Analyzing Math Mistakes

Look at the following multi-digit multiplication problems and see if you can tell why each one produced the wrong answer. I’ll wait…

Okay, so did you figure it out?

• Fig. 1 represents the most common error made when multiplying by a 2-digit number. The student did not adjust for place value when they multiplied using the 4 in the 10s place. This error is easy to spot. First, you don’t see a 0 in the 1s place of the second product. Second, the result is always unreasonably small.
• Fig. 2 is an error I have been noticing more often, and it only occurs when there is a 0 in the top factor. I’ve also noticed that students typically only make this error when multiplying by the 10s digit. Notice that when the student multiplied 3 x 8, they properly regrouped the 2 tens. But when they multiplied 4 x 8, they regrouped the 3 all the way over to the hundreds place. You might look for this error when you have a kiddo who multiplies correctly pretty consistently misses a problem.
• Finally, another 0-in-the-middle problem. For some reason, the 0 in the middle just throws kids off. In this fairly common error, instead of adding the extra tens, students multiply by the regrouping number.

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Which brings me to my next—and really important—point. When you look at student work, focus on why a problem was missed instead of simply marking it right or wrong. Treating all errors the same does students a real disservice, because different mistakes call for different instruction.

Too often, small reteach groups are formed based only on which questions students missed. Looking more closely at their thinking allows us to target the actual misunderstandings and provide instruction that truly moves learning forward.

As you begin each unit of instruction, it helps to know the most common types of errors students make and to proactively address those misunderstandings in your teaching. One excellent resource for this work is Math Misconceptions, PreK–Grade 5, which highlights common student errors and offers insight into the thinking behind them.

Finally, let’s bring students into the work of error analysis. When students examine and discuss mistakes, they strengthen their own analytical thinking and become more aware of common misconceptions. I’ve created a Ticket Out that you can use directly with students, and it can also serve as a template for creating additional error-analysis problems of your own. Download your copy here.

Focusing on student thinking—before, during, and after instruction—allows us to address misconceptions intentionally and support deeper mathematical understanding.