## Fictitious forces (3/5): Coriolis force — how we think it should be taught

So how do we teach about the Coriolis force? The following is a shortened version of an article that Pierre de Wet and I wrote when I was still in Bergen, check it out here.

## The Coriolis demonstration

A demonstration observing a body on a rotating table from within and from outside the rotating system was run as part of the practical experimentation component of the “Introduction to Oceanography” semester course. Students were in the second year of their Bachelors in meteorology and oceanography at the Geophysical Institute of the University of Bergen, Norway. Similar experiments are run at many universities as part of their oceanography or geophysical fluid dynamics instruction.

Materials:

• Rotating table with a co-rotating video camera (See Figure 1. For simpler and less expensive setups, please refer to “Possible modifications of the activity”)
• Screen where images from the camera can be displayed
• Solid metal spheres
• Ramp to launch the spheres from
• Tape to mark positions on the floor

Time needed:

About 45 minutes to one hour per student group. The groups should be sufficiently small so as to ensure active participation of every student. In our small lab space, five has proven to be the upper limit on the number of students per group.

In the demonstration, a metal ball is launched from a ramp on a rotating table (Figure 1A,B). Students simultaneously observe the motion from two vantage points: where they are standing in the room, i.e. outside of the rotating system of the table; and, on a screen that displays the table, as captured by a co-rotating camera mounted above it. They are subsequently asked to:

• trace the trajectory seen on the screen on a transparency (Figure 1C),
• measure the radius of this drawn trajectory; and
• compare the trajectory’s radius to the theorized value.

The latter is calculated from the measured rotation rate of the table and the linear velocity of the ball, determined by launching the ball along a straight line on the floor.

Instructional approach

In years prior to 2012, the course had been run along the conventional lines of instruction in an undergraduate physics lab: the students read the instructions, conduct the experiment and write a report.

In 2012, we decided to include an elicit-confront-resolve approach to help students realize and understand the seemingly conflicting observations made from inside versus outside of the rotating system (Figure 2). The three steps we employed are described in detail below.

1. Elicit the lingering misconception

1.a The general function of the “elicit” step

The goal of this first step is to make students aware of their beliefs of what will happen in a given situation, no matter what those beliefs might be. By discussing what students anticipate to observe under different physical conditions before the actual experiment is conducted, the students’ insights are put to the test. Sketching different scenarios (Fan (2015), Ainsworth et al. (2011)) and trying to answer questions before observing experiments are important steps in the learning process since students are usually unaware of their premises and assumptions. These need to be explicated and verbalized before they can be tested, and either be built on, or, if necessary, overcome.

1.b What the “elicit” step means in the context of our experiment

Students have been taught in introductory lectures that in a counter-clockwise rotating system (i.e. in the Northern Hemisphere) a moving object will be deflected to the right. They are also aware that the extent to which the object is deflected depends on its velocity and the rotational speed of the reference frame.

A typical laboratory session would progress as follows: students are asked to observe the path of a ball being launched from the perimeter of the circular, not-yet rotating table by a student standing at a marked position next to the table, the “launch position”. The ball is observed to be rolling radially towards and over the center point of the table, dropping off the table diametrically opposite from the position from which it was launched. So far nothing surprising. A second student – the catcher – is asked to stand at the position where the ball dropped off the table’s edge so as to catch the ball in the non-rotating case. The position is also marked on the floor with insulation tape.

The students are now asked to predict the behavior of the ball once the table is put into slow rotation. At this point, students typically enquire about the direction of rotation and, when assured that “Northern Hemisphere” counter-clockwise rotation is being applied, their default prediction is that the ball will be deflected to the right. When asked whether the catcher should alter their position, the students commonly answer that the catcher should move some arbitrary angle, but typically less than 90 degrees, clockwise around the table. The question of the influence of an increase in the rotational rate of the table on the catcher’s placement is now posed. “Still further clockwise”, is the usual answer. This then leads to the instructor’s asking whether a rotational speed exists at which the student launching the ball, will also be able to catch it him/herself. Ordinarily the students confirm that such a situation is indeed possible.

1. Confronting the misconception

2.a The general function of the “confront” step

For those cases in which the “elicit” step brought to light assumptions or beliefs that are different from the instructor’s, the “confront” step serves to show the students the discrepancy between what they stated to be true, and what they observe to be true.

2.b What the “confront” step means in the context of our experiment

The students’ predictions are subsequently put to the test by starting with the simple, non-rotating case: the ball is launched and the nominated catcher, positioned diametrically across from the launch position, seizes the ball as it falls off the table’s surface right in front of them. As in the discussion beforehand, the table is then put into rotation at incrementally increasing rates, with the ball being launched from the same position for each of the different rotational speeds. It becomes clear that the catcher need not adjust their position, but can remain standing diametrically opposite to the student launching the ball – the point where the ball drops to the floor. Hence students realize that the movement of the ball relative to the non-rotating laboratory is unaffected by the table’s rotation rate.

This observation appears counterintuitive, since the camera, rotating with the system, shows the curved trajectories the students had expected; circles with radii decreasing as the rotation rate is increased. Furthermore, to add to their confusion, when observed from their positions around the rotating table, the path of the ball on the rotating table appears to show a deflection, too. This is due to the observer’s eye being fooled by focusing on features of the table, e.g. cross hairs drawn on the table’s surface or the bars of the camera scaffold, relative to which the ball does, indeed, follow a curved trajectory. To overcome this latter trickery of the mind, the instructor may ask the students to crouch, diametrically across from the launcher, so that their line of sight is aligned with the table’s surface, i.e. at a zero zenith angle of observation. From this vantage point the ball is observed to indeed be moving in a straight line towards the observer, irrespective of the rate of rotation of the table.

To further cement the concept, the table may again be set into rotation. The launcher and the catcher are now asked to pass the ball to one another by throwing it across the table without it physically making contact with the table’s surface. As expected, the ball moves in a straight line between the launcher and the catcher, who are both observing from an inert frame of reference. However, when viewing the playback of the co-rotating camera, which represents the view from the rotating frame of reference, the trajectory is observed as curved.

1. Resolving the misconception

3.a The general function of the “resolve” step

Misconceptions that were brought to light during the “elicit” step, and whose discrepancy with observations was made clear during the “confront” step, are finally corrected in the “resolve” step. While this sounds very easy, in practice it is anything but. The final step of the elicit-confront-resolve instructional approach thus presents the opportunity for the instructor to aid students in reflecting upon and reassessing previous knowledge, and for learning to take place.

3.b What the “resolve” step means in the context of our experiment

The instructor should by now be able to point out and dispel any remaining implicit assumptions, making it clear that the discrepant trajectories are undoubtedly the product of viewing the motion from different frames of reference. Despite the students’ observations and their participation in the experiment this is not a given, nor does it happen instantaneously. Oftentimes further, detailed discussion is required. Frequently students have to re-run the experiment themselves in different roles (i.e. as launcher as well as catcher) and explicitly state what they are noticing before they trust their observations.

Possible modifications of the activity:

We used the described activity to introduce the laboratory activity, after which the students had to carry out the exercise and write a report about it. Follow-up experiments that are often conducted usually include rotating water tanks to visualize the effect of the Coriolis force on the large-scale circulation of the ocean or atmosphere, for example on vortices, fronts, ocean gyres, Ekman layers, Rossby waves, the General circulation and many other phenomena (see for example Marshall and Plumb (2007)).

Despite their popularity in geophysical fluid dynamics instruction at the authors’ current and previous institutions, rotating tables might not be readily available everywhere. Good instructions for building a rotating table can, for example, be found on the “weather in a tank” website, where there is also the contact information to a supplier given: http://paoc.mit.edu/labguide/apparatus.html. A less expensive setup can be created from old disk players or even Lazy Susans. In many cases, setting the exact rotation rate is not as important as having a qualitative difference between “fast” and “slow” rotation, which is very easy to realize. In cases where a co-rotating camera is not available, by dipping the ball in either dye or chalk dust (or by simply running a pen in a straight line across the rotating surface), the trajectory in the rotating system can be visualized. The method described in this manuscript is easily adapted to such a setup.

Lastly we suggest using an elicit-confront-resolve approach even when the demonstration is not run on an actual rotating table. Even if the demonstration is only virtually conducted, for example using Urbano & Houghton (2006)’s Coriolis force simulation, the approach is beneficial to increasing conceptual understanding.

## Concept maps II

A couple of pointers on how to use concept maps in class.

I recently presented concept maps as a tool both here and in a workshop I co-taught. And I  was pleasantly surprised by how many people said that they were considering employing this tool in their class! So for those of you who might want to use it – here are some more pointers of how I used it. But beware – there is a whole body of literature on this method out there – these are only my own experiences!

So. Firstly – for concept maps to work in class you will have to introduce them the first time round you are using them. What I did was to start drawing a concept maps on the board, and have students tell me what else to add to it and how. I used “roses” as my example, with the question of how roses and people interact.

The way it developed was that students named different parts of roses (stems, petals, thorns, …) and that roses can both hurt people (with their thorns) and make people happy (because of the way they look, because of what they symbolize, because of the context they are presented in, …), that roses use up CO2 and produce O2 which is relevant for us, that roses need soil, that they might need fertilizer, that they become soil again when they die. As you can see, even this very simple example can already produce quite a complex concept map. And it gave me the chance to point out all the different features I wanted the students to include, but without me actually having to give away concepts and connections that I thought were important for the topic they were later working on.

Another very important point: Bring sheets of paper. There will already be enough resistance against trying this (and any) new method – don’t give the students the chance to boycott it because they don’t have anything to write on!

And most importantly – enjoy. It is really amazing to see concept maps develop over time, and it is even more amazing to see how students enjoy seeing their progress mapped out by their maps.

## Concept maps

Drawing concept maps at the beginning, the middle and the end of the course.

Using concept maps in teaching is something that I first tried last year in both the GEOF130 and CMM31 courses. The idea is that coming in, students typically don’t have a very good overview over the topics and concepts that are going to be covered in an introductory oceanography class, but that that will hopefully change over the course of the course.

The reason for trying to use concept maps in teaching was twofold.

Firstly, I wanted students to see how they gradually learned more and more about oceanography, and how they started to see connections between concepts that initially did not seem related.

Secondly, I am a big concept- or mind-map drawer whenever I need to study complex topics. For every big examination at university, be it in physics or ship-building or oceanography, I have drawn concept maps (even though at the time I didn’t know they were called that, and I was using them intuitively to organize my thoughts, rather than purposefully using them as a method). So why not try if it helps students study, too?

So how did it work in practice? Students were asked to draw concept maps during the first lecture, during a lecture some time half-way through the course, and at the end of the course. I collected and scanned the concept maps (out of my own curiosity) but students always had access to them and were encouraged to work on them any time they wanted to. Concept maps got impressively complex fairly quickly, and students reported that the maps helped them both to see their progress and to organize their thoughts.

For one of the courses, I used the concept maps as basis for the oral examination in the end (which was a lot more time-intensive to prepare on my part than I had imagined, and I wouldn’t do that again) and for part of the grade. For that, I had written down a list of concepts that I thought they should definitely have learned in my course, and a list of connection between concepts that I thought were crucial, and I just counted them and ticked them off on a list. Again, this was a lot of work and I am not sure if I would do it again. Not because it was so much work, but because I am not sure if by grading basically whether students went through the table of contents of the textbook and made sure all the headings were included in the map, I am encouraging just that and nothing more (although I actually don’t think this is what happened in either of the courses, but still, thinking of constructive alignment, basically naming concepts is not a learning outcome I want from my class).

So in conclusion, I would definitely use concept maps in teaching again (Isn’t it impressive to see the maps develop?), but not as a tool for evaluation.

P.S.: A big THANK YOU! to the student whose concept maps I am showing here (and who wishes to remain anonymous, but kindly agreed to let me use them as an example).

## Oceanographic concepts and language (part 3)

What level of proficiency do you need to communicate about science?

This post is not strictly about oceanography, but I started thinking about it in the context of a class I taught recently, where I was teaching in a foreign language to me and most of the students.

After one of the classes, a student came to me to thank me that had I continued explaining concepts, even though some of the (native speaker) students thought that that was ridiculous and everybody should know what certain terms meant (posted about here).

And one thing this student and I noted when discussing in a language that was foreign to both of us was that even though our grammar might be not perfect and our vocabulary not as large as that of native speakers, we had a sensitivity for other speakers that many of the native speakers lacked. For example, we discovered that it comes natural to us to speak about “football” to speakers of British English, when we would say “soccer” to speakers of American English. Or that we are aware that trousers and pants might or might not mean the same thing, depending on who you are talking to. And I remember distinctly how on a British ship, sitting at a table with American scientists, I explained that when the stewart asked if we wanted “pudding” we could well end up getting cake, because in the context then what he meant was “dessert”.

When you are a non-native speaker, you get used to listening very carefully in order to understand what is going on around you. In my first months in Norway, for example, I happily watched Swedish TV and would understand as much there as on Norwegian TV. I would recognize words, grammar rules that had been discussed in language class, even phrases. Yet many of my Norwegian friends say they find it hard to understand Swedish.  But on the other hand I remember that I found it much easier to communicate in English when in Vienna than to adapt to their German dialect.

Sports-analogies are another example that is typically very language-dependent. I know by now what “pitching an idea” means, but not because I know pitching from a sports context, but because I have heard that phrase used often enough so it stuck. Same for this teaching assistant who helped with my class who I overheard shouting “mud pit!” when he wanted students to remember something about molecular diffusion (or heat?) – the picture I made up in my head is that of players huddling together in a muddy playing field, but I still don’t know what exactly he was referring to (and I’m sure neither do half of the students of that class).

Now, I am not saying that native speakers of any language are necessarily unaware of those peculiarities. But what I am saying is this: If you are a native speaker, and you are communicating with non-native speakers, try to be aware of how you are communicating your ideas, and be sensitive to whether you are understood. And listen carefully to what your students are saying and don’t just assume that non-native speakers can’t possibly have anything interesting to say. And if you are the teacher who taught the class before I taught the class with the student mentioned above, and you told them that their English was not good enough because they didn’t speak (note: not because they didn’t understand, but because they didn’t speak!) your dialect: Learn their language, or any kind of foreign-to-you language, and then we can talk again.

And on this slightly rant-y note, I’ll leave you for now. I will be back in the new year on Mondays, Wednesdays and Fridays. I have tons of ideas for more posts (you have no idea how many experiments my family will have to endure over the next couple of days! And I have about 30 hands-on experiment posts in various draft stages written already), and if you end up desperately waiting for new content here, how about you try some of my (or other) experiments and let me know how it went? Have fun playing!

## Oceanographic concepts and language (part 2)

How to make lectures in a foreign language less scary for the students.

The class that I have until recently taught in Bergen, GEOF130, is taken by students in oceanography and meteorology in the second year of their Bachelor at the university. It is the first course they take at the Geophysical Institute – their first year is spent entirely at other institutes. The Bachelor is taught in Norwegian – with the exception of GEOF130. This course is taught in English, because it also serves the Nordic Master, which is taught in English, and that brings in many students who don’t speak Norwegian.

While I am glad the course had to be held in Norwegian (I would definitely not have had the time to prepare 4 hours of lectures per week for a whole semester in Norwegian!), many of the students were not happy. They typically understand everything you say just fine, but there is a huge barrier when it comes to speaking in front of their peers in a foreign language.

The easiest way to cope with the shyness I found is to speak to them in my less-than-perfect Norwegian. Seeing the teacher make funny mistakes in a foreign language makes it a lot easier for them to dare making mistakes in another foreign language.

Yet students often choose to write the exam in Norwegian (and yes – I have to pose the questions in English, Nynorsk and Bokmål!). Which often leads to problems, since all of the lectures and all of the reading materials were in English, so the students don’t actually know any of the technical terms in Norwegian and often end up inventing them or, worse, mixing them up with similar sounding but not otherwise related Norwegian terms.

So the next thing to do is to always try and be aware of which terms they are likely to know and which are technical terms. This is not always easy and depends a lot on what their native language is (see this post). One thing I did early on when I started teaching was to create a small dictionary of oceanographic terms in English, Norwegian and German. Anyone out there who wants to help edit that dictionary? And everybody, please feel free to share if you think this might be useful to someone else!

## Student cruises (part 5 of many, or – thank you to a great mentor)

The first student cruise I ever taught while being taught by one of the greatest teachers myself.

As you might have noticed from the last four or so blog posts, I really enjoy teaching student cruises and I think they are a super important part of the oceanography education.

So let me tell you about the first student cruise I taught. I was lucky enough to co-teach it with one of the most experienced and knowledgeable oceanographers out there, who was excited about sharing with me all there is to know about cruise planning, cruise leading, teaching at sea and many other topics.

From the first day of the first cruise onward, my ideas and contributions were welcomed, and I got to heavily influence the scientific program of the cruise. On the second day of the first cruise, I was told to just walk up to the captain and tell him if I wanted to change the course and go measure somewhere else than planned.

The cruise ended up being great learning experiences for me. For the first time, I got to decide how to allocate ship time to best investigate the question that I thought was most interesting, a topic that I had never had (the chance) to deal with previously.

At the same time, I had the opportunity to learn from – and work with – the best. One of the practical highlights: A mooring release had not been working reliably in the past, but it was the one that we had with us on this cruise. So what to do?

Easy! Just tie a rope from the mooring to a tree! (Ok, so maybe this isn’t generally helpful, but if you are in Lokksund, this is genius)

And then I got to spend a lot of my time on watch (and a lot of my time off watch) discussing what we were seeing in the new data, what we could learn from that, where we should go next to prove or disprove our new theories.

And I got to watch a great teacher interact with his students (other than me). I saw how he challenged, how he encouraged, how he helped, how he guided, how he inspired.

Thank you so much, Tor, for being the role model you are and for having given me all of this, which I have since been striving to give to my own students.

All photos in this post were taken by Angus Munro (thanks!) on the 2012 GEOF332 student cruise.

## Student cruises (part 4 of many – weird profiles)

When a CTD profile suddenly looks really weird.

As mentioned before, student cruises seem to bring out the weird experiences with CTDs. My theory is that it’s the world testing us. It would be bad enough to deal with this stuff if we were on CTD watch in the middle of the night on our own, but dealing with it in front of a group of eager students, all asking questions when you just want to think, is the ultimate test of whether you know your stuff and have the nerves to deal with anything.

So, of course, this year’s GEOF130 student cruise couldn’t be an exception. After dealing with an unfortunate encounter of the CTD and the bottom about which we shall not say any more than this, the next profile looked like this:

Not seeing it yet? Let me zoom in for you:

A really weird offset between downcast and upcast occurred in density and salinity, persisted for about 100m, ended with a huge spike and then disappeared.

So what happened? I have actually no idea. I’ve seen jellyfish being sucked into the pump, resulting in fresh spikes. And that salinity and density react very similarly even for anomalies is not that surprising, seeing that one is calculated from the other. But why would the shape of the profile stay the same, only shifted towards fresher values and lower densities? Ideas, anyone?

## Student cruise (part 3 of many, or – when the CTD didn’t start up)

When a CTD just doesn’t start pumping.

In this post, I talked about how student cruises always happen to be on the perfect days, and then in this post I talked about how to read CTD profiles. So now knowing all of this, here is a confession: I have never seen so much weird stuff happen to the CTD as on student cruises!

Last year, I took my students of the GEOF130 course out. We had two groups on a one-day cruise each, on FS G. O. Sars, the new-ish and fancy Bergen-based research ship.

Of course, as any real cruise, we started with a safety briefing with the officers.

But listening to the rules wasn’t enough, students had to also try on the survival suits.

But then at some point, we started doing science.

Since I already talked about what the CTD operator typically sees on the screen, I’m only showing you the ones you haven’t seen yet. Did I mention that the G.O. Sars is a pretty fancy ship? And this doesn’t even show the met data or fish finder, which were on yet another cluster of screens.

Finally, we were on station and ready to deploy the CTD.

But then, when the CTD was finally in the water, we waited. And waited. And waited. And nothing happened! We waited some more, but the pump on the CTD just didn’t switch on. We lowered the CTD. And lowered it some more. And waited. And then, when we were almost ready to bring it back up on deck, we brought it even deeper and it started up! When we got the first readings, we realized what had been the problem. The CTD pumps are set to switch off when salinities fall below a certain value. This is done to make sure the pump switches off when the CTD isn’t in the water any more to avoid having the pump run dry. And since we were in a fjord (where we typically have a fresh layer on top, see this experiment) on a calm day after a very calm week, clearly, the salt stratification had become so strong that we couldn’t even measure the top layer because our CTD didn’t recognize it was in the sea! I’ve never seen this happen before.

But then finally we brought the CTD back up on deck and students could start to practice sampling.

We were incredibly lucky with the weather, and since we had Sindre Skrede visit us, we can even document it with beautiful pictures!

The end! :-)

## Student cruising

Why student cruises always end up being on the most beautiful days of the year, or: why student cruises are an important part of the education.

Remember the picture I showed in the last post, that was worthy of being on an Advent calendar or postcard? The one below?

That was taken on this year’s GEOF130 student cruise.

And remember the ice-on-Hardangerfjorden picture I shared a while back? This one?

Oh, taken on this year’s GEOF332 student cruise.

And the student cruise before, GEOF130 in 2012, looked like this:

See a pattern here?

So how come we always end up being out on the perfect day? Well, firstly, clearly I am that good. Or that lucky. But then, the perfect day only becomes the perfect day when you give it the chance.

What I mean is that on student cruises, it is easy for a day to become perfect. Because it is exciting to be on a research ship for the first time, to figure out how to measure oceanographic data, to develop a feeling for how much the ship is actually supposed to be rolling before you have any reason to become concerned, to see how your oceanography classes apply to the real world, to put on an orange one-fits-all survival suit, to gauge how you can influence the quality of the data by paying attention (or not), to get a break from your everyday life, to eat all the awesome food all the time, to visit the captain on the bridge, to see the familiar city from the water, to see a whole new world opening up to you, to experience what it could be like to be an oceanographer.

Especially in the “introduction to oceanography” lecture GEOF130, the student cruise is so much more than just knowledge transfer – it is an incredibly important part of building a professional identity that helps students to find motivation to sit through boring lectures and to fight through difficult exams because in the end they will then get to do this again: to go an another cruise and have more perfect days at sea.

## Oceanographic concepts and language (part 1)

About teaching in a language that is a foreign language for both your students and yourself.

Most of my teaching so far has happened in English to mainly non-native English speakers with the occasional native speaker thrown in. One thing that I realized recently was that concepts that are definitely not common knowledge at home in Germany and that are described by technical terms in German, are absolute household terms in other language.

Let’s for example think about density.

In German, or Norwegian for that matter, “Dichte” or “tetthet” is not a concept that is used in everyday language very much, and that therefore needs to be explained in introductions to oceanography, and that typically is rather difficult to understand for the students. I usually introduce density both by talking about mass per volume, and then by showing experiments to visualize what differences in density can look like, for example by showing that soda cans with the exact same volume can still sink or swim depending on what’s inside.

In English however, people have an intuitive understanding of what density is – a measure of compactness. A densely populated area is an area where many people live close together. If a lecture is very dense, there is a lot of content for the amount of time you attend. A low-density floppy disk will not be able to contain as much information as a high-density one. So having this background, not a lot of transfer is needed to be able to talk about the density of water.

I am usually pretty aware that I am teaching in a language that is foreign to both the students and to me, and I try to compensate for that by explaining what I perceive as technical terms. But recently I had a native English speaker in one of my classes, and that person got really upset because I spent so much time on what that person thought was trivial. So I guess language awareness needs to go both ways – not only being aware of what kind of vocabulary students of certain nationalities probably won’t be familiar with, but also being aware of the vocabulary that I learned as technical terms and that are not perceived as technical terms by students of other nationalities.

Dear readers, have you come across this? What other terms can you think of that we should be aware of?