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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

 

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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.

Need your help! “Wish list” for a student lab for tank experiments?

I’d love your input: If your student lab for GFD tank experiments had to downsize, but you had to present a “wish list” for a smaller replacement, what would be on that list? Below are my considerations, but I would be super grateful for any additional input or comments! :-)

Background and “boundary conditions”

The awesome towing tank that you have come to love (see picture above) will have to be removed to make room for a new cantina. It might get moved into a smaller room, or possibly replaced all together. Here are some external requirements, as far as I am aware of them:

  • the (new) tank should ideally be movable so the (small) room can be used multi-purpose
  • since the new room is fairly small, people would be happy if the new tank was also smaller than the old one
  • the rotating table is kept (and a second, smaller one, exists in the building)
  • There are other, smaller tanks that will be kept for other experiments, dimensions approximately 175x15x40cm and smaller
  • the whole proposal needs to be inexpensive enough so that the likelyhood that it will actually be approved is moderate to fair ;-)

Here are a couple of things I think need to be definitely considered.

Dimensions of the tank

If the tank was to be replaced by a smaller one, how small could the smaller one be?

The dimension of the new tank depend, of course, on the type of experiment that should be done in the tank. Experiments that I have run in the tank that is to be replaced and that in my opinion should definitely be made possible in the new location/tank include

  1. “Dead water”, where a ship creates internal waves on a density interface (instructions)
  2. Internal lee waves & hydraulic jumps, where a mountain is moved at the bottom of the tank (instructions)
  3. Surface imprints of internal waves (example)
  4. Surface waves (example)
  5. Intrusions (example)
  6. Waves in a density stratification (example)
  7. Surface waves running up on a slope (I haven’t blogged about that yet, movies waiting to be edited)

If we want to be able to continue running these experiments, here is why we should not sacrifice the dimensions of the tank.

Why we need the tank length

The first reason for keeping the length of the tank is that the “mountains” being towed to create the lee waves are already 1 and 1.5m long, respectively. This is a length that is “lost” for actual experiments, because obviously the mountain needs space inside the tank on either end (so in its start and end position). Additionally, when the mountain starts to move, it has to move for some distance before the flow starts displaying the features we want to present: Initially, there is no reservoir on the “upstream” side of the mountain and it only builds up over the first half meter or so.

The second reason for keeping the length of the tank are wave reflections once the ship or mountain comes close to the other side of the tank. Reflected surface waves running against the ship will set up additional drag that we don’t want when we are focussing on the interaction between the ship and the internal wave field. Reflected internal waves similarly mess things up in both experiments

The third reason for keeping the length of the tank is its purpose: as teaching tank. Even if one might get away with a slightly shorter tank for experiments when you just film and investigate the short stretch in the middle of the tank where there are no issues with either the push you gave the system when starting the experiment or the reflections when you get near the end, the whole purpose of the tank is to have students observe. This means that there needs to be a good amount of time where the phenomenon in question is actually present and observable, which, for the tank, means that it has to be as long as possible.

Why we need the tank width

In the experiments mentioned above, with exception of the “dead water” experiment, the tank represents a “slice” of the ocean. We are not interested in changes across the width of the tank, and therefore it does not need to be very wide. However, if there is water moving inside the tank, there will be friction with the side walls and the thinner the tank, the more important the influence of that friction will become. If you look for example at the surface imprint of internal wave experiment, you do see that the flow is slowed down on either side. So if you want flow that is outside of the boundary layers on either side, you need to keep some width.

Secondly, not changing the tank’s width has the advantage that no new mountains/ships need to be built.

Another, practical argument for a wide-ish tank (that I feel VERY strongly about) is that the tank will need to be cleaned. Not just rinsed with water, but scrubbed with a sponge. And I have had my hands inside enough tanks to appreciate if the tank is wide enough that my arm does not have to touch both sides at all times when reaching in to clean the tank.

Why we need the tank depth

The first reason for keeping the height is that for the “dead water” experiment, even the existing tank is a lot shallower than what we’d like from theory (more here). If we go shallower, at some point the interactions between the internal waves and the ground will become so large that it will mess up everything.

Another reason for keeping the depth is the “waves running up a slope” experiment. If you want waves running up a slope (and building up in height as they do), you have the choice between high walls of the tank or water spilling. Just sayin’…

And last not least: this tank has been used in “actual” research (rather than just teaching demonstrations, more on that on Elin’s blog), so if nothing else, those guys will have thought long and hard about what they need before building the tank…

Historical images of research on internal lee waves being done with the tank

Without getting too philosophical here about models and what they can and cannot achieve (and tank experiments being models of phenomena in the ocean), the problem is that scaling of the ocean into a tiny tank does not work, so “just use a mountain/boat half the size of the existing ones!” is actually not possible. Similarly to how if you build the most amazing model train landscape, at some point you will decide that tiny white dots are accurate enough representations of daisies on a lawn, if you go to a certain size, the tank will not be able to display everything you want to see. So going smaller and smaller and smaller just does not work. A more in-depth and scientific discussion of the issue here.

Other features of the tank

When building a new tank or setting up the existing tank in a new spot, there are some features that I consider to be important:

  • The tank needs a white, intransparent back wall (either permanently or draped with something) so that students can easily focus on what is going on inside the tank. Tank experiments are difficult to observe and even more difficult to take pictures of, the better the contrast against a calm background, the better
  • The tank should be made of glass or some other material that can get scrubbed without scratching the surface. Even if there is only tap water in the tank, it’s incredible how dirty tanks get and how hard they have to be scrubbed to get clean again!
  • The tank needs plenty of inlets for source waters to allow for many different uses. With the current tank, I have mainly used an inlet through the bottom to set up stratifications, because it allowed for careful layering “from below”. But sometimes it would be very convenient to have inlets from the side close to the bottom, too. And yes, a hose could also be lowered into the tank to have water flow in near the bottom, but then there needs to be some type of construction on which a hose can be mounted so it stays in one place and does not move.
  • There needs to be scaffolding above the tank, and it needs to be easily modifiable to mount cameras, pulleys, lights, …
  • We need mechanism to tow mountains and ships. The current tank has two different mechanisms set up, one for mountains, one for ships. While the one for the ship is home-made and easily reproducible in a different setting (instructions), the one to tow the mountain with is not. If there was a new mechanism built, one would need to make sure the speeds at which the mountain can be towed matches the internal wave speed to be used in the experiment, which depends on the stratification. This is easy enough to calculate, but it needs to be done before anything is built. And the mechanism does require very securely installed pulleys at the bottom of the tank which need to be considered and planned for right from the start.

“Source” reservoirs

The “source” reservoirs (plural!) are the reservoirs in which water is prepared before the tank is filled. It is crucial that water can be prepared in advance; mixing water inside the tank is not feasible.

There should be two source reservoirs, each large enough to carry half the volume of the tank. This way, good stratifications can be set up easily (see here for how that works. Of course it works also with smaller reservoirs in which you prepare water in batches as you see below. But what can happen then is that you don’t get the water properties exactly right and you end up seeing stuff you did not want to see, as for example here, which can mess up your whole experiment)

Both reservoirs should sit above the height of the tank so that the water can be driven into the tank by gravity (yes, pumps could work, too, more on that below).

“Sink” reservoir

Depending on the kind of dyes and tracer used in the water, the water will need to be collected and disposed of rather than just being poured down the drain. The reservoir that catches the “waste” water needs to

  • be able to hold the whole volume of the tank
  • sit lower than the tank so gravity will empty the tank into the reservoir (or there needs to be a fast pump to empty the tank, more on that below)
  • be able to be either transported out of the room and the building (which means that doors have to be wide enough, no steps on the way out, …) or there needs to be a way to empty out the reservoir, too
  • be able to either easily be replaced by an empty one, or there needs to be some kind of mechanism for who empties it within a couple of hours of it being filled, so that the next experiment can be run and emptied out

If the waste water is just plain clear tap water, it can be reused for future experiments. In this case, it can be stored and there need to be…

Pumps

If reservoirs cannot be located above and below tank height to use gravity to fill and empty the tanks, we need pumps (plural).

  • A fast pump to empty out the tank into the sink reservoir, which can also be used to recycle the water from the sink reservoir into the source reservoirs
  • One pump that can be regulated very precisely even at low flow rates to set the inflow into the tank
  • Ideally, a second pump that can be regulated very precisely, so the double bucket method of setting up a stratification in a tank can be done automated rather than relying on gravity.

Preferable the first and the latter are not the same, because changing settings between calibrating the pump for an experiment, setting it on full power to empty the tank, and calibrating it again will cause a lot of extra work.

Inlets for dyes

Sometimes it would be extremely convenient if there was a possibility to insert dyes into the tank for short, distinct periods of time during filling to mark different layers. For this, it would be great to be able to connect syringes to the inlet

Hoses and adapters

I’ve worked for years with whatever hoses I could find, and tons of different adapters to connect the hoses to my reservoir, the tap, the tank. It would be so much less of a hassle if someone thought through which hoses will actually be needed, bought them at the right diameter and length, and outfitted them with the adapters they needed to work.

Space to run the experiment

The tank needs to be accessible from the back side so the experimenter can run the experiment without walking in front of the observers (since the whole purpose of the tank is to be observed by students). The experimenter also needs to be able to get out from behind the tank without a hassle so he or she can point out features of interest on the other side.

Also, very importantly, the experimenter needs to be able to reach taps very quickly (without squeezing through a tight gap or climbing over something) in case hoses come loose, or the emergency stop for any mechanism pulling mountains in case something goes wrong there.

Space for observers

There needs to be enough room to have a class of 25ish students plus ideally a handful of other interested people in the room. But not only do they need to fit into the room, they also need to be able to see the experiments (they should not have to stand in several rows behind each other, so all the small people in the back get to see are the shoulders of the people in front). Ideally, there will be space so they can duck down to have their eyes at the same height as the features of interest (e.g. the density interface). If the students don’t have the chance to observe, there is no point of running an experiment in the first place.

Filming

Ideally, when designing the layout of the room, it is considered how tank experiments will be documented, i.e. most likely filmed, and there needs to be space at a sufficient distance from the tank to set up a tripod etc..

Lighting

Both for direct observations and for students observing tank experiments, it is crucial that the lighting in the room has been carefully planned so there are minimal reflections on the walls of the tank and students are not blinded by light coming through the back of the tank if a backlighting solution is chosen.

Summary

In my experience, even though many instructors are extremely interested in having their students observe experiments, there are not many people willing to run tank experiments of the scale we are talking about here in their teaching. This is because there is a lot of work involved in setting up those experiments, running them, and cleaning up afterwards. Also there are a lot of fears of experiments “going wrong” and instructors then having to react to unexpected observations. Running tank experiments requires considerable skill and experience. So if we want people using the new room and new tank at all, this has to be made as easy as possible for them. Therefore I would highly recommend that someone with expertise in setting up and running experiments, and using them in teaching, gets involved in designing and setting up the new room. And I’d definitely be willing to be that person. Just sayin’ ;-)

“Continue. Start. Stop.”. An article supporting the usefulness of my favourite method of asking for student feedback on a course!

I’ve been recommending the “Continue. Start. Stop.” feedback method for years an years (at least since my 2013 blog post), but not as a research-backed method but mostly based on my positive personal experience with it. I have used this method to get feedback on courses I’ve been teaching a couple of weeks into the course in order to improve my teaching both within the course as well as over the years. If there was anything that students thought would improve their learning, I wanted to be able adapt my teaching (and also, in a follow-up discussion of the feedback, be able to address student expectations that might not have been explicit before that I might or might not want to follow). I like that even though it’s a qualitative method and thus fairly open, it gives students a structure along which they can write their feedback. Also by asking what should be continued as well as stopped and started, it’s a nice way to get feedback on what’s already working well, too! But when I was asked for a reference for the method today, I didn’t really have a good answer. But then I found one: an article by Hoon et al. (2015)!

Studies on the “continue. start. stop.” feedback vs open feedback

In the first study in the article, two different feedback methods are compared over three different courses: a free form feedback and a structured format, similar to “continue. start. stop.”. From this study, the authors draw pointers for changing the feedback method in the free form course to a more structured feedback. They investigate the influence of this change in a second study.

In that second study, the authors find that using a structured feedback led to an increasing depth of feedback, and that the students liked the new form of giving feedback. They also find indications that the more specific the questions are, the more constructive (as compared to more descriptive texts in the open form; not necessarily more positive or negative!) the feedback is.

My recommendations for how to use the “continue. start. stop.” feedback

If anything, this article makes me like this feedback method even more than I did before. It’s easy and straight forward and actually super helpful!

Use this as formative feedback!

Ask for this feedback early on in the course (maybe after a couple of weeks, when students know what to expect in your course, but with plenty of the course left to actually react to the feedback) and use the student replies to help you improve your teaching. While this method can of course also be used as summative feedback at the end of the course, how much cooler is it if students can benefit from the feedback they gave you?

Ask full questions

One thing that I might not have been clear about before when talking about the “continue. start. stop.” feedback method is that it is important to actually use the whole phrases (“In order to improve your learning in this course, please give me feedback on the following points

  1. Continue: What is working well in this course that you would like to continue?
  2. Start: What suggestions do you have for things that could improve the course?
  3. Stop: What would you like us to stop doing?”

or similar) rather than just saying “continue. start. stop.” and assuming the students know what that means.

Leave room for additional comments

It is also helpful to give an additional field for other comments the students might have, you never know what else they’d like to tell you if only they knew how and when to do it.

Use the feedback for several purposes at once!

In the article’s second study, a fourth question is added to the “continue. start. stop.” method, and that is asking for examples of good practice and highlights. The authors say this question was mainly included for the benefit of “external speakers who may value course feedback as evidence of their own professional development and engagement with education”, and I think that’s actually a fairly important point. While the “continue. start. stop.” feedback itself is a nice addition to any teaching portfolio, why not think specifically about the kind of things you would like to include there, and explicitly ask for them?

Give feedback on the feedback

It’s super important that you address the feedback you got with your class! Both so that they feel heard and know whether their own perception and feedback agrees with that of their peers, as well as to have the opportunity to discuss what parts of their suggestions you are taking on, what will be changing as a result of their suggestions, and what you might not want to change (and why!). If this does not happen, students might not give you good feedback the next time you ask for it because they feel that since it didn’t have an effect last time, why would they bother doing it again?

Now it’s your turn!

Have you used the “continue. start. stop.” method? How did it work for you? Will you continue using it or how did you modify it to make it suit you better? Let me know in the comments below! :-)

Reference:

Hoon, A. and Oliver, E.J. and Szpakowska, K. and Newton, P. (2015) ‘Use of the ‘Stop, Start, Continue’ method is associated with the production of constructive qualitative feedback by students in higher education.’, Assessment and evaluation in higher education., 40 (5). pp. 755-767. [link]

Asking students to take pictures to help them connect theory to the reality of their everyday lives

— This post was written for “Teaching in the Academy” in Israel, where it was published in Hebrew! Link here. —

Many times students fail to see the real-life relevance of what they are supposed to be learning at university. But there is an easy way to help them make the connection: Ask them to take pictures on their smartphones of everything they see outside of class, write a short sentence about what they took a picture of, and why it is interesting, and submit it on an electronic platform to share with you and their peers. And what just happened? You made students think about your topic on their own time!

Does it work?

Does it work? Yes! Obviously there might be some reluctance to overcome at first, and it is helpful to either model the behaviour you want to see yourself, or have a teaching assistant show the students what kind of pictures and texts you are looking for.

Do I have to use a specific platform?

Do I have to use a specific platform? No! I first heard about this method after Dr. Margaret Rubega introduced the #birdclass hashtag on Twitter for her ornithology class. But I have since seen it implemented in a “measuring and automation technology” class that already used a Facebook group for informal interactions (see here), and by a second class on the university’s conventional content management system. All that is required is that students can post pictures and other students can see them.

Do you have examples?

One example from my own teaching in physical oceanography: Hydraulic jumps (see figure below). The topic of hydraulic jumps is often taught theoretically only and in a way that students have a hard time realizing that they can actually observe them all the time in their real lives, for example when washing your dishes, cleaning your deck or taking a walk near a creek. But when students are asked to take pictures of hydraulic jumps, they start looking for them, and noticing them. And even if all of this only takes 30 seconds to take and post a picture (and most likely they spent more time thinking about it!), that’s 30 extra seconds a student thought about your content, that otherwise he or she would have only thought about doing their dishes or cleaning their deck or their car.

hydraulic_jumps

Collection of many images depicting hydraulic jumps found in all kinds of environments of daily life

And even if you do this with one single topic and not every single topic in your class, once students start looking at the world through the kind of glasses that let them spot the hydraulic jumps, they are going to start spotting theoretical oceanography topics everywhere. They will have learned to actually observe the kind of content you care about in class, but in their own world, making your class a lot more relevant to them.

An additional benefit is that you, as the instructor, can also use the pictures in class as examples that students can relate to. I would recommend picking one or two pictures occasionally, and discussing for a minute or two why they are good examples of the topic and what is interesting about them. You can do this as introduction to that day’s topic or as a random anecdote to engage students. But acknowledging the students’ pictures and expanding on their thoughts is really useful to keep them engaged in the topic and make them excited to submit more and better pictures (hence to find better examples in their lives, which means to think more about your course’s topic).

Does this work for subjects outside of STEM, too?

Does this work for subjects outside of STEM, too? Yes! In a language class, for example, you could ask people to submit pictures of something “typically English [or whatever language you are teaching]”. You can then use the pictures to talk about cultural features or prejudices. This could also be done in a social science context. In history, you might ask for examples of how a specific historical period influences life today. In the end, it is not about students finding exact equivalents – it is about them trying to relate their everyday lives to the topics taught in class and the method presented in this article is just a method to help you accomplish that.

P.S.: This text originally appeared on my website as a page. Due to upcoming restructuring of this website, I am reposting it as a blog post. This is the original version last modified on October 1st, 2016.

I might write things differently if I was writing them now, but I still like to keep my blog as archive of my thoughts.

Using real time data of ship positions in teaching?

This morning I was looking for the current position of a research vessel on MarineTraffic.com and noticed something that should maybe not have been surprising, but that I had never really thought about: How all the fishing vessels (orange) are sitting right on the shelf break! I guess that’s where they should be when we think about currents and nutrients and primary production and fish, but how cool is it to actually see it?

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And see that area west of Lofoten where there are a lot of fishing boats in a circle? An unnamed inside source told me that that’s where cod is spawning right now, so everybody is going there to fish. Tomorrow, the cluster might be in a completely different place. And even now, some 10 hours later, it seems to have migrated a little northward? Will definitely check again tomorrow!

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I obviously had to look whether fishing on the shelf break was just a thing in Northern Norway and turns out that it’s the same on the Greenland Shelf.

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Now that I got into playing, I found it also really interesting to see that there is a lot of fishing in the equatorial Pacific going on. And how clearly you can see major traffic routes even in just the distribution of ships.

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And then, ShipTracker even offers a density map of ship traffic:

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Which I had to screen-shoot in two parts because of reasons:

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This site would be such a great tool for all kinds of teaching purposes. Realtime data on shipping is just a click away, even with the free version! There are so many things that students could do estimates on using this site, on transport, fishing, pollution, just pick your topic! And using authentic data makes the whole thing a lot more interesting than looking at maps or numbers a teacher would provide. Pity I’m not teaching right now!

Reflections on reflections

When we think about reflections in water, we usually think of calm lakes and trees on the shore opposite to us. Or clouds. Or at least that’s what I think of: Everything is so far away, that it seems to be reflected at an axis that is a horizontal line far away from us.

Then the other day I walked along Kiel Fjord and it hit me that I had never actually consciously observed reflection of things that are located close to my position, and especially things who are not pretty much equidistant to me, but where one end is a lot closer than another one. Consider the picture below: Do you notice something that looks kinda odd to you (while at the same time looking super familiar)?

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If you are wondering what I mean, I marked it in red in the picture below: The rope and its reflection! It’s embarrassing to say that (as someone who has been sailing A LOT since the age of 7) this was the first time I really noticed, but it struck me how the maximum of the parable of the reflected rope isn’t right below the minimum of the parable of the rope, but seems shifted to the left. Of course this is exactly how it should be if we think about the optics, but I was really shocked that I had never noticed before and never thought about it before! I bet if I had had to draw the reflection I would have done it wrong and probably not even noticed…

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Here is another picture to show you what I mean. This is what it looks like:

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Below I’ve drawn in the original objects in blue, the axis of reflection in red and then the reflection in green:

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So far, so good, everything looking the way it’s supposed to look. Right? Then look at the picture below:
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Sorry if this seems obvious to you, but I’m fascinated with this right now :-)

But it leads to another interesting thought: Asking people to draw stuff in order to both check their understanding and also make them reflect on their understanding. I recently had the opportunity to observe a class of master students draw the SST of the mean state of the Pacific Ocean (which was an exercise that I had suggested in connection with a class on El Nino. I thought it would be neat to have them draw the mean state and then later the anomalies of El Nino and La Nina to activate prior knowledge) and it was surprising how difficult that was even though I’m sure they would all have claimed to know what the mean state looks like. Having to draw stuff really confronts us with how sure we are of things we just assumed we knew…

And then I’m pretty sure that once we’ve drawn something that we have constructed ourselves from what we knew (rather than just copied a drawing from the blackboard or a book, although I think that also helps a lot), we are a lot less likely to forget it again.

Anyway, this is a type of exercise I will use — and recommend — a lot more in the future!

Mirjam Glessmer and Timo Lüth leading a workshop for university instructors

You learn better when you think that you will have to teach

Have you ever worked as student tutor? Then you’ve probably felt like you understood the content of the course you tutored a million times better after tutoring it. Or at least that’s what I hear over and over again: People feel like they understood a topic. Then they prepare to teach it, and realise how much more there was to understand and that they actually understood it.

And there is research that shows that you don’t actually need to teach in order to get the deeper understanding, it is enough to anticipate that you will teach: “Expecting to teach enhances learning and organization of knowledge in free recall of text passages” by Nestojko, Bui, Kornell & Bjork (2014).

In that article, two groups of participants are given texts that they are to study. One group is told that they will be tested on the text, the other one that they will have to teach someone else who then will be tested. After all participants study the text, they are then all tested (and nobody gets to teach). But it turns out that even expecting to teach had similar benefits to what we see in student tutors who actually taught: Participants expecting to teach have a better recall of the text they had to study, can answer more questions about it and especially questions regarding main points.

So what does that mean for teaching? As the authors say: “Instilling an expectation to teach […] seems to be a simple, inexpensive intervention with the potential to increase learning efficiency at home and in the classroom.” And we should definitely use that to our advantage! :-)

Will giving your students more structure make them need more structure?

One of the arguments against offering students practice opportunities online and providing automated feedback right then and there is that that way, they will never learn to work independently. Since I am working on e-assessment a lot and with many different courses at the moment, this is a fear that I definitely need to take seriously. I don’t believe that the danger is as big as it is sometimes made out to be, but I do believe that there is a vicious circle to be aware of.

It all starts with the instructor having the impression that students are not able to organize their learning on their own. Since the instructor wants the students to succeed, she offers them a clear structure, possibly with bonus points or other kinds of rewards, so they have a safe space with instantaneous feedback to practice skills that are required later. So far, so good.
Now the students are given this structure, and get used to working on problems that are presented in small portions and with instantaneous feedback. They start believing that it is the instructor’s job to organize their learning in such a way, and start relying on the instructor to provide both motivation and bite-sized exercises.
Which the instructor, in turn, notices and interprets as the students becoming less and less able to structure their learning.
At this point it is very easy to fall in the trap of trying to provide an even better, more detailed, structure, so that the students have a better chance of succeeding. Which would likely lead to the students relying even more heavily on the instructor for structure and motivation.

Teufelskreis

It is easy to fall into a vicious circle where the instructor feels like they need to provide more and more structure and motivation, and the students feel less and less responsible for their own learning.

So what can we do? On the one hand we want to help students learn our content, on the other hand they also need to learn to learn by themselves. Can both happen at the same time?
I would say yes, they can.
The first step is recognizing the danger of entering into this downward spiral. There is absolutely no point in hoping that the students will take the initiative and not fall into the trap of relying on us, even if we point out that the trap is there. Of course they might not fall in, but whether they do or not is beyond our influence. We can only directly influence our own actions, not the students’, so we need to make sure to break the spiral ourselves.
The second step is to make sure that we resist the urge to give more and more detailed exercises and feedback.
The third step is to create an exit plan. Are we planning weekly quizzes as homework that students get a certain number of bonus points for? Then we should make sure that over time, either the number of bonus points will decrease, the time interval will become longer, the tasks become more difficult, or a combination of all three. The idea is to reward the behaviour we want just long enough that students establish it, but not any longer than that.
And of course, last but not least, instead of giving students more structure, we can help them learn the tools they need to organize their learning. Be it training skills to organize yourself, or helping them find intrinsic motivation, or teaching them to ask the right questions so they can walk themselves through complex problems until they find an answer.
It’s a pretty thin line to walk, and especially the fourth step might really be out of an instructor’s control when there is a lot of content to go through in very little time and the instructor isn’t the one deciding how much time is going to be spent on which topic. Most TAs and even many teaching staff won’t have the freedom to include teaching units on learning learning or similar. Nevertheless, it is very important to be aware of the vicious circle, or of the potential of accidentally entering it, to be sure that our best intentions don’t end up making students depending on us and the structures we provide, but instead make them independent learners.

Bridging the gap between conventional mathematics teaching and the topics that engineering students are really interested in

I’m very excited to announce that I, together with Christian Seifert, have been awarded a Tandem Fellowship by the Stifterverband für die Deutsche Wissenschaft. Christian, among other things, teaches undergraduate mathematics for engineers, and together we have developed a concept to improve instruction, which we now get support to implement.

The problem that we are addressing is that mathematics is taught to 1300 students from 12 different engineering study programs at once. At the moment, in addition to lectures and practice sessions in both very large and small groups, students get weekly online exercises that they can earn bonus points with. Student feedback is positive – they appreciate the opportunity to practice, they like that they are nudged towards continuously working on whatever is currently going on in class, and obviously they like to earn bonus points they can use on the exam.
However, mathematics is not typically a subject that non-mathematicians are very keen on. Many feel like there is no relevance of the content to their lives or even their studies. And many don’t feel confident they have a chance to succeed.
As I wrote in my recent posts on motivation, both believing that you can succeed and seeing the relevance of things you are supposed to be studying to your life are necessary for people to feel intrinsically motivated. So this is where we want to start.
Since the experience with the weekly online tests is so positive, we want to develop exercises that apply the mathematics they are currently learning to topics from their own, chosen fields. So if they are supposed to practice solving a set of linear equations, students of mechanical engineering, for example, might as well use one from a mechanical engineering case. Or even better: they might be asked to develop this set of equations first, and then solve it. By connecting mathematics with topics students are really interested in, we hope to get them to engage more with matematics.
More engagement will then likely mean that they improve their understanding both of mathmatics itself and – equally important – of their main subjects, where currently manystudents lack the math skills required. At the same time, we hope this will increase student motivation for both subjects.
Of course, there is still a lot of work to be done to first implement this concept and then evaluate whether it is working as well as we thought it would, and then probably modifying it and evaluating some more. But I am excited to get started!

What does the awkward silence mean?

I really want to recommend a blog post by Paul T. Corrigan that I recently read on “Teaching and Learning in Higher Ed”: When students don’t answer a question, what does the awkward silence mean?

We’ve all been there: We’ve asked a question and nobody replied. Worse, even, they avoid our eyes. What can we do? Check out the post for a surprisingly simple idea!