“I hate math.” “Math is boring.” “I’m scared of math tests.”
You would think students said these common statements, but you would be wrong. These were adults. Of course, my students said these things as well but it really hits home when your eye doctor says he was bad at mathematics. Then you find out in history class that even Albert Einstein failed math and you have to wonder: What is wrong with the way we teach math??
It’s a culture of fear we’ve cultivated, we’ve experienced, and perpetuated. Often, without even realizing it. This culture can’t be changed with common core. It won’t be changed with projects or materials. No matter how much independent help you give each child. The culture can only be changed by you, the teacher. In this article, I give you the top four things you can do right now to start improving the culture in the classroom.
Don’t Avoid Mistakes
So, we all know that when a child makes a mistake we shouldn’t treat him like an idiot. We say out loud, “That’s ok.” But then we quickly show the right way and hope the child can follow it. The child learns that mistakes are something bad, something to be avoided.
We start this lesson early, as young children. Take, for instance, a child learning the hand-eye coordination it takes to put colored rings on a toy. He is nowhere near developmentally ready to discern between the colors and the sizes. He can barely hold the ring steady enough to fit over the post. Whether it’s missing the post or choosing the wrong color, I often see adults “come to the rescue” of the child.
What we need to change, in ourselves, is the idea that placing the wrong ring, the wrong color, or missing the post altogether is a bad thing. Every single time he picks up that ring, he learns a lesson. By missing the post, he learns where the post is.
This is the same attitude we need to carry into the math classroom for the older child.
Mistakes are learning opportunities.
Yeah, yeah. We say this, but what does it mean in the classroom? It means when a mistake is made, you slow down and revere the mistake. Don’t avoid it. Especially those really good ones. The ones logical and interesting, though still wrong. The ones where you see why the child got the answer he did.
You might even say, “This is right!! But for the wrong question.” Then make a point to cross out the question and have the child rewrite it. Give him the power to reverse the process and show why he is great at mathematics.
Here are a few specific things you can do to allow mistakes to become lessons:
- Play Jeopardy.
This one is fun. Jeopardy gives the answer and you are supposed to ask the question. Create a Jeopardy board on the white board by writing answers and covering them up with sheets of paper (placed with tape or magnets). You can have categories to give clues. Reveal the answer and have teams of students try to determine what the question is. If the question is logical, it’s right!
- Play “Where’s the Mistake?”
His one has a huge impact. It starts to teach students to search for mistakes like bloodhounds. Place a math sentence on the board with a common error and ask students to identify it. After they do, follow the question up by asking them to correct the question, not the answer. By going after the question, students are given the power to change their circumstances. Forward or backward, math problems are math problems. They don’t realize yet that in math questions are answers too if you turn the paper upside-down.
· Reward students finding your mistakes.
I don’t mean give them candy. I mean don’t act like a blustering ass if they correct your negative. Don’t get flustered. Say thank you! Say, “Wow I didn’t even see that. Look how easy it is to make a mistake!” Tell them they are helpful and that it’s always nice to have someone watching your back and teaching you things. Put them on the same level as yourself. Model how to respond when mistakes are made.
Stop Correcting Inefficiency
Inefficient does not mean incorrect. Mathematics is a game. It has rules, it has pathways, and it has problems to solve. Nothing bothers me more than when I see a teacher correcting a child for not following the rules simply because the path they were taking was long. Here’s an example:
I know that made math teachers cringe. LOL. Admit it. But it’s not wrong. If you see students start out at that first step, by dividing through with 2, and you STOP THEM…they think they aren’t allowed to do that.
The truth is, they are!! It’s totally legal! No foul made! No correction necessary!
What’s bothering you is that it’s not efficient. You might even be bothered by the fact that they are creating a fraction they have to deal with unnecessarily. You might be reasoning with yourself that this child is horrible at fractions so he shouldn’t be allowed to create ones he isn’t going to be able to solve.
OMG, can you just stop your brain for a moment?
This child, who may be awful at fractions—which, in my experience, about 80% of adults are too—needs fraction practice and has just made his own fraction problem. Huzzah!! We don’t need to force him into drills. He’s willing to do it himself! More importantly, look how much practice he’s imbedded in this one problem! We categorize these in “Two-Step Equations” and, boy, does that drive me insane. Way to set them up for failure before he’s even started. Why would we ever discourage a child who wants to practice more?
In this example, the child followed all the rules and meandered his way to the correct answer. This should be celebrated. If he doesn’t follow a rule along the way, the rule should be corrected. Ideally, the rule should be corrected with materials…not with you…but I’m getting ahead of myself (see next section).
Slowly, over time, the young child learns where that post is by missing it. Slowly, over time, this child will learn to take shorter paths by practicing them. You can elicit this change by asking for a different way to solve the problems. Make sure to ask this of all children as though it is a game. Because…well…it is!
Student: “Did I do this right?”
Me: “Hmm…I don’t know. Let’s check the materials.”
Group of students: “Is this the right answer?”
Me: “How many of you got the same answer? Well if you all agree, it must be correct. Why do you doubt yourself? How can you verify?”
I don’t tell students if they are wrong or right. I slip, trust me. I will say, “This one needs further review.” Fancy way of saying it’s wrong. But I try, really hard, to not be their source of validation. This is actually step one of the next suggestion, “Remove yourself as a source of power.”
After all, I’m not going to be doing their taxes with them as 45-year-old adults. Why should I do them now?
There is a simple way to give students the same power that real mathematicians have. It’s with this process:
When students work on problems together, place them into pairs, teams, or let them choose their own. Solve each problem individually and teach them to come together for this process.
Students compare the results and the process they took. If both the result and the process are identical, they can say it’s “probably correct.”
If either the result or the process is wrong, students need to debate.
Speak of the problem, never personal attacks. Students should propose that their method is correct. Then they should rebuttal their partner’s method. Often students will see their own mistakes when they have to explain their mathematics.
This step requires adult supervision to avoid some problems. Some students are convinced they are correct and convince other students simply with their power of their conviction. Students should always have to explain the mathematics. Also, if you notice a student is having trouble asserting himself—even if the student has the wrong method—assist the child. Make a mistake yourself and be proud of it.
Vocabulary Affects Attitude
Please whatever you do, do not ask students whether they are good enough to do it without the materials yet. You’ll have them running for the hills and they’ll never touch another material again.
Instead of: “Without materials.”
Rather than: “Still needing the materials.”
Say: “Give your hands as much practice as your head.”
Tell them: “The best mathematicians work with their hands and their head equally”.
Students should have methods for resolving the debate. This could be materials, calculators, or answer keys. But, it should not be you! Real mathematicians don’t have the word of God to tell them they correctly solved an age-old math problem. Neither should your students
Which leads me to the last topic…
Remove Yourself as the Source of Power
I walk out of university lectures and classroom observations whenever I see teachers acting like Gods in the classroom. Students are compelled to sit and listen, even when the yodeling jackass in the front of the room is sucking all the air out of the place. I get super irritated when I see teachers demean a child, ignore a child, or just plain talk too long! You aren’t on Ted Talk! You’re guiding children to become awesome adults. Start acting awesome yourself.
Here are some ways to avoid the God-Complex:
- Use small group tables to give small group lessons.
- Keep your lesson to less than 10 minutes.
- Create a game day and participate. LOSE gracefully, and often.
- Teach materials, materials, materials—and let students determine how the rules of mathematics work. Here’s a great reference to material lessons in the Algebra classroom: Michael Waski’s Montessori Algebra for the Adolescent
- Allow calculators when it’s to resolve a debate.
- Intentionally have the students prepare a lesson to teach you. Act like you learned something…you might even have learned something.
- When you see a correct answer, but you don’t recognize the method…have the child teach the whole class. Sit in the student’s seat and take notes. Be his student. Because at that moment, you are