upper waypoint

Embracing Incorrect Student Thinking to Improve Learning

Save ArticleSave Article
Failed to save article

Please try again

 (Mark Koehler)

Earlier this year my students were teaching each other about taxes. One student was struggling to explain how a progressive tax system works.  He was getting really upset with himself so I went over to him and said, “You’re doing great. It’s a hard concept to explain. Teaching is hard; be patient with yourself.”  At that moment, Stephen walked over, leaned in, and said, “Teaching isn’t hard. Teaching is so damn easy.”

So far in this series (How Do You Teach Thinking?How Emotions Can Support Critical Thinking) I’ve focused on student thinking. This post is about teacher thinking and how hard it is to get good at the important, but crazy challenging job of thinking about other people’s thinking – lots of people, and often on the fly. Elizabeth Green in her book “Building a Better Teacher” says this is what makes teaching so complex.

Magical (Thinking) Moments in the Classroom

This year I worked with some colleagues to create a vision for more effective teacher learning and professional development. In our discussions, we talked about those important “magical moments” that occur during a classroom discussion or conversation that we wish we could capture on film and analyze. These are the moments when how the teacher responds shapes student thinking for better or worse.

Researchers and teachers alike have spent quite a lot of time investigating, researching and dissecting these types of moments. A classic example of this phenomenon is an incredibly cool teaching moment involving Dr. Deborah Ball as she teaches prime numbers in her elementary classroom. A student named Sean makes what appears to be a mistake when explaining what makes a prime number. Dr. Ball’s response to this student gives me chills every time I watch it (even though it’s about elementary school math and I teach secondary social studies!) She allows the student’s thinking process to become the class lesson and presents Sean’s explanation as an idea worthy to be examined by the class. This magical teaching moment transformed how I thought about teaching. It deepened my appreciation and interest in student “mistakes” and “sort-of right” answers. Instead of correcting them and moving on; these are the moments to embrace and encourage. Often, they bring deeper and wider knowledge of the content to class.

Since my colleagues and I discussed these important moments earlier this year, I’ve become a little obsessed with creating and capturing them in my class. It’s hard to explain but I can feel the moment arrive. It’s a little like a mix of getting kicked in the stomach while simultaneously seeing a celebrity you love eating at the same restaurant as you. Sick and excited all at once, and trying to make the most of this opportunity while all eyes are on you.


Deborah Ball makes utilizing this moment and saying and doing the right thing to unlock student thinking look effortless. But my daily experiences tell me how getting it right is incredibly hard. It is also really fun. Fun to lay witness to learning in real time. I want to tell the story of one such moment in my classroom.

The Anatomy of a Moment

I had just finished teaching about market equilibrium and the role of prices in the market.  Students seemed to get it but I wanted to give them one more chance to review the concept so we worked on a practice problem around setting the price for a box of girl scout cookies. The students had to graph the numbers and choose the best price for a troop to sell the cookies.  Essentially, I was looking for them to choose the equilibrium point ($5) on the graph because that is the place where demand and supply are equal and everyone feels ok about the transaction. In a market, the equilibrium point is king. Everything looked good at first. Students graphed and then wrote.  I felt good but want to quickly check for understanding so I called on Andrew to share out. He says confidently “4 dollars is best price.” I re-explain equilibrium and look for someone else to try and explain why $4 is not the best price (answer: $4 will cause excess demand for girl scout cookies-too many people want to buy them, but only a few will supply them at that low of a price.). Stephen, yep-“teaching is so damn easy”, quickly jumps in and complicates things further by saying “it’s $3 – people like low prices. 3 dollars is best price. You’ll sell out quick and make hella money.”

This is the moment where time stood still. What I say next to the 35 students in front of me matters. Inside my head so many questions and decisions about what to say next swirl around at what feels like is the exact same moment.  Here they are:

Who else is confused in the room? One kid getting the answer wrong might be an outlier but two…who else misunderstands equilibrium in this room? Do I stop and go over the concept again even though I see a chunk of students look surprised that the answer has been given incorrectly two times? One student has already put her head down because she understood equilibrium point the first time. What is a new entry point into the discussion that will make the concept stick for the students who are struggling yet will also broaden the depth of knowledge for the the students who currently get it? What is the magical real life example?

The very next concept I teach is about price controls where I am going to complicate the concept of equilibrium. I can’t just say to the class “the equilibrium point is always the answer when setting prices” because I am about to teach how, in some situations, prices are intentionally set below equilibrium-the exact thing I am about to tell the student is wrong in the girl scout scenario! I don’t want to give an absolute answer/rule about equilibrium but I don’t want to be unclear either.

How can I correct Stephen without making him feel dumb in front of the class? Stephen is sensitive. Sometimes, he tries to mask it but his eyes give him away. There have been a few times students have made gentle teasing remarks to him and he lashes back. I don’t want him to shut down because then it doesn’t matter what I say. But, if I don’t clearly say that his answer is incorrect then I confuse other students.

Oh yeah and the bell is going to ring in six minutes. Spring break is in one week and I want to give their exam before break. Every moment in the next week is planned out. So, I need to get it right and get it right quickly.

Ok. Ok. How did I respond to Stephen?  I made up a quick simulation with real numbers. I made him a girl scout cookie supplier (he has told me countless times that he is a real businessman) and told him that it costs him $3 to make the cookies. If the girl scouts only charge $3 a box, they can only pay him $2 box for the cookies because girl scouts need to make some cash too! He loses $1 every time he sells a box to them. He said, “Ahhh-I forgot about the supplier. The price needs to account for the cost of the actual cookie maker not just the girl scout and the customer. Cookie man needs to get paid so he will make thin mints for the people!” We all laughed and I wrapped class with a question which teased the price control lesson the next day.


Teaching is NOT easy. The pressure of this moment is real.  And these moments happen many times every day, in every classroom. How teachers think matters!


Did I get it right? I don’t know. I’m still thinking about that.

lower waypoint
next waypoint