Category Archives: hand-on activity (difficult)

Working on our own affordable rotating table for oceanographic experiments!

Inspired by the article “Affordable Rotating Fluid Demonstrations for Geoscience Education: the DIYnamics Project” by the Hill et al. (2018), Joke, Torge and I have been wanting to build an affordable rotating table for teaching for a while now. On Saturday, we met up again to work on the project.

This post is mainly to document for ourselves where we are at and what else needs to happen to get the experiments working.

New this time: New rotating tables, aka Lazy Susans. After the one I’ve had in my kitchen was slightly too off-center to run smoothly, we bought the ones recommended by the DIYnamics project. And they work a lot better! To center our tank on the rotating table and keep it safely in place, we used these nifty LEGO and LEGO Duplo contraptions, which worked perfectly.

We also used a LEGO contraption to get the wheel close enough to drive the rotating table. The yellow line below shows where the rim of the rotating table’s foot needs to sit.

And this is how the engine has to be placed to drive the rotating table.

First attempt: Yes! Very nice parabolic surface! Very cool to see time and time again!

Now first attempt at a Hadley cell experiment: A jar with blue ice is placed at the center of the tank. Difficulties here: Cooling sets in right away, before the rotating tank has reached solid body rotation. That might potentially mess up everything (we don’t know).

So. Next attempt: Use a jar (weighted down with stones so it doesn’t float up) until the tank has reached solid body rotation, then add blue ice water

Working better, even though the green dye is completely invisible…

We didn’t measure rotation, nor did we calculate what kind of regime we were expecting, so the best result we got was “The Heart” (see below) — possibly eddying regime with wavenumber 3?

Here is what we learned for next time:

  • use better dye tracers and make sure their density isn’t too far off the water in the tank
  • use white  LEGO bricks to hold the tank in place (so they don’t make you dizzy watching the tank)
  • measure the rotation rate and calculate what kind of regime we expect to see — overturning or eddying, and at which wave number (or, even better, the other way round: decide what we want to see and calculate how to set the parameters in order to see it)
  • use white cylinder in the middle so as to not distract from the circulation we want to see; weigh the cylinder down empty and fill it with ice water when the tank has reached solid body rotation
  • give the circulation a little more time to develop between adding the cold water at the center and putting in dyes (at least 10 minutes)
  • it might actually be worth reading the DIYnamics team’s instruction again, and to buy exactly what they recommend. That might save us a lot of time ;-)

But: As always this was fun! :-)

P.S.: Even though this is happening in a kitchen, I don’t think this deserves the hashtag #kitchenoceanography — the equipment we are using here is already too specialized to be available in “most” kitchens. Or what would you say?

Supporting conceptual understanding of the Coriolis force through laboratory experiments

My friend Pierré and I started working on this article when both of us were still working at the Geophysical Institute in Bergen. It took forever to get published, mainly because both of us had moved on to different jobs with other foci, so maybe it’s not a big deal that it took me over a year to blog it? Anyway, I still think it is very important to introduce any kind of rotating experiments by first making sure people don’t harbour misconceptions about the Coriolis effect, and this is the best way we came up with to do so. But I am happy to hear any suggestions you might have on how to improve it :-)

Supporting Conceptual Understanding of the Coriolis Force Through Laboratory Experiments

By Dr. Mirjam S. Glessmer and Pierré D. de Wet

Published in Current: The Journal of Marine Education, Volume 31, No 2, Winter 2018

Do intriguing phenomena sometimes capture your attention to the extent that you haveto figure out why they work differently than you expected? What if you could get your students hooked on your topic in a similar way?

Wanting to comprehend a central phenomenon is how learning works best, whether you are a student in a laboratory course or a researcher going through the scientific process. However, this is not how introductory classes are commonly taught. At university, explanations are often presented or developed quickly with a focus on mathematical derivations and manipulations of equations. Room is seldom given to move from isolated knowledge to understanding where this knowledge fits in the bigger picture formed of prior knowledge and experiences. Therefore, after attending lectures and even laboratories, students are frequently able to give standard explanations and manipulate equations to solve problems, but lack conceptual understanding (Kirschner & Meester, 1988): Students might be able to answer questions on the laws of reflection, yet not understand how a mirror works, i.e. why it swaps left-right but not upside-down (Bertamini et al., 2003).

Laboratory courses are well suited to address and mitigate this disconnect between theoretical knowledge and practical application. However, to meet this goal, they need to be designed to focus specifically on conceptual understanding rather than other, equally important, learning outcomes, like scientific observation as a skill or arguing from evidence (NGSS, 2013), calculations of error propagations, application of specific techniques, or verifying existing knowledge, i.e. illustrating the lecture (Kirschner & Meester, 1988).

Based on experience and empirical evidence, students have difficulties with the concept of frames of reference, and especially with fictitious forces that are the result of using a different frame of reference. We here present how a standard experiment on the Coriolis force can support conceptual understanding, and discuss the function of employing individual design elements to maximize conceptual understanding.

HOW STUDENTS LEARN FROM LABORATORY EXPERIMENTS

In introductory-level college courses in most STEM disciplines, especially in physics-based ones like oceanography or meteorology and all marine sciences, laboratory courses featuring demonstrations and hands-on experiments are traditionally part of the curriculum.

Laboratory courses can serve many different and valuable learning outcomes: learning about the scientific process or understanding the nature of science, practicing experimental skills like observation, communicating about scientific content and arguing from evidence, and changing attitudes (e.g. Feisel & Rosa, 2005; NGSS, 2013; Kirschner & Meester, 1988; White, 1996). One learning outcome is often desired, yet for many years it is known that it is seldomly achieved: increasing conceptual understanding (Kirschner & Meester, 1988, Milner-Bolotin et al., 2007). Under general dispute is whether students actually learn from watching demonstrations and conducting lab experiments, and how learning can be best supported (Kirschner & Meester, 1988; Hart et al., 2000).

There are many reasons why students fail to learn from demonstrations (Roth et al., 1997). For example, in many cases separating the signal to be observed from the inevitably measured noise can be difficult, and inference from other demonstrations might hinder interpretation of a specific experiment. Sometimes students even “remember” witnessing outcomes of experiments that were not there (Milner-Bolotin et al., 2007). Even if students’ and instructors’ observations were the same, this does not guarantee congruent conceptual understanding and conceptual dissimilarity may persist unless specifically addressed. However, helping students overcome deeply rooted notions is not simply a matter of telling them which mistakes to avoid. Often, students are unaware of the discrepancy between the instructors’ words and their own thoughts, and hear statements by the instructor as confirmation of their own thoughts, even though they might in fact be conflicting (Milner-Bolotin et al., 2007).

Prior knowledge can sometimes stand in the way of understanding new scientific information when the framework in which the prior knowledge is organized does not seem to organically integrate the new knowledge (Vosniadou, 2013).The goal is, however, to integrate new knowledge with pre-existing conceptions, not build parallel structures that are activated in context of this class but dormant or inaccessible otherwise. Instruction is more successful when in addition to having students observe an experiment, they are also asked to predict the outcome before the experiment, and discuss their observations afterwards (Crouch et al., 2004). Similarly, Muller et al. (2007) find that even learning from watching science videos is improved if those videos present and discuss common misconceptions, rather than just presenting the material textbook-style. Dissatisfaction with existing conceptions and the awareness of a lack of an answer to a posed question are necessary for students to make major changes in their concepts (Kornell, 2009, Piaget, 1985; Posner et al., 1982). When instruction does not provide explanations that answer students’ problems of understanding the scientific point of view from the students’ perspective, it can lead to fragmentation and the formation of synthetic models (Vosniadou, 2013).

One operationalization of a teaching approach to support conceptual change is the elicit-confront-resolve approach (McDermott, 1991), which consists of three steps: Eliciting a lingering misconception by asking students to predict an experiment’s outcome and to explain their reasons for the prediction, confronting students with an unexpected observation which is conflicting with their prediction, and finally resolving the matter by having students come to a correct explanation of their observation.

HOW STUDENTS TRADITIONALLY LEARN ABOUT THE CORIOLIS FORCE

The Coriolis force is essential in explaining formation and behavior of ocean currents and weather systems we observe on Earth. It thus forms an important part of any instruction on oceanography, meteorology or climate sciences. When describing objects moving on the rotating Earth, the most commonly used frame of reference would be fixed on the Earth, so that the motion of the object is described relative to the rotating Earth. The moving object seems to be under the influence of a deflecting force – the Coriolis force – when viewed from the co-rotating reference frame. Even though the movement of an object is independent of the frame of reference (the set of coordinate axes relative to which the position and movement of an object is described is arbitrary and usually made such as to simplify the descriptive equations of the object), this is not immediately apparent.

Temporal and spatial frames of reference have been described as thresholds to student understanding (Baillie et al., 2012, James, 1966; Steinberg et al., 1990). Ever since its first mathematical description in 1835 (Coriolis, 1835), this concept is most often taught as a matter of coordinate transformation, rather than focusing on its physical relevance (Persson, 1998). Most contemporary introductory books on oceanography present the Coriolis force in that form (cf. e.g. Cushman-Roisin, 1994; Gill, 1982; Pinet, 2009; Pond and Pickard, 1983; Talley et al., 2001; Tomczak and Godfrey, 2003; Trujillo and Thurman, 2013). The Coriolis force is therefore often perceived as “a ‘mysterious’ force resulting from a series of ‘formal manipulations’” (Persson, 2010). Its unintuitive and seemingly un-physical character makes it difficult to integrate into existing knowledge and understanding, and “even for those with considerable sophistication in physical concepts, one’s first introduction to the consequences of the Coriolis force often produces something analogous to intellectual trauma” (Knauss, 1978).

In many courses, helping students gain a deeper understanding of rotating systems and especially the Coriolis force, is approached by presenting demonstrations, typically of a ball being thrown on a merry-go-round, showing the movement simultaneously from a rotating and a non-rotating frame (Urbano & Houghton, 2006), either in the form of movies or simulations, or in the lab as demonstration, or as a hands-on experiment[i]. After conventional instruction that exposed students to discussions and simulations, students are able to do calculations related to the Coriolis force.

Nevertheless, when confronted with a real-life situation where they themselves are not part of the rotating system, students show difficulty in anticipating the movement of an object on a rotating body. In a traditional Coriolis experiment (Figure1), for example, a student launches a marble from a ramp on a rotating table (Figure 2A, B) and the motion of the marble is observed 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. When asked, before that experiment, what path the marble on the rotating surface will take, students report that they anticipate observing a deflection, its radius depending on the rotation’s direction and rate. After having observed the experiment, students report that they saw what they expected to see even though it never happened. Contextually triggered, knowledge elements are invalidly applied to seemingly similar circumstances and lead to incorrect conclusions (DiSessa & Sherin, 1988; Newcomer, 2010). This synthetic model of always expecting to see a deflection of an object moving on a rotating body, no matter which system of reference it is observed from, needs to be modified for students to productively work with the concept of the Coriolis force.

Figure 1: Details of the Coriolis experiment

Figure 1: Details of the Coriolis experiment

Despite these difficulties in interpreting the observations and understanding the underlying concepts, rotating tables recently experienced a rise in popularity in undergraduate oceanography instruction (Mackin et al., 2012) as well as outreach to illustrate features of the oceanic and atmospheric circulation(see for example Marshall and Plumb, 2007). This makes it even more important to consider what students are intended to learn from such demonstrations or experiments, and how these learning outcomes can be achieved.

Figure 2A: View of the rotating table including the video camera on the scaffolding above the table. B: Sketch of the rotating table, the mounted (co-rotating) camera, and the marble on the table. C: Student tracing the curved trajectory of the marble on a transparency. On the screen, the experiment is shown as captured by the co-rotating camera, hence in the rotating frame of reference. 

Figure 2A: View of the rotating table including the video camera on the scaffolding above the table. B: Sketch of the rotating table, the mounted (co-rotating) camera, and the marble on the table. C: Student tracing the curved trajectory of the marble on a transparency. On the screen, the experiment is shown as captured by the co-rotating camera, hence in the rotating frame of reference.

A RE-DESIGNED HANDS-ON INTRODUCTION TO THE CORIOLIS FORCE

The traditional Coriolis experiment, featuring a body on a rotating table[ii], observed both from within and from outside the rotating system, can be easily modified to support conceptual understanding.

When students of oceanography are asked to do a “dry” experiment (in contrast to a “wet” one with water in a tank on the rotating table) on the Coriolis force, at first, this does not seem like a particularly interesting phenomenon to students because they believe they know all about it from the lecture already. The experiment quickly becomes intriguing when a cognitive dissonance arises and students’ expectations do not match their observations. We use an elicit-confront-resolve approach to help students observe and understand the seemingly conflicting observations made from inside versus outside of the rotating system (Figure 3). To aid in making sense of their observations in a way that leads to conceptual understanding the three steps elicit, confront, and resolve are described in detail below.

Figure 3: Positions of the ramp and the marble as observed from above in the non-rotating (top) and rotating (bottom) case. Time progresses from left to right. In the top plots, the positions are shown in inert space. From left to right, the current positions of the ramp and marble are added with gradually darkening colors. In the bottom plots, the ramp stays in the same position relative to the co-rotating observer, but the marble moves and the current position is always displayed with the darkest color.

Figure 3: Positions of the ramp and the marble as observed from above in the non-rotating (top) and rotating (bottom) case. Time progresses from left to right. In the top plots, the positions are shown in inert space. From left to right, the current positions of the ramp and marble are added with gradually darkening colors. In the bottom plots, the ramp stays in the same position relative to the co-rotating observer, but the marble moves and the current position is always displayed with the darkest color.

2. What do you think will happen? Eliciting a (possibly) lingering misconception

Students have been taught in introductory lectures that any moving object in a counter-clockwise rotating system (i.e. in the Northern Hemisphere) 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. In our experience, due to this prior schooling, students expect to see a Coriolis deflection even when they observe a rotating system “from the outside”. When the conventional experiment is run without going through the additional steps described here, students often report having observed the (non-existent) deflection.

By activating this prior knowledge and discussing what students anticipate observing under different conditions before the actual experiment is conducted, the students’ insights are put to the test. This step is important since the goal is to integrate new knowledge with pre-existing conceptions, not build parallel structures that are activated in context of this class but dormant or inaccessible otherwise. Sketching different scenarios (Fan, 2015; Ainsworth et al., 2011) and trying to answer questions before observing experiments support the learning process since students are usually unaware of their premises and assumptions (Crouch et al., 2004). Those need to be explicated and documented (even just by saying them out loud) before they can be tested, and either be built on, or, if necessary, overcome. 

We therefore ask students to observe and describe the path of a marble being radially launched from the perimeter of the circular, non-rotating table by a student standing at a marked position next to the table, the “launch position”. The marble is observed rolling 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 marble dropped off the table’s edge so as to catch the marble in the non-rotating case. The position is also marked on the floor with tape to document the observation.

Next, the experimental conditions of this thought experiment (Winter, 2015) are varied to reflect on how the result depends on them. The students are asked to predict the behavior of the marble 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 marble 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 marble, will also be able to catch it themselves. Usually the students confirm that such a situation is indeed possible.

2. Did you observe what you expected to see? Confronting the misconception

After “eliciting” student conceptions, the “confront” step serves to show the students the discrepancy between what they expect to see, and what they actually observe. Starting with the simple, non-rotating case, the marble is launched again and the nominated catcher, positioned diametrically across from the launch position, seizes the marble as it falls off the table’s surface right in front of them. As theoretically discussed beforehand, the table is then put into rotation at incrementally increasing rates, with the marble being launched from the same position for each of the different rotational speeds.  It becomes clear that the catcher can – without any adjustments to their position – remain standing diametrically opposite to the student launching the marble – the point where the marble drops to the floor. Hence students realize that the movement of the marble 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; segments of circles with decreasing radii as the rotation rate increases. Furthermore, to add to the confusion, when observed from their positions around the rotating table, the path of the marble 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. marks on the table’s surface or the bars of the camera scaffold, relative to which the marble does, indeed, follow a curved trajectory. To overcome this optical illusion, 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 marble is observed to indeed be moving in a straight line towards the observer, irrespective of the rotation rate of the table. Observing from different perspectives and with focus on different aspects (Is the marble coming directly towards me? Does it fall on the same spot as before? Did I need to alter my position in the room at all?) helps students gain confidence in their observations.

To solidify the concept, the table may again be set into rotation. The launcher and the catcher are now asked to pass the marble to one another by throwing it across the table without it physically making contact with the table’s surface. As expected, the marble moves in a straight line between the launcher and the catcher, whom 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[iii].

3. Do you understand what is going on? Resolving the misconception

Misconceptions that were brought to light during the “elicit” step, and whose discrepancy with observations was made clear during the “confront” step, are finally resolved in this step. While this sounds very easy, in practice it is anything but. For learning to take place, the instructor needs to aid students in reflecting upon and reassessing previous knowledge by pointing out and dispelling 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 does not happen instantaneously. Oftentimes further, detailed discussion is required. Frequently students have to re-run the experiment themselves in different roles (i.e. as launcheras well as catcher) and explicitly state what they are noticing before they trust their observations.

For this experiment to benefit the learning outcomes of the course, which go beyond understanding of a marble on a rotating table and deal with ocean and atmosphere dynamics, knowledge needs to be integrated into previous knowledge structures and transferred to other situations. This could happen by discussion of questions like, for example: How could the experiment be modified such that a straight trajectory is observed on the screen? What would we expect to observe if we added a round tank filled with water and paper bits floating on it to the table and started rotating it? How are our observations of these systems relevant and transferable to the real world? What are the boundaries of the experiment?

IS IT WORTH THE EXTRA EFFORT? DISCUSSION

We taught an undergraduate laboratory course which included this experiment for several years. In the first year, we realized that the conventional approach was not effective. In the second year, we tried different instructional approaches and settled on the one presented here. We administered identical work sheets before and after the experiment. These work sheets were developed as instructional materials to ensure that every student individually went through the elicit-confront-resolve process. Answers on those worksheets show that all our students did indeed expect to see a deflection despite observing from an inert frame of reference: Students were instructed to consider both a stationary table and a table rotating at two different rates.  They were then asked to, for each of the scenarios, mark with an X the location where they thought the marble would contact the floor after dropping off the table’s surface.  Before instruction, all students predicted that the marble would hit the floor in different spots – diametrically across from the launch point for no rotation, and at increasing distances from that first point with increasing rotation rates of the table (Figure 4). This is the exact misconception we aimed to elicit with this question: students were applying correct knowledge (“in the Northern Hemisphere a moving body will be deflected to the right”) to situations where this knowledge was not applicable: when observing the rotating body and the moving object upon it from an inert frame of reference.

Figure 4A: Depiction of the typical wrong answer to the question: Where would a marble land on the floor after rolling across a table rotating at different rotation rates? B: Correct answer to the same question. C: Correct traces of marbles rolling across a rotating table.

Figure 4A: Depiction of the typical wrong answer to the question: Where would a marble land on the floor after rolling across a table rotating at different rotation rates? B: Correct answer to the same question. C: Correct traces of marbles rolling across a rotating table.

In a second question, students were asked to imagine the marble leaving a dye mark on the table as it rolls across it, and to draw these traces left on the table. In this second question, students were thus required to infer that this would be analogous to regarding the motion of the marble as observed from the co-rotating frame of reference. Drawing this trajectory correctly before the experiment is run does not imply a correct conceptual understanding, since the transfer between rotating and non-rotating frames of references is not happening yet and students draw curved trajectories for all cases. However, after the experiment this question is useful especially in combination with the first one, as it requires a different answer than the first, and an answer that students just learned they should not default to.

The students’ laboratory reports supply additional support of the usefulness of this new approach.  These reports had to be submitted a week after doing the experiment and accompanying work sheets, which were collected by the instructors.  One of the prompts in the lab report explicitly addresses observing the motion from an inert frame of reference as well as the influence of the table’s rotational period on such motion. This question was answered correctly by all students. This is remarkable for three reasons: firstly, because in the previous year with conventional instruction, this question was answered incorrectly by the vast majority of students; secondly, from our experience, lab reports have a tendency to be eerily similar year after year which did not hold true for tis specific question; and lastly, because for this cohort, it is one of very few questions that all students answered correctly in their lab reports, which included seven experiments in addition to the Coriolis experiment. These observations lead us to believe that students do indeed harbor the misconception we suspected, and that the modified instructional approach has supported conceptual change.

CONCLUSIONS

We present modifications to a “very simple” experiment and suggest running it before subjecting students to more advanced experiments that illustrate concepts like Taylor columns or weather systems. These more complex processes and experiments cannot be fully understood without first understanding the Coriolis force acting on the arguably simplest bodies. Supplying correct answers to standard questions alone, e.g. “deflection to the right on the northern hemisphere”, is not sufficient proof of understanding.

In the suggested instructional strategy, students are required to explicitly state their expectations about what the outcome of an experiment will be, even though their presuppositions are likely to be wrong. The verbalizing of their assumptions aids in making them aware of what they implicitly hold to be true. This is a prerequisite for further discussion and enables confrontation and resolution of potential misconceptions. Wesuggest using an elicit-confront-resolve approach even when the demonstration is not run on an actual rotating table, but virtually conducted instead, for example using Urbano & Houghton (2006)’s Coriolis force simulation. We claim that the approach is nevertheless beneficial to increasing conceptual understanding.

We would like to point out that gaining insight from any seemingly simple experiment, such as the one discussed in this article, might not be nearly as straightforward or obvious for the students as anticipated by the instructor. Using an intriguing phenomenon to be investigated experimentally, and slightly changing conditions to understand their influence on the result, is highly beneficial. Probing for conceptual understanding in new contexts, rather than the ability to calculate a correct answer, proved critical in understanding where the difficulties stemmed from, and only a detailed discussion with several students could reveal the scope of difficulties.

ACKNOWLEDGEMENTS

The authors are grateful for the students’ consent to be featured in this article’s figures.

 

RESOURCES

Movies of the experiment can be seen here:

Rotating case: https://vimeo.com/59891323

Non-rotating case: https://vimeo.com/59891020

Using an old disk player and a ruler in absence of a co-rotating camera: https://vimeo.com/104169112

 

REFERENCES

Ainsworth, S., Prain, V., & Tytler, R. 2011. Drawing to Learn in Science Science, 333(6046), 1096-1097 DOI: 10.1126/science.1204153

Baillie, C., MacNish, C., Tavner, A., Trevelyan, J., Royle, G., Hesterman, D., Leggoe, J., Guzzomi, A., Oldham, C., Hardin, M., Henry, J., Scott, N., and Doherty, J.2012. Engineering Thresholds: an approach to curriculum renewal. Integrated Engineering Foundation Threshold Concept Inventory 2012. The University of Western Australia, <http://www.ecm.uwa.edu.au/__data/assets/pdf_file/0018/2161107/Foundation-Engineering-Threshold-Concept-Inventory-120807.pdf>

Bertamini, M., Spooner, A., & Hecht, H. (2003). Naïve optics: Predicting and perceiving reflections in mirrors. JOURNAL OF EXPERIMENTAL PSYCHOLOGY HUMAN PERCEPTION AND PERFORMANCE29(5), 982-1002.

Coriolis, G. G. 1835. Sur les équations du mouvement relatif des systèmes de corps. J. de l’Ecole royale polytechnique15: 144–154.

Crouch, C. H., Fagen, A. P., Callan, J. P., and Mazur. E. 2004. Classroom Demonstrations: Learning Tools Or Entertainment?. American Journal of Physics, Volume 72, Issue 6, 835-838.

Cushman-Roisin, B. 1994. Introduction to Geophysical Fluid DynamicsPrentice-Hall. Englewood Cliffs, NJ, 7632.

diSessa, A.A. and Sherin, B.L., 1998. What changes in conceptual change?. International journal of science education20(10), pp.1155-1191.

Durran, D. R. and Domonkos, S. K. 1996. An apparatus for demonstrating the inertial oscillation, BAMS, Vol 77, No 3

Fan, J. (2015). Drawing to learn: How producing graphical representations enhances scientific thinking. Translational Issues in Psychological Science, 1(2), 170-181 DOI: 10.1037/tps0000037

Gill, A. E. 1982. Atmosphere-ocean dynamics(Vol. 30). Academic Pr.

James, E.L., 1966. Acceleration= v2/r. Physics Education1(3), p.204.

Kornell, N., Jensen Hays, M., and Bjork, R.A. (2009), Unsuccessful Retrieval Attempts Enhance Subsequent Learning, Journal of Experimental Psychology: Learning, Memory, and Cognition 2009, Vol. 35, No. 4, 989–998

Hart, C., Mulhall, P., Berry, A., Loughran, J., and Gunstone, R. 2000.What is the purpose of this experiment? Or can students learn something from doing experiments?,Journal of Research in Science Teaching, 37(7), p 655–675

Kirschner, P.A. and Meester, M.A.M., 1988. The laboratory in higher science education: Problems, premises and objectives. Higher education17(1), pp.81-98.

Knauss, J. A. 1978. Introduction to physical oceanography. Englewood Cliffs, N.J: Prentice-Hall.

Mackin, K.J., Cook-Smith, N., Illari, L., Marshall, J., and Sadler, P. 2012. The Effectiveness of Rotating Tank Experiments in Teaching Undergraduate Courses in Atmospheres, Oceans, and Climate Sciences, Journal of Geoscience Education, 67–82

Marshall, J. and Plumb, R.A. 2007. Atmosphere, Ocean and Climate Dynamics, 1stEdition, Academic Press

McDermott, L. C. 1991. Millikan Lecture 1990: What we teach and what is learned – closing the gap, Am. J. Phys. 59 (4)

Milner-Bolotin, M., Kotlicki A., Rieger G. 2007. Can students learn from lecture demonstrations? The role and place of Interactive Lecture Experiments in large introductory science courses.The Journal of College Science Teaching, Jan-Feb, p.45-49.

Muller, D.A., Bewes, J., Sharma, M.D. and Reimann P. 2007.Saying the wrong thing: improving learning with multimedia by including misconceptions, Journal of Computer Assisted Learning (2008), 24, 144–155

Newcomer, J.L. 2010. Inconsistencies in Students’ Approaches to Solving Problems in Engineering Statics, 40th ASEE/IEEE Frontiers in Education Conference, October 27-30, 2010, Washington, DC

NGSS Lead States. 2013. Next generation science standards: For states, by states. National Academies Press.

Persson, A. 1998.How do we understand the Coriolis force?, BAMS, Vol 79, No 7

Persson, A. 2010.Mathematics versus common sense: the problem of how to communicate dynamic meteorology, Meteorol. Appl. 17: 236–242

Piaget, J. (1985). The equilibration of cognitive structure. Chicago: University of Chicago Press.

Pinet, P. R. 2009. Invitation to oceanography. Jones & Bartlett Learning.

Posner, G.J., Strike, K.A., Hewson, P.W. and Gertzog, W.A. 1982. Accommodation of a Scientific Conception: Toward a Theory of Conceptual Change. Science Education 66(2); 211-227

Pond, S. and G. L. Pickard 1983. Introductory dynamical oceanography. Gulf Professional Publishing.

Roth, W.-M., McRobbie, C.J., Lucas, K.B., and Boutonné, S. 1997. Why May Students Fail to Learn from Demonstrations? A Social Practice Perspective on Learning in Physics. Journal of Research in Science Teaching, 34(5), page 509–533

Steinberg, M.S., Brown, D.E. and Clement, J., 1990. Genius is not immune to persistent misconceptions: conceptual difficulties impeding Isaac Newton and contemporary physics students. International Journal of Science Education12(3), pp.265-273.

Talley, L. D., G. L. Pickard, W. J. Emery and J. H. Swift 2011. Descriptive physical oceanography: An introduction. Academic Press.

Tomczak, M., and Godfrey, J. S. 2003. Regional oceanography: an introduction. Daya Books.

Trujillo, A. P., and Thurman, H. V. 2013. Essentials of Oceanography, Prentice Hall; 11 edition (January 14, 2013)

Urbano, L.D., Houghton J.L., 2006. An interactive computer model for Coriolis demonstrations.Journal of Geoscience Education 54(1): 54-60

Vosniadou, S. (2013). Conceptual change in learning and instruction: The framework theory approach. International handbook of research on conceptual change2, 11-30.

White, R. T. 1996. The link between the laboratory and learning. International Journal of Science Education18(7), 761-774.

Winter, A., 2015. Gedankenexperimente zur Auseinandersetzung mit Theorie. In: Die Spannung steigern – Laborpraktika didaktisch gestalten.Schriften zur Didaktik in den IngenieurswissenschaftenNr. 3, M. S. Glessmer, S. Knutzen, P. Salden (Eds.), Hamburg

Endnotes

[i]While tremendously helpful in visualizing an otherwise abstract phenomenon, using a common rotating table introduces difficulties when comparing the observed motion to the motion on Earth. This is, among other factors, due to the table’s flat surface (Durran and Domonkos, 1996), the alignment of the (also fictitious) centrifugal force with the direction of movement of the marble (Persson, 2010), and the fact that a component of axial rotation is introduced to the moving object when launched. Hence, the Coriolis force is not isolated. Regardless of the drawbacks associated with the use of a (flat) rotating table to illustrate the Coriolis effect, we see value in using it to make the concept of fictitious forces more intuitive, and it is widely used to this effect.

[ii]Despite their popularity in geophysical fluid dynamics instruction at many 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, or found on playgrounds in form of merry-go-rounds. In many cases, setting the exact rotation rate is not as important as having a qualitative difference between “slow” and “fast” rotation, which is very easy to realize. In cases where a co-rotating camera is not available, by dipping the marble 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 instructional approach described in this manuscript is easily adapted to such a setup.

[iii]We initially considered starting the lab session by throwing the marble diametrically across the rotating table.  Students would then see on-screen the curved trajectory of a marble, which had never made physical contact with the table rotating beneath it, and which was clearly moving in a straight line from thrower to catcher, leading to the realization that it is the frame of reference that is to blame for the marble’s curved trajectory. However, the speed of a flying marble makes it very difficult to observe its curved path on the screen in real time. Replaying the footage in slow motion helps in this regard.  Yet, replacing direct observation with recording and playback seemingly hampers acceptance of the occurrence as “real”. We therefore decided to only use this method to further illustrate the concept, not as a first step.

 

Bios

Dr. Mirjam Sophia Glessmer, holds a Master of Higher Education and Ph.D. in physical oceanography. She works at the Leibniz Institute of Science and Mathematics Education in Kiel, Germany. Her research focus lies on informal learning and science communication in ocean and climate sciences.

Pierre de Wet is a Ph.D. student in Oceanography and Climatology at the University of Bergen, Norway, and holds a Master in Applied Mathematics from the University of Stellenbosch, South Africa. He is employed by Akvasafe AS, where he works with the analysis and modelling of physical environmental parameters used in the mooring analysis and accreditation of floating fish farms.

Tank demonstration of the circulation in a fjord

It has been a long time in the making, but finally we have a nice fjord circulation in our tank!

Pierre and I tried to improve it 6 years ago, Steffi, Ailin and I have been working on it for a couple of days last August, then finally this morning, Steffi and I tried again — and it worked beautifully right away!

We now have an experiment that shows how a fresh, yellow inflow (representing the freshwater input into fjords close to their heads by rivers) flows over a initially stagnant pool of salt water. As the freshwater plume flows out of the fjord, it entrains more and more salt water from below, thus thickening and setting up a return flow that brings in more salt water from the reservoir (representing the open ocean) on the right.

We drop dye crystals to visualize the surface current going out of the fjord and the return flow going in, and draw the profiles on the tank to be able to discuss them later.

Here is a movie of the whole thing:

But there is more to see!

When tipping the tank to empty it, a lot of turbulence was created at the sill (see movie below). While a fjord typically isn’t tipped very often, what we see here is basically what tides do on the sill (see the waves that keep going back and forth over the sill after the tank is initially lifted? Those are exactly like tides). This could purposefully integrated in teaching rather than only happen by accident, those waves could be created just by surface forcing rather than by tipping the tank. That’s a very nice demonstration to explain high mixing rates in the vicinity of steep topography!

And then there is also the issue of very low oxygen concentrations in some Norwegian fjords, and one proposed solution is to bring the river inflow deep down into the fjord. The idea is that the less dense river water will move up to the surface again, thereby creating mixing and oxygenating the stagnant deep water that, in some cases, hasn’t been renewed in many years.

We model this by putting the inflow (the hose) down into the tank and see the expected behaviour. What we also see: Since the water has a quite strong downward component as it enters the fjord, it stirs up a lot of old dye from the bottom. So possibly something to be aware of since there might be stuff dumped into fjords that you might not necessarily want to stir up…

And last, not least, a bonus picture: This is how we measure temperature at GFI. You would think it should be possible to find a smaller thermometer that isn’t an old reversing mercury one? But in any case, this worked very well, too :-)

Lee waves with an asymmetrical “mountain”

How will lee waves look differently if we are using the asymmetrical mountain instead of the symmetric one? And is symmetry actually important at all or are we just looking at different slopes downstream while the upstream slope doesn’t have an influence on the wave field?

After admitting I had only ever used the symmetrical mountain to generate lee waves in the long tank in the GFI basement, I had to try the asymmetrical one!

There are a couple of reasons why I had not done that before:

  • It’s longer (1.5 m instead of the 1 m of the other mountain), therefore the tank is, relatively speaking, shorter. And since being close to the ends of the tank leads to weird interferences, this limits the distance over which observations can be made
  • Since it’s asymmetrical, pulling one way or the other would likely show different wave fields, so you couldn’t just run it back and forth and have students observe the same thing several times in a row

But then it would be really interesting to see what the difference would be, right?

I tried two different stratifications.

Weak stratification, shallow water

Since I just wanted a quick idea of what this mountain would do, I used leftover water I had prepared for the moving mountain experiment. Since there wasn’t a lot left, I ended up with 11.5 cm fresh water, but only 4 cm salt water at approximately 20 psu (since I stretched the 35 psu a little).

What I noticed: A LOT more mixing than with the other mountain! Stratification is pretty much destroyed after the first run, usually we run back and forth a lot. This can be for several reasons:

  • The water is very shallow, meaning mixing is happening over the whole water column. It might not actually be more mixing than in the other case, but since it’s affecting the whole water column, it might just seem like more because no clearly visible stratification is left above and below the layer which is mixed by the mountain?
  • The left side of the mountain was bent up a little (as in 2 or 3 cm), meaning that especially on the way back it was flapping up and down on the upstream side, doing a lot of mixing that wasn’t due to the shape of the mountain, just of bits of it being loose.

And the shape of the “reservoir” that is being built up upstream of the mountain is different to what I have observed before: Running in either direction, the reservoir didn’t built up smoothly, but as a hump that was pushed in front of the mountain. Maybe because the internal wave speed in this case was very close to the speed of the mountain, something like 7cm/s, so the disturbance created by the mountain couldn’t propagate upstream. Is that an upstream hydraulic jump we are seeing there?!

What’s also cool: Lee waves are now not only happening as internal waves, but you see a very clear signature in surface waves! Usually all we see are surface convergences and divergences, adjusting the surface layer to the internal waves underneath. That we now see surface waves is, I am assuming, mainly due to the shallow water relative to the height of the obstacle.

Since I was not satisfied with this at all, I ran a second experiment:

Strong stratification, deep water

First, I tried to set up the same stratification as for this lee wave experiment with the symmetrical mountain because I thought that would be easiest to compare. But I aborted that after having moved the mountain just a little because it was mixing so much that there stratification was destroyed completely and nothing could be seen. I ended up putting more dense water in and ended up with 12 cm pink (35 psu) and 4 cm clear freshwater. And this is what this looked like:

You now see a wave train with wave lengths longer than in the symmetrical case. Probably due to the longer length of the obstacle (even thought the waves are still shorter than the obstacle)? Or what sets the wavelength?

This time, with a faster internal wave speed of around 10cm/s while the mountain is still pulled with 7cm/s, we don’t see the “hump” in the upstream reservoir — the signal can propagate faster than the mountain and thus smoothes out.

So that is what I think is going on here. While the first experiment mainly showed effects of the stratification compared to previous experiments, the second one might provide some insight on the different slopes of the mountain, although I am not sure in what way. Do you see something I didn’t observe? How would you expect the different slopes to influence the lee waves?

I am so glad I tried this and I’m looking forward to thinking about this more! :-) Any insights you’d care to share with me?

Instructions: Dead water demonstration in the GFI basement

This blog post is meant as guidelines if someone other than me might have to set up this demonstration at some point… Have fun! :-)

Setting up the stratification

If I am working fast and nothing goes wrong, this takes almost 2.5 hours. Make sure you have enough time to set this up! Filling the tank takes time and there is not much you can do to speed up the process once you’ve started…

  • Fill in what will end up being the top layer: 5 cm at 0 psu. For this, connect the tap to the bottom inlet in the left corner of the mountain with one of the hoses. When you are done, make sure to close the lock at the tank!
  • Move “mountain” over inflow to contain mixing to the volume underneath the mountain (better for your nerves, trust me)
  • Prepare the future bottom layers one by one (35 cm at 35 psu). We will need four full fillings of the 80l barrel (which doesn’t empty all the way because the tap is slightly elevated from the bottom, in case you were calculating ;-)), each with 2.8kg salt dissolved in it. To prepare that, connect the hose from the tap to the outlet of the barrel, put in the salt, put in the dye, use a paddle while you fill the barrel with water to stir. This way the salt will be pretty much dissolved by the time the barrel is full.
  • Note: Make sure the barrel is located high enough so that gravity will pull the water down in the tank from the barrel!
  • Note: When the barrel is filled, close the lock at the barrel before disconnecting the hose to reconnect it to the tank!
  • Fill in the bottom layers into the tank one by one. While one layer is slowly running into the tank, you have time to measure the salt for the next one.

Pulling the boat

Here is a sketch of the contraption that pulls the boat:

  • Put 4 or 5 gram in the little zip lock bag (called “weight” in the sketch above). This only works  when the ship
  • Set up bumper to stop the ship before weights reach the floor (too much slack on the line, line might come off pulleys)
  • Stern rope on one of the tank’s braces is set up so the line is stretched as far as it can safely go
  • Check that there are marks on the tank which help measuring the speed of the boat (6 marks over 3 meters work well)

Trouble shooting

  • If there is suddenly too much friction in the system, check: Did the pulley on the left edge of the tank fall down? Did the rope come off the pulleys (sometimes happens if there was too much slack in the system, e.g. if the bag has been lifted or the bumper is too far left)
  • If the boat is moving a lot faster in the beginning than in the end, even though waves haven’t caught up with it, and it bothers you, move the two fixtures that hold the line at the ceiling closer together. Ideally, they should be in the same place, but this didn’t work for us because of tangling lines. Compromise between “constant” force and being able to run the experiment at all…

Observations

Ask students to observe:

  • Speed of the boat (actually take the time for a set distance)
  • Development of the boat’s speed over time, especially when waves are catching up with it
  • Generation of internal waves. Is there one, are there many? What are their wavelengths and speeds?
  • Generation of surface waves and their size relative to the internal waves. Why?

Movies

Below are movies of a couple of experiments which you could use in teaching instead of running the experiment for real (if for some reason running the experiment is not possible. But I would totally 100% recommend doing the experiment!). For a fun video, watch the one above (the ones below are cut to only show the tank so might be a little boring less exciting ;-))

Experiment 1

Ship pulled with 5g in the bag

Experiment 2

Ship pulled with 4g in the bag (for a repeat, see experiment 4!)

Experiment 3

Ship pulled with 3g in the bag

Experiment 4

Ship pulled with 4g in the bag (again, because we like repeat experiments ;-))

Instructions: Lee wave demonstration in the GFI basement

This blog post is meant as guideline if someone other than me might have to set up this demonstration at some point… Have fun! :-)

Lee waves

Lee waves are the kind of waves that can be observed downwind of a mountain in the clouds, or downstream of an obstacle in a current as a series of undulations with crests parallel to the disturbance.

Why move the mountain?

Students sometimes find it hard to imagine that a moving mountain should be equivalent to flow across a ridge. It helps to discuss how it would be really difficult to set up a flow in a tank: A huge amount of water would need to be moved without too much turbulence. Instead, it’s a lot easier to imagine the water is moving by moving a mountain through the tank, so the water is moving relative to it if not relative to the lab.

Dimensions

The size of the tank is 60×1.5×5 dm, so it can hold a total of 450l of water.

The mountain we use is 10.5 cm high and 1 m long and it’s symmetric, so pulling it either way shows similar lee waves (which is why I’ve always used it). There is a second, asymmetrical mountain on the shelf that I have never used*.

Setting up the stratification

The stratification that we’ve found works well is 10 cm at 35 psu (here dyed pink) and 9 cm at 0 psu. This leads to an internal wave speed of approximately ~11cm/s.

Prepare the dense water in a barrel that sits high enough so gravity will bring the water down into the tank (see picture below). For the 80l barrel, you need 2.8kg of salt and 1/3 tea spoon of dye MAX.

Elin's GEOF213 class observing lee waves

Elin’s GEOF213 class observing lee waves

You achieve the stratification by filling in the fresh water first through the bottom left inlet, moving the mountain over it, and filling in the dense water. That way the mixing is contained to the volume underneath the mountain which will be a lot better for your nerves (believe me!).

Moving the mountain

The system that pulls the mountain can go at two speeds: “fast” and “slow”, “slow” meaning 5m in 1:11min (7cm/s) and “fast” meaning 5m in 0:36min (14cm/s).

Here is where you run the mountain from:

Troubleshooting if the mountain doesn’t move:

  • you might be trying to pull the mountain in the wrong direction (into the wall)
  • the mountain might not be located on the sledge well. There is a tongue on the sledge that needs to sit in the groove in the mountain
  • the mountain might not be sitting well in the tank so an edge digs into the side
  • the belt that pulls the tank might not be tight enough (always make sure the two weights at both ends of the tank are actually hanging down to put tension on the belt!)
  • the belt might have come off the axle that drives it (the white plastic above the left end of the tank)
Elin's GEOF213 class observing lee waves

Elin’s GEOF213 class observing lee waves

Observations

As you see in the pictures above (or the movie below), there is a lot to observe!

  • Lee waves (not one, but a whole train!)
  • Different flow regimes: supercritical shooting down the lee side of the mountain, then a hydraulic jump, and then a normal flow
  • The reservoir upstream of the mountain that builds up as the mountain is moving
  • Even after the mountain has stopped, you see waves travelling through the tank and being reflected at the ends
  • Turbulence!

Movie

Here is a movie of the lee wave experiment. Feel free to use it in teaching if you like! And let me know if you need the movie in a higher resolution, I am happy to share!

*Yes, this was true at the time of writing. But I am setting up that experiment as we speak. Write. Read. Whatever. Will post movies tomorrow!

Demonstration: Nansen’s “dead water” in a tank!

A ship that is continuously pulled with a constant force suddenly slows down, stops, and then continues sailing as if nothing ever happened? What’s going on there? We will investigate this in a tank! And in order to see what is going on, we have dyed some of the water pink. Can you spot what is going on?

The phenomenon of “dead water” is probably well known to anyone sailing on strong stratifications, i.e. in regions where there is a shallow fresh or brackish layer on top of a much saltier layer, e.g. the Baltic Sea, the Arctic or some fjords. It has been described as early as 1893 by Fridtjof Nansen, who wrote, sailing in the Arctic: “When caught in dead water Fram appeared to be held back, as if by some mysterious force, and she did not always answer the helm. In calm weather, with a light cargo, Fram was capable of 6 to 7 knots. When in dead water she was unable to make 1.5 knots. We made loops in our course, turned sometimes right around, tried all sorts of antics to get clear of it, but to very little purpose.” (cited in Walker,  J.M.; “Farthest North, Dead Water and the Ekman Spiral,” Weather, 46:158, 1991)

When observing the experiment, whether in the movie above or in the lab, the obvious focus is on the ship and the interface between the clear fresh water layer (the upper 5cm in the tank) and the pink salt water layer below. And yes, that’s where a large-amplitude internal wave develops and eats up all the energy that was going into propulsion before! Only when looking at the time lapse of the experiments later did I notice how much more was going on throughout the tank! Check it out here:

The setup for this experiment is discussed here and is based on the super helpful website by Mercier, Vasseur and Dauxois (2009). In the end, we ended up without the belt to reduce friction, and with slightly different layer depths than we had planned, but all in all it works really well!

Accidental double-diffusive mixing

When setting up the stratification for the Nansen “dead water” demo (that we’ll show later today, and until then I am not allowed to share any videos, sorry!), I went into a meeting after filling in layer 4 (the then lowest). When I came back, I wanted to fill in layer 5 as the new bottom layer. For this experiment we want the bottom four layers to have the same density (so we would actually only have one shallow top layer and then a deep layer below [but we can’t make enough salt water at a time for that layer, so I had to split it into four portions]), and I had mixed it as well as I could. But two things happened: a) my salinity was clearly a little fresher than the previous layer, and b) the water in the tank had warmed up and the new water I was adding with layer 5 was cold tap water. So I accidentally set up the stratification for salt fingering: warm and salty over cold and fresh! Can you spot the darker pink fingers reaching down into the slightly lighter pink water? How cool is this??? I am completely flashed. Salt fingering in a 6 meter long tank! :-D

 

The one where it would help to understand the theory better (but still: awesome tank experiment!)

The main reason why we went to all the trouble of setting up a quasi-continuous stratification to pull our mountain through instead of sticking to the 2 layer system we used before was that we were expecting to see a tilt of the axis of the propagating phase. We did some calculations of the Brunt-Väisälä frequency, that needs to be larger than the product of the length of the obstacle and the speed the obstacle is towed with (and it was, by almost two orders of magnitude!), but happy with that result, we didn’t bother to think through all the theory.

And what happened was what always happens when you just take an equation and stick the numbers in and then go with that: Unfortunately, you realize you should have thought it through more carefully.

Luckily, Thomas chose exactly that time to come pick me up for a coffee (which never happened because he got sucked into all the tank experiment excitement going on), and he suggested that having one mountain might not be enough and that we should go for three sines in a row.

Getting a new mountain underneath an existing stratification is not easy, so we decided to go for the inverse problem and just tow something on the surface rather than at the bottom. And just to be safe we went with almost four wavelengths… And look at what happens!

We are actually not quite sure if the tilting we observed was due to a slightly wobbly pulling of the — let’s use the technical term and go for “thingy”? — or because of us getting the experiment right this time, but in any case it does look really cool, doesn’t it? And I’ll think about the theory some more before doing this with students… ;-)

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
folie1

Figure 1A: View of the rotating table. Note the video camera on the scaffolding above the table and the red x (marking the catcher’s position) on the floor in front of the table, diametrically across from where, that very instant, the ball is launched on a ramp. B: Sketch of the rotating table, the mounted (co-rotating) camera, the ramp and the ball on the table. C: Student tracing the curved trajectory of the metal ball on a transparency. On the screen, the experiment is shown as filmed by the co-rotating camera, hence in the rotating frame of reference.

 

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.

Student task:

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.

folie2

Figure 2: Positions of the ramp and the ball as observed from above in the non-rotating (top) and rotating (bottom) case. Time progresses from left to right. In the top plots, the position in inert space is shown. From left to right, the current position of the ramp and ball are added with gradually darkening colors. In the bottom plots, the ramp stays in the same position, but the ball moves and the current position is always displayed with the darkest color.

  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.