Why is Rounding Whole Numbers So Difficult?

While scrolling through my Facebook timeline, a post from one of the teacher groups caught my eye. The post was a teacher asking the question, “Why is rounding so hard? What do you use to teach rounding?”

The first thought that came to my mind was it’s not the rounding that’s difficult, it’s the disconnect from the prerequisite skills for rounding that causes students not to grasp the full concept of rounding,

If you follow me on social media, you know that I’m a National Board Certification Candidate in Early Adolescence Mathematics. As I think about the question why is rounding so hard, the National Board Certification Math Standards come to mind more specifically Standard II.

Among all of the other qualifications of an Accomplished Math Teacher under this standard what stood out me was this:

“To help students acquire and then build on the ideas, methods, and skills that underlie mathematics; to see relationships among these elements; and to make significant applications of them, mathematics teachers must have a broad and well-integrated knowledge of these underlying ideas, as well as the methods and techniques of mathematics.”

This just means that you have to know math in order to teach math. In addition to knowing the math, you have a strong pedagogy to teach the students to build and connect the prerequisite skills to other math concepts.

While the teacher’s math content knowledge is one part of why rounding is difficult, the other piece are the instructional strategies that teachers choose to use to teach rounding.

Why does the math content knowledge matter?

The content knowledge of a teacher matters because a math teacher who only knows the abstract process of mathematics will not be able to reach all learners. 

National Council of Teachers of Mathematics President (1998-200), Glenda Lappan wrote in her President’s Message in the NCTM News Bulletin, November 1999:

“Our own content knowledge affects how we interpret the content goals we are expected to reach with our students. It affects the way we hear and respond to our students and their questions. It affects our ability to explain clearly and to ask good questions. It affects our ability to approach a mathematical idea flexibly with our students and to make connections.”

When I think about the teacher’s question, why is rounding so hard? I would have to disagree because rounding is not hard. I’ve personally had good success with teaching rounding to my students. I also understand that rounding is NOT an isolated skill. Most teachers try to teach five or more to raise the score nonsense to their students in lieu of teaching them the math.

I’m not saying that this method doesn’t work, but most students and teachers can’t explain why it works. Not to mention, if you’re a fifth-grade teacher like I was and have to teach rounding decimals to students who only know this rule. It’s a nightmare!

Are your instructional strategies part of the problem?

One of the battles that I have had to fight with my school administration were about the instructional strategies I chose to use to teach certain concepts. They would visit my classroom and then based on their limited math content knowledge suggest that I use an instructional strategy that doesn’t support the vertical alignment or progression of math skills.

When I choose to use an instructional strategy, it is based on the vertical and horizontal alignment of skills. I also look at my students’ math deficits. Sometimes an instructional strategy that works for one group of students may not work with another group of students you teach because the students may not have the prerequisite skills needed for that particular strategy.

Choosing an appropriate instructional strategy happens to be one of the biggest issues with teaching rounding. Oftentimes teachers choose instructional strategies that don’t support the curriculum alignment of skills. Instead of using place value concepts and a number line to introduce rounding many teachers rely on the circle the number to right and if it’s more than five go up. What you fail to understand about teaching this is that it creates the misconception about how much goes up. This is the place value connection to rounding that students need to make sense of in order to be successful when it comes to rounding whole numbers.

What is needed to effectively teach rounding?

When teaching students to round whole numbers there are five actions that teachers need to take:

  1. Identify the prerequisite skills needed to learn how to round.
  2. Differentiate between rounding and estimating. 
  3. Cement students’ understanding of friendly numbers when necessary.
  4. Use halfway points, number lines and segments of number lines.
  5. Connect 10, 100, and 1,000 more to rounding to the nearest tens, hundreds, and etc.

Using number lines and line segments will provide the students with a sound conceptual understanding of why the five on the number line is important. Teaching rounding whole numbers this way also supports the vertical alignment of skills by allowing the teacher who teaches rounding decimals to add decimals to the number line. The teacher could then easily extend the students’ understanding of the halfway point to halfway points with rounding decimals.

Teaching rounding doesn’t have to be hard for you. If you’re willing to increase your math content knowledge and choose instructional strategies that build your students’ conceptual understanding of rounding, then teaching this concept will be much easier.

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