Elementary Student Math Misconceptions

Second-grade students are often taught to line up columns of numbers to add them. This works when they are adding whole numbers. But in third grade, when they add decimals, lining up

numbers can produce the wrong sum if the numerals have different significant digits.

The key is to make sure students understand the mathematical concept of addition, not just the procedure for how to do it.

The following math misconception examples are a result of students memorizing procedures and not actually understanding math concepts.

Example 1

While giving a ‘standardized’ test to a group of students I had never worked with before, one student called me over and asked how to ‘round off’ 65.23. I explained that this was a test and I couldn’t actually teach how to do things. She looked up plaintively and said, “Please just tell me if it’s closer to the 65 or the 23.”

Example 2

If a company can make 500 cartons in .8 hours, how many cartons can it make in 2 hours?

Conrad insisted it was a unfair question since they did not tell how many cartons were made in 1 hour and it could not be solved without that information. Carmen had used 8 hours instead of .8 hours and insisted her answer of 125 cans was correct because only the decimal point was in the wrong place.

Example 3

Today student Sara was angry at me after taking a test on fractions. She said it was unfair for me to ask what 2/3 of 12 was when I had not used 2/3 in an example in class. She said she had studied only halves, fourths, eighths and sixteenths so she could not do thirds.

She said she had memorized the rules and could do the problems from the book, but she could not do such difficult problems as shading in 2/3of 12 squares.

Shade in 2/3 of 12