Space for contrast

Lately I’ve been thinking about how to present multiple similar ideas to students in a way that doesn’t cause confusion.

Examples: transverse vs longitudinal waves, how to find the number of protons, electrons and neutrons in an atom, accuracy and precision, distance-time and velocity-time graphs. Things where students make the simple mistake of “getting things the wrong way around”.

Let’s take transverse and longitudinal waves. I could write an explanation that perfectly elucidates the idea of transverse waves, gives concrete examples, and checks for understanding. We say “this concept, this idea, this THING, is called a transverse wave”. Concept (a) has been given a label (A) i.e. we’ve taught the idea of transverse waves, and labelled it to the class as being “transverse wave”-ness.

I then go on to do the same thing for longitudinal waves in the same lesson. Great explanation (even if I do pretend so myself), logically clear, well-chosen examples, checks for understanding. And I label this new concept “longitudinal waves”. So concept (b) has been given a label (B).

But unless the link between the label ((A) or (B)) and the underlying concept ((a) or (b)) is incredibly clear, there’s nothing to stop students confusing them instantly. The rationale for transverse waves being named as such isn’t something that will be memorable or visceral to students, so they are free to get the labels mixed up immediately.

The same goes for calculating the number of protons, electrons and neutrons. There are three methods (a – read the atomic number), (b – copy the number of protons so it’s neutral), and (c – mass number minus atomic number) to find the numbers of subatomic particles. But there’s no clear link between the method and the labels of the particles themselves (Protons, electrons, neutrons) so students can instantly confuse them.

I’m coming around to thinking that the only way to make the distinction clear (when there’s no tangible link between the label and concept that allows us to instantly differentiate) is to space out the teaching in time, reasonably significantly, so that students can master and learn one concept (a) and it’s label (A) thoroughly before we move to concept (b). My instinct is that this spacing wouldn’t be just one or two lessons, they need to be at the point of having successfully retrieved concept (a) and it’s label (A) a number of times first.

For example: I teach transverse waves. I then teach about the properties of light, and reflection and then refraction. Lenses too whilst we’re at it. Giving lots of opportunities to retrieve the definition and concept of transverse waves. Only then, AFTER all of this, would you look at longitudinal waves, because you know they’re successful with transverse waves now and have built some automaticity around it.

I’d love to hear people’s thought on this curriculum-based solution to students conflating labels.

I reached out to some people to get their takes and a number said that they still felt that the best option is still to teach A, do lots of CFU, then teach B, with lots of CFU, and then do a comparison between A and B, with lots of CFU.

I think I’ve been doing this a lot recently yet I’m still having students getting mixed up. Our curriculum is not set up to space these ideas, so I can’t lean on my original solution right now.

Instead, I’ve been doing a retrieval-based solution. My Y9s were still not consistently getting finding the numbers of protons, electrons and neutrons right from the periodic table. And with every further time they got it wrong, they only seemed emboldened to remember it the wrong way.

So our retrieval practice is now just “find the number of protons in…” And until they reach automaticity about this, and are getting it right every time, we won’t move on to doing retrieval practice on finding the number of electrons (and it’ll be even longer before we do the number of neutrons). I know I’ll have to reintroduce/recap how to find the numbers of electrons/neutrons when we move on to them, but that’s fine by me.

Anyways, a curriculum-based spacing approach to students appreciating the contrast between similar ideas, and a retrieval-based spacing approach for the same problem.

I’d genuinely love to hear your thoughts (@tchillimamp on twitter).