Thank you, Archimedes!

I really like hydrostatics. Of course I like moving water even better, but even static water is great. And there are so many things to explore! If I was to teach hydrostatics any time soon, there are so many little teasers I would use.

For example this one:

A sailor is standing on the bottom step of a rope ladder, painting the outside of his ship. The bottom step is 50 cm above the water, the distance between steps is 30 cm. The flood is coming in, and the water is expected to rise by 1.5 m. How many steps will the sailor have to climb in order to keep his feet dry?

Or this one:

How much heavier will a trough in a ship lift get when a ship is inside?

A: the weight of the ship
B: the weight of all parts of the ship above the water line
C: not at all
D: I don’t know*

Ship lift Scharnebek

You might think that these are really easy questions, but then you might be surprised! Funnily enough I drafted this post weeks ago, and then last week a colleague of mine talked about how this was a really difficult question, so I had to post it now ;-)

Another question that he mentioned that students found really difficult is similar to this one:

If an anchor is dropped from a boat into a pond, what will happen to the water level?

A: It will rise
B: It will sink
C: Nothing
D: I don’t know

Answer to that one in this post

*Remember why we always include the “I don’t know” option? If not, check out some more posts on multiple choice questions under the MCQ-tag!

Peer instruction! Combine it with individual thinking or discussions with the whole class?

Make sure it stays silent during the first step of the clicker process.

When using clickers in class, there are many different possible ways of implementing clicker questions and peer instruction, for example the Mazur sequence (which is our default sequence) and the Physics Education Research Group at UMass (PERG) sequence. Let’s recall:

The Mazur sequence:
1. A concept question is asked
2. Students think individually for a couple of minutes
3. Students vote on the question
4. The result of the vote is shown as a histogram
5. Students are asked to convince their neighbor of their answer (“peer instruction”)
6. Students vote again on the same question
7. The result of the second vote is shown as a histogram
8. Lecturer explains correct response and why the distractors were incorrect

The PERG sequence:
1. A concept question is asked
2. Students discuss the question for a couple of minutes in small groups
3. Students vote (individually or as a group)
4. The result of the vote is shown as a histogram
5. Students discuss their answers with the whole class, lecturer facilitates the discussion
6. Lecturer explains correct response and why the distractors were incorrect

So the difference here is that in the Mazur sequence, students get the chance to think and vote individually before entering the peer-instruction phase, whereas in the PERG sequence, students first discuss and then discuss in an even bigger group (which is, in my experience, basically what happens when you don’t explicitly ask students to think for them selves first in the Mazur sequence).

Firstly, for both models students report that the clickers helped them learn compared to a conventional lecture, because they were more actively involved, felt motivated by receiving the immediate feedback, and felt that the instructor adapted instruction to meet their learning needs.

Secondly, in both cases students liked peer instruction, for many of the reasons we use it: They felt like they were convinced by the best arguments in the discussion, thus practicing putting forward strong arguments as well as learning the “actual content” of the course. They also mention how scaffolding, i.e. learning something from someone who only just learned it themselves is easier than learning from an expert, helps, because it is more accessible both in language and in explanation itself.

But do the different sequences make a difference? Rhetorical question, of course they do!

Almost all students preferred starting with individual thinking and voting rather than with peer discussion. They state that the individual vote forced them to think for themselves, whereas in an initial peer discussion they might slide into a passive role and unthinkingly accept answers from others.

As for class-wide discussions, while some students liked hearing both correct and incorrect responses from outside their own peer group, and some also liked the pressure that comes with knowing that you might be called upon to answer a questions as a motivator for staying focussed in class, there are drawbacks to it, too. For example, it takes a lot of time, it is easy to drift away from the question and it can easily become confusing, in addition to threatening. Benefit of class-wide discussion is seen mostly in cases where the class was clearly divided between two answer choices.

So based on this study, we should definitely make sure to have students vote individually before peer discussion, and this means enforcing silence in the classroom while the students think about what to vote.


David J. Nicol, & James T. Boyle (2003). Peer Instruction versus Class-wide Discussion in Large Classes: a comparison of two interaction methods in the wired classroom Studies in Higher Education, 28 (4)

What do I want from my students – sense-making or answer-making?

On different approaches to peer-instruction and why one might want to use them.

Having sat in many different lectures by many different professors over the last year, and having given feedback on the methods used in most of those lectures, I find myself wondering how we can define a standard or even best practice for using clickers. Even when professors go through the classical Mazur steps, there are so many different ways they interpret those! Do we, for example, make sure that the first vote is really an individual vote, so that no interaction happened between students before they have to make this very first decision? I have not seen that implemented at my university. But does that matter? And why would one decide for or against it? I would guess that in most cases I have observed there was really no conscious decision being made – things just happen to happen a certain way.

A paper that I liked a lot and which describes a framework for describing and capturing instructional choices is “Not all interactive engagement is the same: Variations in physics professors’ implementation of Peer Instruction” by Turpen and Finkelstein (2009). I don’t want to talk about their framework as such, but there are a couple of questions they ask that I think are a helpful basis for reflection on our own teaching practices. For example there are questions clustering around the topic of listening to students and using the information from their answers. For example “what do I want students to learn, and what do I want to learn from the students?” might seem basic at first, but it is really not. What do I want students to learn? No matter what it is, what this question implies is “is the clicker question I am about to ask going to help them in that endeavor?”. The clicker question might be just testing knowledge, or it might make students think about a specific concept which they might get an even better grasp of by reflecting on your question.

And what do I want to learn from my students? The initial reaction of people I have talked with over the last year or so is puzzlement at this question. Why would I want to learn anything from my students? I am there to teach, they are there to learn. But is there really any point in asking questions if you are not trying to learn from them? Maybe not “learn” as in “learn new content”, but learn about their grasp of the topic, their learning process, where they are at right now. Do I use clicker questions as a way to test their knowledge, to inform my next steps during the class, to help them get a deeper understanding of the topic, to make them discuss? Those are all worthwhile goals, for sure, but they are different. And any one clicker question might or might not be able to help with all of those goals.

Another question is “do I need to listen to students’ ideas and reasoning and what are the benefits of listening to students’ ideas?”. Again, this is a question that I am guessing many people I have recently worked with would find strange. Why would I listen to student reasoning that doesn’t lead to the correct answer, or student reasoning that is different from how I want them to reason? Yes, I might learn something about where they go wrong, which might make it easier for me support them in getting it right. But isn’t it a really bad idea to expose the other students to something that is wrong? I would argue that no, it is not a bad idea. Students need to learn to distinguish between good reasoning and bad reasoning. And they can only do that if they see both good and bad reasoning, and learn to figure out why one is good and one is bad. I know many people are very reluctant of having students explain their reasoning that lead them to a wrong answer. It takes time and it doesn’t seem to lead towards the correct answer. But then what do we want? Answer-making or sense-making? Sense-making might involve taking a wrong turn occasionally, and realizing why it was a wrong turn before taking the right turn in the end. If the wrong answer isn’t elicited, it can’t be confronted or resolved.

I would really recommend you go read that paper. The authors are describing different instructional choices different instructors made, for example how they interact with students during the clicker questions. Did they leave the stage? Did they answer student questions? Did they discuss with students? (And yes, answering questions and discussing with students is not necessarily the same!). Even though there is not one single best practice to using clickers, it is definitely beneficial to reflect on different kinds of practice, or, at to at least become aware that there ARE different kinds of practice. Plenty to think about!