What Students Lose When They Know They’re Right

How immediate feedback invites students to STOP thinking.

Most of my recent writing and speaking has been concerned with wrong answers—how they’re often wasted, how to interpret rather than evaluate them, how they’re often very smart, etc. 

But I have just as many concerns about correct answers.

For example, I taught this Desmos card sort in seventh grade recently in Oakland, CA.

Card sorts are interesting because the Desmos platform knows whether or not the student is correct—whether the right algebra card is matched with the right graph card and the right story card. Desmos lets the teacher know whether or not the student is correct via the teacher dashboard. 

But Desmos doesn’t tell students whether or not they’re correct. 

We have that information. We just withhold it.

Teachers have occasionally felt antagonized by that choice. They have frequently taken matters into their own hands, either by projecting the teacher dashboard in front of the class or by adding a custom-designed screen to the activity, giving students access to that same information.

I get it. Speaking pragmatically, it’s hard to have students sitting around, feeling like they’re done with a task, feeling like they don’t have options for feedback or follow-up.

I’m not here to judge anyone’s pragmatism. But I would like to offer what I see are the opportunity costs of letting students know they’re correct.

The students and I worked with card sorts during that recent demo lesson in several productive ways, all of which would have been lost if students knew beyond doubt that their card sort was correct.

Self-reflection

For example, two students weren’t sure how to group a particular card. Does a point with an open circle imply “less than” or “at most”? If the students had access to immediate digital feedback, they might check to see if their first idea was correct, change it if it wasn’t, and then check it again. Without that information, though, the students did something extremely productive. They moved back to an earlier screen where they could build a story using inequalities. They tested several ideas, then returned to the card sort where they transferred their understanding from one task to the other.

Group Discussion

After different groups of students finished the card sort, I didn’t want them to sit around unengaged, so I invited them to pick up their laptops and join up with another group of students. I asked them to check out one another’s card sorts and reconcile the differences. It seemed to me those conversations would have been much shorter and much less mathematically rich if one group had received a green check mark from the computer for their card sort and one group hadn’t. All debates would have come pre-settled.

Whole Class Discussion

Here is a feature that I have learned no one knows exists. The Desmos platform collects all the card sorts in the class and lets you know which card is incorrectly grouped most often. (Click “Overview” in the teacher tab.)

This winds up being a powerful conversation starter!

“This card is the one that is in the wrong group most often. Check yours. Let’s get real confident about it.” If students know their card is correct, they’ll be less inclined to scrutinize their reasoning. So we don’t tell them whether or not their card is correct.

No one ever got thrown out of an edtech party for talking about how great computers are at providing immediate feedback. But computers are only good at providing certain kinds of feedback and only on certain kinds of thinking. And that feedback is often evaluative–immediately telling students they are right or wrong. What I'm suggesting is that what students gain when they know they’re right and wrong is often exceeded by what they lose in opportunities to learn about mathematics and about themselves as mathematicians.

BTW

The International Society for Technology in Education’s standards are pretty good here. Their teaching standards for feedback encourage teachers to provide “timely feedback” rather than “immediate feedback.” Its student standards describe students who “use technology to seek feedback that informs and improves their practice.” Nothing about immediate feedback there either. It seems important, also, to know when humans, rather than computers, can offer the best feedback.

What Else

• Fawn Nguyen and Lauren Baucom have joined Amplify. Congrats to all of us. I’m very lucky to work with so many people who operate at the extreme end of the talent, intelligence, and character scales.

• Speaking of talented colleagues, check out the Kolam Tiles Christopher Danielson is now offering in his Talking Math With Your Kids store. Or the Mega Pattern Machine he set up at the Mall of America.

• Karim Ani’s Follow Up to Dear Citizen Math is a double shot of energy at the start of the school year. I note with some interest that he’s now describing teachers as the most influential actors in a math classroom rather than the most influential actors in a democracy, which IMO seems right.

• My children started school in Oakland Unified School District this week, which has me tuned into elementary education in a new and incredibly intense way. Yes, Ms. Holley! Ask me what’s the best thing about my kids. I will need several more sticky notes, please!

• Recent surveys indicate a) a lot of teachers are thinking about leaving teaching, b) teacher autonomy is strongly associated with teacher satisfaction and retention. All of which indicates that, administrators, if you want your teachers to stick around, don’t do this.