Even Teachers
Make Mistakes

We all make mistakes. Even teachers do. I've seen spelling mistakes on teacher-made bulletin boards, tests, and newsletters and usually I say nothing. I've watched a math teacher make a careless mistake during a mini-lesson, and no one said anything during the long minutes that the mistake remained on the chalkboard. I've wondered, "Do the students not notice? Or do they think it's disrespectful to correct the teacher?"

Until last year, I managed to get through many years of teaching without any student pointing out a mistake I had made in math or anything else. I came to think of myself as nearly infallible. Last year, when a student caught me in a careless math mistake for the first time ever, I was genuinely surprised, but I laughed it off and said, "This is amazing! This is the first math mistake I've ever made!" From that point on, the students took it as a friendly challenge to catch the math teacher making another math mistake. By the end of the school year, my most alert class had caught me in four or five mistakes. Some of my other classes never noticed one mistake by the end of the year.

That all changed this year when the first student who caught me in a mistake asked in fun, "Do I get a prize for that?" I had a jar of small prizes left over from a Math Family Fun Night, so I was happy to oblige. I had no idea that the prize incentive would inspire my students to pay rapt attention to my every word and chalk mark! And I certainly had no idea how many mistakes I actually do make, until my students started pointing them out to me.

I now throw myself open to your questions.

MATH CHAT FAQS

Why would you want to encourage students to catch your mistakes? Isn't it embarrassing? Doesn't it erode your credibility or authority?

• When a student catches the teacher in a mistake, it is a moment of friendly celebration for the whole class.
• Yes, sometimes it's embarrassing. I'd rather be perfect! But since I'm not, I think my students respect me for being able to laugh about my mistakes.
• When students see teachers taking correction in stride, it sets a positive tone for everyone to accept correction with good grace and humor.
• If I've made a mistake, I'd rather know about it and clear it up than confuse anyone.
• I'm impressed with what close attention my students pay to my every word and chalk mark!
• The students have become more comfortable about speaking up when something doesn't make sense to them or they have come up with a different answer than I have, because sometimes they suspect a mistake on my part might be causing the confusion. Whether it turns out to be my confusion or theirs, it's great to have a classroom environment where students are eager and increasingly confident taking risks.

You're a math teacher -- you shouldn't be making math mistakes! What kinds of mistakes have your students caught?

• Typically, mistakes happen when I'm explaining something while writing on the board, and my words don't match the numbers I'm writing or I make an oversight while I'm multi-tasking. For example, when I was transferring students' heights from paper to a white board, I accidentally left off the inch symbol from one of the measurements, and one of my students noticed a moment before I did.
• Every now and then I've made a careless mistake when marking quizzes or tests. (Getting a prize for catching a scoring error can help redeem a disappointing grade!)
• A few times, I've started to tell a student that their oral answer was incorrect, and then I've realized the student is correct. Even if no one else has challenged me before I catch myself, I give the original student a prize.
• Occasionally, I've been astonished to be caught doing bad math! Again, it comes from sheer carelessness while I'm multi-tasking. It happened twice in the past week:
  • I had just cautioned my students to be careful when converting a fraction to a decimal. For example, 3/8 means 3 divided by 8: A few students had accidentally reversed numbers: . I could hardly believe it when I made the same mistake within minutes of pointing out this potential pitfall! I realized my carelessness within moments, but too late -- they already had caught me!
  • When we were going over the answer to a multi-digit multiplication problem, I multiplied the digits in the ones column and said, "6 x 0 = 6." Whoops! Again, my students noticed my silly mistake instantly.
• Sometimes my work has been incomplete. For example, on a quiz I asked students to find the 6 factor pairs for a given number, and one of my students quickly realized there were actually 7 factor pairs for that number.
• Once, it was a mistake of ignorance. I'm conscientious in my lesson preparations and I'm usually well-informed, but recently a student was better-informed that I was. We were comparing the sales tax on meals in D.C., Maryland, and Virginia. I had double-checked the sales tax rates online. I learned that Virginia had recently raised its sales tax from 4.5 percent to 5 percent. I learned that DC's meal tax is 10 percent, considerably higher than its shopping sales tax of 7 percent. As a resident of Maryland, I was quite confident of the tax rate (5 percent) but I double-checked on a 50-state chart to be extra-sure of the accuracy of my handouts and my lesson. So I was quite surprised when one of my students informed me that Maryland's sales tax had risen to 6 percent during the previous week. I vaguely had heard that the tax rate would be rising, but I had not known the effective date and had forgotten all about it; and the online tax chart I'd used was out of date. I congratulated my student on being so well-informed. He asked hesitantly if he would get a prize (we didn't have a precedent for the teacher's ignorance!). I said, "By all means, if you know more real life math than the math teacher does, you get a prize!"

Do you give prizes if the students catch mistakes in written language?
As a math teacher, I give prizes only for catching math mistakes. I want to keep the focus on math, and I don't want to start debating whether or not items in a list should be capitalized (for example). But it would seem appropriate for a teacher of multiple subjects to give prizes for catching mistakes in any of those subjects.

Do your students call out or raise their hands to point out a mistake?
While our general participation policy is to raise a hand and wait to be called on, students may call out if they catch a mistake. That's part of the fun. Otherwise, sometimes I would be able to catch my own mistakes before turning around from the chalkboard to call on raised hands.

I'm assuming that it's your most talented students who catch your mistakes... right?

• I've been surprised and delighted that catching the teacher in a mistake has been the grand equalizer. It's all about paying attention, and some of my less able students pay much closer attention than some of the students who think they know it all already.
• Sometimes it's about confidence, too. There have been times when a mistake sat on the board for many long minutes before someone raised a hesitant hand to say, "This doesn't quite make sense to me," and it turns out to be a mistake on my part. Then other students will pipe up, "Oh, I wondered about that too, but I thought I was just still a little confused." Sometimes, it is the less able students who dare to ask for clarification when they don't understand something.

What do you do if nearly the whole class notices a mistake as soon as you make it -- do they all get prizes?
In the hubbub when it seems that nearly the whole class has noticed a silly mistake of mine, I usually don't have a clue who caught me first, but the students nearly always agree on which one or two students spoke up first. If it's a tie, they both get prizes.

Do students mind if some students get several prizes over time and others don't get any?
They don't seem to mind at all. Also, two of my classes enjoy singing a silly song when I'm caught in a mistake, so everyone gets to share the moment. (They sing the "Spider Pig" song from The Simpsons, which in its nonsensical lyrics turns out to be quite a fitting way to celebrate a teacher's silly mistake!)

What happens if your students catch a substitute teacher making a mistake?
A substitute teacher apparently mixed up two related math terms repeatedly while covering my classes. She duly noted which students should get prizes upon my return. I told my classes I wasn't going to be held accountable for another adult's math mistakes; they understood and said they had still had fun singing the "Spider Pig" song so many times. I'm glad she was a good sport about it, but you might forego the silly celebrations if you don't want to risk rattling a substitute.

What kind of prizes do you give out?

• Pencil top erasers in a fun shape have been a big hit. We've used the "Foohy" brand, in the shape of monkey heads. They are festive, silly, functional, and inexpensive. A student can quietly enjoy and "advertise" his or her prize (or multiple prizes, in different colors) without distracting others. I bought a large quantity online for roughly 10 cents apiece.
• Consider other inexpensive prizes or acknowledgements, such as: a more conventional pencil-top eraser, a decorated pencil, a sticker, a light-hearted certificate, an origami animal or box, or the student's name or photo added to a small classroom display.

In addition to all the benefits mentioned above, opening up myself to my students' correction has helped keep me on my toes. Catching me in mistakes has not been just a grand equalizer for the students -- it has been an equalizer for all of us. We all make mistakes. We're all in this together. We all can take our mistakes in good humor and benefit from friendly correction. Those are fine lessons to learn, along with the math lesson of the day.

About the Author Wendy Petti is the creator of the award-winning Math Cats Web site, author of Exploring Math with MicroWorlds EX (LCSI, 2005), and a frequent presenter at regional and national math and technology conferences. She teaches grades 4 and 5 math at Washington International School.

Article by Wendy Petti
Copyright © 2008 Education World