share some ways to care for themselves and their friends. It went okay, but really not as well as I'd hoped. My voice sounded funny because I have a cold, and something about the atmosphere of the room was distancing them from me. They were courteous, but I don't think I had them really buying in. This was one of the most important lessons of the year to me, and I was very sad to have taught it poorly. When these sorts of classes happen - when I'm not the teacher I want to be - it's hard not to feel very discouraged.

Yet last week, we sang the Palestrina in our concert, and it went so well. As an alto (the most fun part to sing), I got to be right in the middle of six different melodies intertwining, related but distinct, rising and falling together, but separately. Everything came together, and it was a great experience to sing such a difficult piece well.

This semester has contained those sorts of moments in teaching as well. There have been classes when the students were asking great questions, and classes when I was able to ask them guiding questions and see their eyes light up when they suddenly got it - I love that moment! Last week, I got to teach a few lectures, and they went so well - the participation level was high, with the majority of the time spent in peer instruction during which the students talked with each other to make sense of the physics concepts in specific practical applications. We were learning about rotational dynamics - really tough topics like "what is the moment of inertia?", "when can I think about an object as a point mass, and when can't I?", etc. It was exciting to teach, since these ideas were new to nearly everyone but were still relevant to their everyday experiences. It was very encouraging to see good attendance and participation in the lectures (Though this might have just been for the "special guests": Dr. Suess and Darth Vader, not for me). The students' positive responses really boosted my confidence that I'm on the right track to being an ever-improving teacher. But not every lesson is like that, and that's alright. Even the lessons gone wrong are part of this process of becoming a better teacher - a path that I'll always be on.

It's an interesting journey in that there is no end destination, but there is still a defined path of improvement. That paradoxical nature of learning to teach is challenging in that I will never be the perfect teacher I want to be, but also exciting in that I will always be getting better and learning more.

My alternate NSERC application

I know it's just how the system works. I have a small space on my NSERC application forms to list the experiences which have developed my communication and interpersonal skills. The reviewers are looking for conference presentations, positions chairing committees, classroom teaching experiences, etc. for a good funding application. And no doubt, those sorts of things are important. What is distressing me is not that these things are valued, but what they are valued above.

Where have I learned the most about communication? In communicating with people who are non-verbal, in the complex process of enabling independence with people with disabilities, and most of all, in listening to those who have so much to say of great importance, but don't talk the way I do - those who persevere in communicating despite day after day, sometimes year after year of being unheard. Where have I learned the most about interpersonal skills? In working through tensions among people living in community, in revealing to another person, who feels useless and unwanted, their incredible value and beauty, and in receiving unconditional trust and love from people with disabilities.

Imagine what our world could be if we all learned from some of the greatest teachers of trust, love, forgiveness and acceptance! What an incredible gift we have in knowing these people with intellectual disabilities - I wish that I was more worthy of that honour.

So here is my alternate "Applicants Statement" of my NSERC application. The good one. The one that most accurately answers NSERC's question to describe the experiences that have formed my communication and interpersonal skills.

I'd like to share with you about Audrey (not her real name). Audrey is an incredible teacher of what it means to love, to trust, and to forgive. During the time I've spent with Audrey, she never missed an opportunity to teach me something new and reveal something beautiful about our world. In terms of how we typically assess people, Audrey is unable to speak verbally, she cannot feed herself, she requires assistance to walk and to do most things, and she is blind. Here I will describe just a few experiences with Audrey which highlight how she taught me so much about interpersonal and communication skills. 

Interpersonal skills cannot be just a set of well-timed head nods, "thank you for sharing your concerns" comments, and fake smiles. Interpersonal skills require a genuine love for another person. I'm referring to love, not in a romantic sense of course, but in the sense that the welfare of others must truly and deeply matter to me. This kind of love can only be unconditional - it needs to wrapped in forgiveness in order to mean anything. 

Audrey spent most of her life in an institution. I'm not aware of all of the details of this experience, but from my knowledge of Audrey and of many institutions, it is not unlikely that Audrey spent perhaps 20 years sitting alone. Try to imagine 20 years of isolation. On a tight schedule, an overworked nurse would have probably come by, quickly put food or medications in her mouth, and then would have had to move on, leaving Audrey alone in her dark world of blindness. Her lack of speech would have made it impossible for her to express the pain this must have caused. I cannot even imagine a single day living in such isolation, with no way to make it better.

Audrey has every right to be bitter and angry against the world. And yet, she has chosen to love others, and she is one of the most loving women I have ever met. As an aside, it makes me wonder what our world could look like if nations could forgive other nations with the kind of unconditional love that Audrey can give. But in this alternate application, I'll just describe a bit of the interpersonal skills that Audrey taught me personally. One key aspect of Audrey's ability to love is that it is two-way: she is both strong enough to give unconditional love regardless of past hurts and humble enough to receive it. In knowing Audrey, I discovered the importance of not only my caring for others, but also my accepting love from others, which can sometimes be hard on my pride. Audrey also taught me a great deal about the importance of focused time - of sitting with another person, and being fully focused on relating to them. When I'm sitting with someone who is non-verbal, it is tempting to just start thinking ahead to tasks that I need to do, rather than focusing on them. Audrey could sense if I was not 100% connecting with her, and she kept me accountable. This is of course very important for interpersonal skills - that I take the time to fully focus on the student who I am talking to, so that they know they are valued and their learning as well as they themselves matter to me.

Audrey also shared with me much about communication. Typically, when I sing and play guitar, it's just about enjoying a nice song. Audrey taught me that music is all about connecting with people. I would sit down beside her, and she would hear me opening my guitar case. Her head would tilt a bit to the side as if to ask, "is that the sound I think it is?" And from the first chord, her face would light up in the most beautiful smile. She'd lean in towards me so her ears could be as close to the sound as possible. But it wasn't just about hearing the sound for her; if we played her music on a CD, she didn't experience the same joy (though the music itself sounded much better than what I could sing). Singing with Audrey was to communicate with her, so I sang with her all the time - outside on walks, during personal care, and of course during our evening guitar time. And I am intentionally using the phrase "I sang with her"; Audrey may not have been able to verbally sing along, but she participated in the music much more fully than most people who can hum along. She taught me by example, how to communicate enormous gratitude, to share a joy for the beauty of the world, and to connect with another person - all without using words.

Audrey's lack of verbal language encouraged me to pay closer attention to her sometimes subtle communications, which is a highly transferable skill particularly for teaching. Only the bravest students will tell the teacher how they are feeling in a course verbally, but all of the students will share their concerns and fears non-verbally - all the teacher needs to do is know how to listen. I have much more to learn about listening, but I am very grateful to Audrey for the lessons she taught me on communication so far. 

Giving and receiving trust is essential to both good communication and interpersonal skills. To assist Audrey in transferring to her wheel chair, I would start by explaining where we were going and then say something like, "Audrey, will you stand up with me?" And she would reach out her hands - these beautiful weathered wrinkled hands with her palms up and open. In those hands was her trust, freely given to me. She trusted that when I lifted her, I would not drop her fragile frame. She also knew that I was trusting her not to lunge to the side which could seriously hurt me as well. She trusted that wherever I was taking her, it would be good, even though I don't know how much she could understand of my description of where we were going. It is a huge honour and responsibility to be given someone's complete trust - particularly from someone who is vulnerable. For me, this is one of my greatest motivators - to know that someone trusts me; it would break my heart to let them down. For successful communication and interpersonal connection with students, trust is essential. Like Audrey, my students need to know that I will do everything I can to not let them fall. Also, just as I trusted Audrey to stand up with care, my students need to know that I am trusting them to put their best effort into learning physics. And like Audrey, my students need to know that in this course or tutorial, I am taking them somewhere worthwhile. 

There is so much more to write about on this topic. I could describe what I have learned about genuine and continual encouragement and thankfulness from a beautiful woman, who is the only person to never miss a chance to excitedly tell me that she liked my leading worship in church and has thanked me at least once or twice a week for the last year for a painting that I gave her and her sister last summer. I could write about the lessons in patience and perseverance even in the seemingly unimportant things from a man who could only communicate by blinking because he was paralyzed except for his eyes. I could write about what I have learned from a good friend of mine with aspergers, who has many gifts, one being that she has a remarkable ability to accept herself and others simply for who they are. I could share what I've learned about truly listening and valuing what others say from a woman who seems to string non-nonsensical words together, but then suddenly out of this string of words, she speaks something profound. This is truly just scratching the surface. If I began to describe what I have learned from the many people with disabilities who I have had the great honour to know, I would be writing a novel.

So why is it that titles, such as "support worker", don't look well on most resumes or NSERC applications requiring interpersonal and communication skills? I think this is because readers, who haven't had the opportunity to experience the field, see support work as simply cleaning and feeding people. But just to write that makes me cringe. To be a good support worker requires continual learning and growth in interpersonal, communication and many other skills - it was inspiring to see the ability and commitment of my co-workers who have made this challenging work their career. Of course, the adjective "good" is necessary in that sentence - technically, it is possible for a support worker to completely blind themselves to the value of the people with disabilities they see everyday, and simply perform routine tasks without thought of the person in front of them, but this was certainly not the norm among my co-workers.

So truth be told, this post isn't really about my less than impressive NSERC application. It's about what our lack of valuing work done with people with disabilities represents. It reflects a society which far too often views people with intellectual or other disabilities as a group to pity or avoid. It represents our tragic failure to learn from people who could change the world with their ability to love. Gosh, that makes me so so sad.

In the end, I couldn't help myself - I just couldn't leave all this out of my real NSERC application. So my "support worker experiences" did make it squeezed into at least one tiny line on the real application. I hope that the reviewers have also known a person with a disability, partly so that when they read that short line they understand that really, what I am describing is the paragraphs above. But mostly, I hope the reviewers have known a person with a disability, so that they can be as fortunate and blessed as I've been.

Becoming Human

I’m currently reading the most beautiful book by Jean Vanier. It’s a series of lectures he gave entitled, Becoming Human. It’s not explicitly related to education, but I think his insights are very much worth sharing in this blog, none-the-less. So, here’s my take on the first chapter.

Vanier writes that loneliness is an essential aspect of being human.  We can cover over loneliness by surrounding ourselves with busy work, but it is always still a part of who we are. Loneliness can by a force for good, however - we can give our lives meaning through occupations and volunteer work that makes us feel useful and needed. It can lead us to creative expression and even lead us to seek God. Vanier describes an experience of God as paradoxically both satisfying our thirst for the absolute and at the same time whetting it, leaving us seeking more. I think this is certainly true in my experiences. I write my best songs, paint my best art, and often accomplish my most meaningful work when I am lonely. And the feeling of loneliness is often a reminder to me to take more time for my relationship with God. I appreciate that Vanier doesn't write loneliness off as a purely tragic thing; he acknowledges both sides of this essential aspect of human beings.

Unfortunately, while loneliness can inspire creative fulfilling work and faith, it can also birth apathy and depression. When a person is unsuccessful in filling this hole of loneliness with anything, they can give up. They can begin to believe that there is nothing they can ever do to make the world better of find any meaning in their life. This sort of loneliness, Vanier describes as "a feeling of not being part of anything, of being cut off", and it doesn't necessarily have anything to do with whether the person is alone. This is too often the case for people with disabilities, or for people who are disabled by their life situation of poverty or discrimination, since such people don't always have as easy access the positive growth opportunities that loneliness could inspire them into. 

Vanier describes loneliness as a paradox; we need connectedness with other human beings to quench our loneliness and bring us feelings of security and order. Yet that same connectedness can stifle the positive loneliness which encourages us to take new creative paths. So how do we live with others in this paradoxical world? I like how Vanier puts it,

"All humans are sacred, whatever their culture, race, or religion, whatever their capacities or incapacities, and whatever their weaknesses or strengths may be. Each of us has an instrument to bring to the vast orchestra of humanity, and each of us needs help to become all that we may be."

Vanier's ideas aren't specific to education of course, but they are easily relateable. As a teacher, revealing to my students what instrument they play well is a great responsibility and honour. Of course, by the time my students have reached first year, they've done quite a lot of figuring out what their role in the world is already. But I don't think this revealing ever stops in life, so I hope that I can be a part of that for my students at their current stage of life as well. Showing them their uniqueness, and striving to understand who they are and where they are in their life - these things encourage the inspiring creative side of loneliness. Vanier specifically mentions the importance of celebrating the person for who they are and the abilities they do have. Pity is the opposite of empowerment - regardless of ability.

It is also my role as an educator, to guide my students away from the tragic side of loneliness and towards community with each other. Creating community is one of my biggest goals with my students this year. Of course, I intend to build community in the context of teaching them a good conceptual understanding and strong problem solving skills, but I want to make sure they all finish the year with the community that they need to grow those skills and conceptual understanding in the future.

I am trying to structure my tutorial so that my students each feel that they are an essential contributing member of a team with a common goal. That's a big learning process for both me and the students! It's been a challenge for me to set up the teams, and especially to set up my physical classroom space (which consists of 70 chairs, with mini desks bolted to the floor in rows - it's taken a lot of different attempts to try to make this a space for collaboration as you can imagine!) It's also taking time for the students to figure out how to solve a problem in a team, and I've definitely seen lots of bumps so far in tutorial. There are cultural barriers, the challenge of being humble enough to ask for a friend's help, and issues of impatience with team members who aren't "getting it" quickly enough. It's not easy to learn to value the different contributions classmates can make, but I've seen enough successful teamwork and improvements in teamwork to trust that we're learning how to do community as a class. And I'm excited about that.

Don't pull the weeds in this studio

When people ask me what I study, I do try really hard to fight the temptation to ramble on and on about physics education research, but you know how it is - sometimes I can't help but let it slip out. And it really is exciting stuff (I like to think); I get to look at the gender gap in physics, and try to work my way through the complex weave of issues that contribute to this gap, with the hope of finding some positive solutions. Specifically, I'm looking at the impacts of physics self-efficacy (which just refers to how confident you are in your ability to do physics) on the success and retention of women in physics. A lot of very fascinating research has been done in this field, and I am quite looking forward to learning more.

So yes, admittedly it just happened now; it really is so hard to mention physics education research without rambling on for at least a paragraph. This blog post, however, is about such a rambling that happened recently when I was talking with a person who teaches in the engineering department. I assumed that as a female educator in a similar field, she would be enthused to hear that such research was going on in a nearby department. But her response to my excitement about self-efficacy was:

 "Oh, well you know, in engineering, our students aren't touchy feely like that."

I didn't know what to say. How could an educator completely ignore study after study done on engineering students showing that they are touchy feely like that?

Through educators who think this way, we have created a "weed-out" system, without taking the time to think about how this affects our students' self-efficacy or the future of engineering as a whole. In this type of system, which views students as disembodied transcript numbers, professors have even been known to say,

"Look to your left. Look to your right. One of them will be gone by Christmas."

Of course, we like to think that in such a system, we are weeding out the academically "weak" students - these students would make poor engineers anyway, right? But I believe that such a system is actually hurting or even eliminating the innovative, collaborative, ethical, and diverse engineers - the very engineers who we need to discover solutions for the challenges to be faced by our changing world.

• Firstly, such a system weeds out students with a strong sense of ethics who care about their fellow student. A student who genuinely cares and tries to help their classmates succeed does poorly because this kind of cut-throat system requires that your fellow classmates to do worse than you so that you can "win". 
• Secondly, we weed out minority groups using subtle and sometimes even overt discrimination as described in Malicky's A Literature Review on the Under-representation of Women in Engineering. We make sexual jokes about women in engineering - we mean it all in fun of course, but objectification can not help but wear down a person's self-efficacy. In lab experiments, a woman can find her role in writing down the data rather than actually using the equipment because of the unspoken assumption that she is not as good at engineering as her male lab partner. Women who do persist in the sciences can find themselves acting more masculine than they might like to blend in. In my observations, the discrimination towards students with faith backgrounds in the sciences is even greater than that towards women. Students and professors toss in jokes or even overt insults directed towards people of faith, often leaving those who believe in God with a damaged self-efficacy and a strong sense that they are not welcome to study the field that they love.
• Lastly, we weed out those with new innovative perspectives. I believe that creativity needs a positive environment to flourish. Any artist will tell you that their studio space is essential in their creative process - some artists need to listen to music, some need to be in nature, some need to be in community with other artists, I need tea, chocolate and natural light - the specifics of the studio differ, but the theme is the same: artists need an environment which uplifts their soul to produce great work. I believe that creativity in engineering design requires the same uplifting environment. How can a "weed-out" atmosphere, in which the constant fear of "I'm not smart enough" plagues many students, be a studio space for engineering innovation?

I think we need to take a step back, study the literature on self-efficacy and the gender gap in engineering and science education, and re-assess the sometimes unspoken, but still prevalent "weed-out" attitude that exists in the sciences and engineering.

Thoughts on Teaching in the Tutorial

I find that teaching does something ridiculous to me. It's similar to the effect of drinking five cups of coffee before entering a ball pit. I sometimes think that if I could step outside my body while I'm teaching, and watch, I'd surely be saying to myself, "who is that?" This afternoon, I found myself quite literally leaping over chairs, acting out graphs with my body, and feeling ridiculously gleeful when my students experienced success in their problem solving. I honestly don't know how it happens; before tutorial, I was really quite tired, but as soon as the students walked in the room, I was on cloud nine. I can't help but wonder, is teaching secretly some form of a caffeine pill?

I'm still on the fence about how effective this high degree of excitement is for student learning. For some students, the excitement seems to be contagious - it gets a positive atmosphere in the room which spurs them on to learn more and have fun while learning. That is of course exactly what I love to see. For other students, however, I'm afraid that it distances them. The student who is really struggling doesn't want to see someone else having a jolly good time doing physics. They need a TA who comes along side them to meet them where they are at, in the emotional state that they are experiencing - a TA who they can relate to. This is of course much easier one-on-one; when a student approaches me individually with a stressed look on their face, of course that automatically changes my approach with them. But in the classroom, I am finding it very challenging to be the sort of TA that each of my very different students need.

We started our first tutorial with a great POE from Tom - the one with three tracks: (A) has a ramp followed by a hill, (B) has a ramp followed by a flat stretch, and (C) has a ramp followed by a valley. They all start and finish at the same height, but their paths are different. It's a fun POE to talk about kinematics, misuse of conservation of energy laws, and how the normal force can change the horizontal velocity when something is rolling (unlike a projectile which has the same horizontal velocity all through its path). The students got right into it! As soon as they entered the room, ten minutes before the start of class, they began investigating the tracks and trying to work out a solution. I love working with these students - you couldn't possibly ask for a better class.

During the first round of tutorials, I used this POE as a stepping stone to kinematics/ dynamics, but I also used it as a way to draw out and validate the curiosity they all have as physicists. Once we had discussed as a class the various possibilities for a little while, I asked them to vote if they would like to actually observe what happens, or just move on to the rest of the tutorial. Of course, all of them really wanted to see what really happens - and made this very clear to me verbally when I pretended to suggest that it didn't really matter. I was able to encourage them to hold onto this curiosity that has gotten them here studying physics. I shared with them briefly about my undergraduate experience - how my learning community of friends and my curiosity and love of learning made undergrad a truly enjoyable and enriching experience. Of course, after all this, we did observe which ball won the race, and everyone was surprised and interested. Three of the students explained why things resulted in the way that they did.

After this, we dove into problem solving. I had used another combination of my supervisor's and Tom's great ideas and cut up a giant sheet of whiteboard material into 2ft x 2ft whiteboards for teams of 3 students each to use to work out problems together. I gave the teams one of two different problems to solve and 40mins to solve them. One of the problems, given to me by my supervisor, was particularly successful in getting the students really thinking:

Before the Golden Gael’s football game this past Saturday, the quarter back was warming up by tossing the football straight up in the air and then catching it again. Determine the percentage of the total flight time during which the football is in the top half of its trajectory.

 I love this problem because there are no numbers! Of course that was the student's first response too: "I can't solve this without any numbers!" It was also a great chance for them to see just how essential it is to have a really good picture and well defined variables with useful subscripts. Of course, all of the groups required considerable support/questioning to reach the solution because it's not an easy problem. A few students came up with some creative approaches too.

After our 40 minutes of problem solving in teams, I had the students find their lab partner (who did the other problem), and teach them how to solve the problem they did. I like this strategy because it requires every student in the problem solving team to have a firm grasp of what is going on. Knowing that you have to teach this problem to someone else really motivated the students to participate in the problem solving.

I had a specific plan for these teaching partners. Last week, I made a lovely colour coded spread sheet to set up optimal lab/teaching partners. We had given the students a diagnostic test on the first day to determine where they were at in their understanding. The spread of overall grades was huge - from 33% to 100%, and everything in between. I took the questions from the test and divided them into questions which tested an understanding of inertia, of Newton's 3rd law, etc. This was a very imprecise science, of course, since most good physics questions require students to synthesize more than one idea, but I did my best. Then I matched students who achieved approximately only a 15-25% difference in their overall score, but scored very differently on the different aspects of the test. For example, I would put a student who achieved an overall score of 75% but achieved 100% on inertia problems and only 50% on 3rd law problems with a student who achieved an overall score of 55%, but achieved 100% on 3rd law problems and only 10% on inertia problems. My thinking was that the lab/teaching partners will be able to teach each other, but neither partner will get frustrated as the one who is always helping the other, since they both have different strengths. So far in the first two tutorials, this appears to be going well. I have yet to decide if the gains have been worth the significant amount of time that I put into sorting the data from the diagnostic test.

The second tutorial followed a similar structure. This time, we started with a brief class discussion about their feedback from an online get-to-know-you survey I had put out to them in the first week. They had shared with me what they love about physics, what they were most concerned about in the course, their plans for the future, and their hobbies (so that I can make them the stars of my tutorial problems). We specifically addressed the top three concerns they had brought up:

1) Keeping up with the workload
2) Maintaining high grades
3) Worries about having an incomplete math background. 

We chatted about some strategies to keep up with the work, maintain high grades without obsessing over grades, and I asked them for their advice with how to bring their math skills up to speed.

Following this, we entered the usual pattern of team problem solving with the whiteboards followed by teaching your lab partner how to do the problem you solved. All this went quite well - they were comfortable with the system, and did a great job solving the problems and teaching each other.

The difference with this week's tutorial was that it also ended with a quiz. I had written a quiz problem that I was really quite pleased with: it was about a student playing piano - one hand is playing a scale (consecutive notes) at constant speed, and the other hand is just starting to play a scale accelerating from rest. The question was to draw a position vs time graph for the two hands relative to the piano, and then to draw a graph of the right hand's position relative to the left hand. The final part was to find the time when the hands met. I thought it was a really fun question - the students would get to combine their understanding of position vs time graphs with their understanding of relative motion, and that would feel oh-so-rewarding. I definitely had my head in the clouds on this one.

The students really struggled with the quiz. One girl was actually shaking for the full half hour and several were visibly distressed. I felt so badly. In the end, I was able to find enough part marks to pass all but one of the students, but these students are used to getting 98% on physics tests - a 50%, even though it was on a quiz worth next to nothing in their final grade, was really hard on them. I think it's a very positive and important thing for them to be highly challenged by the problems they do in teams - this stretches them in an environment that has all sorts of supports. I didn't intend, however, to give them such a difficult problem in the already stressful situation of a quiz assessment.

I think I need to begin the next tutorial by apologizing. I hope I can also use it as a bit of teaching about teaching for my con-ed students - to share with them one of the challenges of teaching is to think like a student - and I didn't do that very effectively in writing the first quiz. While the students do need to be able to solve problems of this difficulty by the time the midterm arrives, it wasn't fair of me to expect them to be awesome problem solvers, able to synthesize different concepts, on the very first quiz. I hope that my apology reassures them that I have no desire to "weed them out" of physics, that I care about them, and that they aren't stupid.

I must admit, I'm glad that I'm not a doctor. As a teacher, I make a lot of mistakes, but at least there's always that next tutorial to try to set things right again.