Math class goes like this: Teachers give problems; students do problems; teachers give the answers. Teachers give more problems; students do more problems; teachers give more answers. Repeat. Eventually, students get a grade. And then they know if they are good at math. My students know this is how it is by the time they start middle school. But in my class it doesn’t work that way. Sure, I give problems, and yes, students do problems. And I have answers, but I keep them to myself. Knowing their answers make sense has to come from students themselves. My job is not to let them know whether they are right or wrong, but instead my job is to convince them that they have power and control over their own problem solving.

This may seem strange. You may wonder, “How will the students know they are right if the teacher doesn’t give the answers?” Here’s what I wonder “The last time you had to figure something out, how did you know you were right?” I’m guessing you probably didn’t find someone in a position of authority and ask them to look it up in an answer key to confirm that you are a good problem-solver. Genuine problems come our way without solutions. If we had solutions, they wouldn’t be problems. I’d be willing to bet you did one of the following as you solved the last problem mattered to you:

- You didn’t what do do and you talked it over with your friends.
- You slept on it, hoping it would go away and woke up ready to work on solutions.
- You had an idea, tried it out mentally, and satisfied it might work, you took action.
- You had an idea, shared it with a trusted friend or co-worker or family member to make sure it made sense to them too, and if it didn’t, you adjusted accordingly.
- You tried your solution, saw it didn’t work, learned from your mistake and tried something else instead.

My math class offers students the opportunity to do what we all do when we have problems. And if they knew I would provide answers as soon as they get stuck, the game would be over. They wouldn’t that they are in charge of solving the problems that matter to them.

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Yes – this is how we hand over mathematical authority to our students. I see the same process happening in my classroom when we don’t go over answers to thought provoking problems. The students have to make a case for their answer in what I call “The Court of Math.” You can’t just walk into a regular court and announce that your client is innocent and rest your case… you need to justify your argument. Same applies in my math class. The students are the lawyers, judges, and juries. And if we walk away with the wrong impression one day, you can bet we’re going to come back the next for a closer examination.

But first they have to believe in their answers.

Fantastic article. As these kids become our next employees, knowing how to critically think and solve problems is the number one skill set they have to have. Like Mr. Olmsted, my Dad used to hold a court of law at home (he was a lawyer). You couldn’t go to him to say “She did it, not my fault.” You had to justify your case with facts and examples. Inevitably that would cause the other one to realize both sisters were in the wrong 🙂

Thank you for what you both do to teach our kids these important foundational skills.

You don’t have a re-blog button, so I have posted a link to your post on my site.

Your message needs to be shouted from the rooftops !

Each day, my math class starts out with kids in teams. They are to correct their homework. By “correct”, I mean they have to see that they all came up with the same sollution. If not, the expectation is that they argue; not the “did so/did not” variety, the “this is why I think you are mistaken” kind. It is nice to see that there are other math teachers who recognize the power of practicing math.

We spend a lot of time explaining answers in my class – rather than focusing on the solution, we focus on the strategy. This approach has made my classroom a comfortable place for all students to share their thinking and approaches. I’m going to add in your idea of not confirming their answers – thanks for the brilliant idea!