# Designing exercises with the right amount of guidance as well as the right level of difficulty

An example of one topic at different levels of difficulty.

Designing exercises at just the right level of difficulty is a pretty difficult task. On the one hand, we would like students to do a lot of thinking themselves, and sometimes even choose the methods they use to solve the questions. On the other hand, we often want them to choose the right methods, and we want to give them enough guidance to be able to actually come to a good answer in the end.

For a project I am currently involved in, I recently drew up a sketch of how a specific task could be solved at different levels of difficulty.

The topic this exercise is on “spotting the key variables using Shainin’s variables search design”, and my sketch is based on Antony’s (1999) paper. In a nutshell, the idea is that paper helicopters (maple-seed style, see image below) have many variables that influence their flight time (for example wing length, body width, number of paper clips on them, …) and a specific method (“Shainin’s variables search design”) is used to determine which variables are the most important ones.

Paper helicopter

In the image below, you’ll find the original steps from the Antony (1999) paper in the left column. In the second column, these steps are recreated in a very closely-guided exercise. In the third column, the teaching scenario becomes less strict, (and even less strict if you omit the part in the brackets), and in the right column the whole task is designed as a problem-based scenario.

Flight time of a helicopter investigated at different levels of difficulty

Clearly, difficulty increases from left to right. Typically, though, motivation of students tasked with similar exercises also increases from left to right.

So which of these scenarios should we choose, and why?

Of course, there is not one clear answer. It depends on the learning outcomes (classified, for example, by Bloom or in the SOLO framework) you have decided on for your course.

If you choose one of the options further to the left, you are providing a good structure for students to work in. It is very clear what steps they are to take in which order, and what answer is expected of them. They will know whether they are fulfilling your expectations at all times.

The further towards the right you choose your approach, the more is expected from the students. Now they will need to decide themselves which methods to use, what steps to take, whether what they have done is enough to answer the question conclusively. Having the freedom to choose things is motivating for students, however only as long as the task is still solvable. You might need to provide more guidance occasionally or point out different ways they could take to come to the next step.

The reason I am writing this post is that I often see a disconnect between the standards instructors claim to have and the kind of exercises they let their students do*. If one of your learning outcomes is that students be able to select appropriate methods to solve a problem, then choosing the leftmost option is not giving your students the chance to develop that skill, because you are making all the choices for them. You could, of course, still include questions at each junction, firstly pointing out that there IS a junction (which might not be obvious to students who might be following the instructions cook-book style), and secondly asking for alternative choices to the one you made when designing the exercise, or for arguments for/against that choice. But what I see  is that instructors have students do exercises similarly to the one in the left column, probably even have them write exams in that style, yet expect them to be able to write master’s theses where they are to choose methods themselves. This post is my attempt to explain why that probably won’t work.

* if you recognize the picture above because we recently talked about it during a consultation, and are now wondering whether I’m talking about you – no, I’m not! :-)

# “Isostasy” of ships

Empty ships look weird.

Since we talked about the ship-and-anchor thing last week (you know – what happens to the water level when an anchor that was previously stored on board is thrown into the sea) I remembered that I took pictures when I went to Gothenburg in September that I had been meaning to share on here.

We (or I, at least) hardly ever see empty ships. For one, it doesn’t make a whole lot of sense economically to have ships driving around empty, but also the stability of ships is maximal at a certain position of the ship in the water. Therefore people will always try to drive a ship that is neither loaded too full or not enough. But don’t empty ships just look funny?

Ships in the port of Gothenburg

Especially when you see sister ships next to each other where one is full and the other is empty (below).

Ships in the port of Gothenburg

# Balls balancing on water jets

Water is just endlessly fascinating.

When I was recently at the ThinkTank science museum in Birmingham, UK, they had water fountains that you could balance balls on, like so:

Even though it was raining, you can probably imagine how much time I spent there… But I made a video for you so you can enjoy it, too. Have fun!

# Double overflow

Because sometimes one overflow simply isn’t enough.

Finn’s group came up with – and ran – an overflow experiment with many different densities and even more colors. While the movie didn’t turn out too well, the idea was pretty awesome.

Rolf went ahead and modeled the experiment right away. And because the plume didn’t go across the second ridge in a dramatic enough fashion, he did the same experiment again, this time with a higher density contrast.

Salinity – the higher, the redder, the lower, the bluer. Density higher than in the figure above. Figure courtesy of Rolf Käse

If you compare those two figures, you notice that the second one is a lot more diffusive than the first one. To test whether the model was doing well, we obviously had to run both experiments in the tank, too. Watch the movie below to see how they turned out:

Turns out that also for us, the run with the higher density contrast is a lot more diffusive. Kelvin-Helmholtz-instabilities develop on the first down slope of the first ridge, and generally a lot more mixing is going on. To get an impression of the regions of high mixing and recirculation, rather than guessing from the diffusing salinities, Rolf displayed the horizontal velocity:

Along-tank velocity. Blue to the left, red to the right. Figure courtesy of Rolf Käse.

Notice the high mixing whenever the plume is running down a slope, and then the recirculations in the valleys. Pretty awesome, huh?

# Tagebuch – Tag 7

Von Carolin und Marie

Am heutigen Tage wurden auch das Salz, die Dichte und die Wellen endgültig überführt. Das, was jetzt noch alles abschließt, ist die morgige Gerichtsverhandlung.

Darauf haben sich alle Detektive genauestens vorbereitet und sie haben sich überlegt, wer welche Beweise im Gerichtssaal vorstellt. Genauere Details werden aber Morgen noch geklärt.

Die Salzüberführung erfolgte, indem die zugeteilte Lehrlingsgruppe herausfand, wo das Salz seine Finger mit im Spiel hatte. Dieses Experiment nannten sie Salzfinger.

Langsam wurden die drei mutigen Lehrlinge, die schon die ganze Zeit die geheimen Versuche der Meisterdetektive beobachtet hatten, ungeduldig. Als sie den Meisterdetektiven ein weiteres Mal zugeschaut hatten, durften sie sogar selbst Hand anlegen.

Bald müssen sie sich jedoch verabschieden und ihren eigenen Weg durch das gefährliche, aber spannende Leben gehen. Sie werden noch viele weitere hundert Male mit Schiffen zum Tatort reisen und auch noch viele weitere Täter schnappen.

Das war`s für Heute und bis Morgen,

Eure Berichterstatter.

# Hadley cell circulation – slow rotation

In order to not be in the eddying regime, this time we are rotating our tank as slowly as possible.

Since we ran the Hadley cell experiment the other day, I’ve been obsessed with running it again, this time with the slowest rotation possible in order to visualize a different flow regime – one were the heat transport happens through an overturning circulation rather than through eddies.

Unfortunately the camera we had mounted above the tank only started up halfway through the experiment (no idea how that happened!), so today you’ll only get snippets of this experiment. But all the more reason for us to run it again soon!

And I promise you’ll get a discussion of the differences between this and the Hadley cell experiment with the higher rotation rate soon. I just don’t have the time or mental space to write more than a couple of incoherent sentences while I’m still at the JuniorAkademie

# Happy Birthday, my dear blog!

Adventures in Oceanography and Teaching has been around for a full year today!

So today marks the first anniversary of this blog’s existence. Coincidentally, it also marks another anniversary – congratulations, A&I! You are the best!

But anyway, now I had a blog. In addition to the first hesitant “hello world!” post, I posted six other posts that first evening! The next day, I posted “only” two posts and then went down to one post every day of the week for some time. After a while, I went to only posting on working days, and now I’ve been at 3 posts a week for the last couple of months. Which is probably more sustainable in the long run. Sometimes I have a lot more content, but then I force myself to save it up a bit and schedule it for those weeks when I’m on conference travel or on no-internet vacation (it does happen!).

In any case, except for on one rare occasion when I wrote a blogpost to force myself to think a concept through for work, blogging has never felt like work to me. Yes, I had those Sunday nights when I thought “ooops, I have no content lined up for next week”, and then I went to my kitchen and got out the food dye and straws or test tubes or kettle or whatever other props. But that never felt like a chore, it was always more of a reminder that even though I really really do enjoy doing experiments, I had not done enough of it recently, so when I started doing something about it I was always really happy to do it. So in addition to professional benefits, this is what the blog does to me – it forces me to do stuff I love more regularly than I would do it otherwise.

Thanks for reading and joining me on this journey!

# Tagebuch – Tag 6

Von Carolin und Marie

Heute haben sich die Lehrlinge gegenseitig ihre beantworteten Fragen vorgestellt. Vollständig überführt wurden zurzeit das Klima und die Strömungen, die Gezeiten und das Eis. Beim Salz und der Dichte, sowie bei den Wellen, sind noch einige wenige Fragen zu klären. Die Übrigen Lehrlinge beantworten nun einige Fragen, denen kein Täter zuzuordnen war. Sie beschäftigen sich jetzt mit der Plattentektonik, der Corioliskraft und einigen anderen, kleinen Themen.

Doch am heutigen Tage haben die anderen Lehrlinge nichts von Meisterdetektiven Glessmers geheimen Versuch mitbekommen. Auch am heutigen Abend haben die Meisterdetektive wieder ein geheimes Experiment durchgeführt, wobei die drei neugierigen Lehrlinge sie gesehen haben, doch sie wissen dieses Mal nicht genau, worum es sich dabei handelt.

# Currents on soap bubbles

There are currents and eddies and whirls everywhere!

Today, Rolf showed us currents on soap bubbles.

Check out the movie below for moving pictures!