(And how to help students avoid them)
Everyone makes mistakes. It’s inevitable. And that’s certainly true in math. The real learning takes place when teachers can show students where they made a mistake and how to avoid them in the future.
But as a former math teacher, I also know that it’s also important to create an environment where students feel comfortable making mistakes and can talk with the teacher and their fellow students about where they may have gone wrong. Publicly calling out a student’s mistakes or looking disappointed or frustrated with a student’s work is never helpful.
We never want to hear students say
- “I just can’t do this and will never be able to.”
- “I hate math.”
- “Making mistakes means I am dumb.”
ESGI and ThinkFives surveyed hundreds of teachers and here are the top five most common mistakes made by elementary school students.
Order of Operation
Order of operations is a difficult concept to understand even as an adult. How many social media quiz problems do we see that ask people if they can solve a simple short equation (or maybe that’s just me because the more I answer these questions, the more Facebook shows me them).
There are usually two issues with order of operation.
- Many times, a student may get the equation wrong because they confuse one mathematical symbol or operator for another. Certain symbols can look like one another for first-time users. A student can confuse the symbol for subtraction with that of division and the same goes for the addition and multiplication. A student may say that 2 X 4 = 6 because they misread “X” as “+.” It’s important that teachers review the symbols and make sure it’s not a conceptual math issue instead of simply misusing a symbol.
- The most common problem with order of operations is just remembering whatever they are. Many teachers use songs or rhymes to have their students understand the order (PEMDAS). Another example is to use the acronym, “Please Excuse My Dear Aunt Sally.”
- Parentheses are always the first place we look (“Please”).
- Next up is always Exponents (“Excuse”).
- Multiplication is next and we go from left to right (“My”).
- Division follows and again left to right (“Dear”).
- And finally, it’s Addition and Subtraction (“Aunt Sally”).
For many students, fractions are a difficult concept to understand. Children may not see a fraction as a single quantity but rather as a pair of whole numbers. They may compare whole numbers which leads to a complete misunderstanding.
Why is 1/4 + 1/4 = ½?
Early mistakes may begin with not understanding what a numerator and denominator indicate. For some teachers, it helps to visually introduce students to this concept. Presenting fractions in a fun way with items that are common to them such as pizza slices is a great way to start.
Would you rather have 1 of the 6 slices of pizza or 2 of the slices? If I took both, I would have 3 of the 6 slices (or if you’re like me I’d take 6/6 of the slices).
Other teachers use a Fraction Wall to show the sizes of the fractions. They can explain that the number on the bottom means how many parts the whole has been divided into, and the number on the top means how many of those parts are chosen.
Khan Academy or other sites have many great videos and ideas for teaching fractions.
Not Checking Their Work
One of the most helpful skills that teachers can reinforce is the importance of checking your work. It not only shows a possible miscalculation, but it helps students avoid making careless mistakes.
An important part of checking your work is trying to arrive at the answer in a different way if possible. For example, adding three numbers in a row might be rechecked by adding them in reverse order. Or if numbers are being multiplied, a student could check their work by using their answer and using division to arrive at the number in the question.
There are also several other suggestions to help students avoid making careless mistakes.
This seems obvious, but students are often in a rush to finish so that they can move on to something else. Encourage kids to take it slow and pay attention to what they’re doing.
Circle important information
Whether it’s a worksheet or word problems, circling important information will help students know what to do. Circling something in the directions will help them follow them correctly. And this is especially true when you introduce word problems.
Working out their problems on paper or using graph paper is especially helpful. Simple questions might be able to be derived in one’s mind, but solving it on paper can expose a computational error.
Regrouping is when students make groups of ten when performing operations such as addition or subtraction. This typically takes place when an answer is larger than 10 or we need to subtract from the tens column.
Example: 15 + 17. Adding 5 + 7 gives you 12, which is one ten and two units. Regrouping carries the ten into the tens column and leaves the two units. The answer is 32.
Here are a few tips in teaching regrouping.
You can use a manipulative for this. Have students count out the units and exchange them for tens. Or, in subtraction, have them exchange a ten bar for ten units. This will help them see and experience the regrouping.
Visuals also help your students understand regrouping and help children move away from the help of manipulatives. Using an activity sheet or online visual so they can begin to see the calculations is especially helpful for visual learners.
After children add and subtract using manipulatives and visuals, you can teach the traditional steps to perform these operations using just pencil and paper. By this point, students will have internalized the process of regrouping in math.
Adding and Subtracting Integers
It may be the most basic mistake on this list, but that’s probably why it’s #1.
Applying mathematical functions to more than 2 numbers can get tricky for some students and can be a reason for frustration. When students add numbers such as 13, 26 and 7, some may incorrectly place 7 in the tens place which results in a wrong answer.
There are a lot of great resources and videos for teaching addition. Here’s on suggested way:
- Introduce the concept using countable manipulatives.
- Transition to visuals.
- Use a number line.
- Show students counting up.
- Help students to find the ten.
It also helps to have Number Talks with students. This is a great way to break this strategy down. Model it first, and then ask students to talk through their approach to a question in the same way.
What are some of the most common math mistakes you see your students making?