Toilets, Helicopters, and Punnett Squares

The Penrose triangle - an impossible-to-create 3D shape that looks possible in 2 dimensions.

Do you know how a ballpoint pen works? If you’re immediate answer was “yes”, you are in a majority that includes people who think they know how a ballpoint works (though in actuality their understanding is superficial) or people who believe it isn’t too complicated and they could immediately look it up and understand it pretty easily (this phenomena is known as the “natural born cyborg” and toes the line of the extended mind thesis, a conversation for another time).

What about a toilet? Do you know how a toilet works?

My first reaction is, “I sure do! I use toilets all the time! How could I not know how they work? I depress the handle, water comes down into the bowl and then everything goes away.” Which is technically right. That is how a toilet functions. But the physics and magic about how all that happens is not easy to articulate.

I don’t think I could draw an accurate diagram though. Gosh – maybe I don’t know how toilets work after all (spoiler alert, it’s not just gravity – siphoning is a big part, too, and helps explain how ratssnakes, and – eek! – even spiders have no issues crawling up toilet plumbing).

This is what is known as the Illusion of explanatory depth and was studied by two Yale scientists in 20021.

In their study, the researchers asked participants to rate their understanding of a device or phenomenon on a scale of one to seven (shallow, partial, or deep understanding). In addition to toilets, the researchers asked for personal ratings on a speedometer, a zipper, a piano key, a cylinder lock, a helicopter, a quartz watch, and a sewing machine (side note – if you had an affinity for the book series “The Way Things Work” by David Macaulay you would have loved this experiment as that was the source of the concepts participants had to rate).

Guess what?

“Nearly all participants showed drops in estimates of what they knew when confronted with having to provide a real explanation, answer a diagnostic question, and compare their understanding to an expert description.”

And these are things that they use all the time!!!

Now imagine students trying to learn new, complex information. Our brains convince us that we have learned things we don’t quite fully understand. In the book Make it Stick, Peter Brown posits:

When they hear a lecture or read a text that is a paragon of clarity, the ease with which they follow the argument gives them the feeling that they already know it and don’t need to study it. In other words, they tend not to know what they don’t know; when put to the test, they find they cannot recall the critical ideas or apply them in a new context. Likewise, when they’ve reread their lecture notes and texts to the point of fluency, their fluency gives them the false sense that they’re in possession of the underlying content, principles, and implications that constitute real learning, confident that they can recall them at a moment’s notice2.”

This danger is amplified by students who encounter the same (misleading) feelings when reading and highlighting in a textbook – students have a familiarity with the ideas (even to the point of knowing exactly where on a page the idea was written) though that is no indication that students can adequately describe the idea; they are just comfortable with the idea.

How do we help students overcome this illusion? In Uncommon Sense Teaching, Barbara Oakley suggests that it’s important to tell students that it’s perfectly normal not to understand something difficult on their first attempt. For particularly complex content, I preempt the class by reminding students that “it isn’t important that you remember how to do something – just remember that it can be done. You can always look up how to do something (a call to build a cadre of auto-didactic learners!).

You could also tell students about the illusion of explanatory depth (IOED) – metacognition goes a long way.

Oakley also suggests a scaffolded, active learning approach to lessons. For instance, in a lesson for Punnett squares she suggests two main stages – making the Punnett square and then deciphering the Punnett square. Each stage has three phases – “I do“, “We do“, and “You do3.

Making the Punnett Square

In the I do phase, the teacher slowly presents the facts. Perhaps talk about eye colors and how one might predict the eye color of offspring. Invite students to share the colors of their parents’ eyes. The teacher might externalize their inner monologue as they draw the first Punnett square.

In the We do phase the students practice creating their own. The teacher would encourage each dyad to verbalize their thought process and use the vocabulary that was introduced (dominant, recessive, heterozygous, and homozygous) in the first example. This affords the learner a sandbox to play in and make small corrections to their thinking. In this sandbox, students can help each other – or neighboring groups.

In the last part of the “making” part, You do, students are tasked with solving some similar problems on their own “to solidify the learning and build automaticity”.

Deciphering the Punnett Square

Now the teacher can introduce more complexity (like probability). It is okay to amplify the complexity here – students have already had some hands-on experience with the basic framework.

In the I do phase, the teacher is again slowly describing what they are doing as they are constructing the Punnett squares. In fact multiple examples should be provided, eliciting input from the students. The teacher leaves the three or four examples visible for the next two phases.

The penultimate phase, the We do phase, is the same as it was before – students work with a partner to explore more examples, wondering aloud and helping each other out.

Finally, in the You do phase, students have no support and should work through some more examples. It is okay to have problems of varying complexity – part of the challenge is having the student pause to reflect on what type of problem each example is.

Helping students understand the illusion of explanatory depth (also known as the illusion of mastery) is a good first step for teaching foreign material. And scaffolding the examples while providing time for students to engage with them is a great active learning experience. You might also want to check out Webb’s Depth of Knowledge framework.

Next time we will look at the flip side of this – the Curse of Knowledge (and how it gets in the way of teaching).


1   Rozenblit, L., & Keil, F. (2002). The misunderstood limits of folk science: An illusion of explanatory depth. Cognitive science, 26(5), 521-562.

2   Roediger, H. L., McDaniel, M. A., & Brown, P. C. (2014). Make it stick: The science of successful learning. Harvard University Press.

3   Oakley, B., & Sejnowski, T. J. (2021). Uncommon sense teaching: Practical insights in brain science to help students learn. Penguin.

Photo by Sachin Khadka on Unsplash