“Right and Wrong” vs. “Good, Better, Best”

So, I’m finding that I am becoming hooked on showing student work back to the students for them to explore as an opportunity to develop a deeper understanding of mathematical topics. But I’m learning there are a couple ways to handle this situation.

I could show this picture…

… and ask if the reflection is right or wrong. Which would activate a certain type of thinking. But it is a short and stifling line of thinking, especially when you consider that most hand-drawn student work isn’t perfect so “wrong” is the most likely answer. Then it risks becoming an annoying knit-picking session, which might have a negative effect on engagement.

A different approach would be to acknowledge that which we all know (that nobody’s perfect) and ask the question differently. Suppose I show the follow four photos together…

… and ask “Which of the reflections is the best?”

That question opens up a lot of potential thought-trails to wander down. As I did this activity with students today, the class settled on three criteria for rating these reflection attempts. The first is that the image and pre-image should be congruent. Attempt A won that battle (with B at a close second). The next thought was that the image and pre-image should be the same distance away from the line of reflection. Attempt B was the closest (with D pretty good, too.) Finally, the students thought that the segment connecting the image/pre-image pairs would should be just about perpendicular to the line of reflection. Attempt B took that contest quite comfortably.

The students concluded that attempt B was the best reflection and I was able to confirm that by showing them this photo, which seems to agree quite strongly with that conclusion.

If you want to try this activity, go ahead. I’d love to hear some feedback on how it went in your class. I’m still dealing with some quality control issues with some of my multi-media projects, so I apologize for that. I didn’t notice it to be too distracting when I was showing it to the students, but there is still room for improvement.

Best Reflection – Act I

Best Reflection – Act II (reflection distances)

Best Reflection – Act II (reflection angles)

Best Reflection – Act II (segment lengths of image and preimage)

Best Reflection – Act III