Resources mentioned in this episode:

Fluency in subtraction compared with addition by Constance Kamii, Barbara A. Lewis, Lynn D. Kirkland

How to Make Subtraction NOT so Hard video

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Welcome fellow Recovering Traditionalists to Episode 86.  Today we are looking at Why Subtraction Is So Hard.

The topic of subtraction has come up a lot recently in my life and while I was digging into some research I came across an article by Constance Kamii, Barbara A. Lewis, and Lynn D. Kirkland titled Fluency in subtraction compared with addition.  As I was reading through it, I found a section that was thought provoking and I wanted to share with you.

On p. 41 they write:

“The educational implication of this research is that we need to deemphasize fluency in subtraction in the primary grades and emphasize addition. Our reason for saying this is that if children become fluent in addition, they will later become fluent in subtraction. However, we recommend giving plenty of word problems involving subtraction (as well as ‘‘multiplication’’ and ‘‘division’’). The reason for this statement is that first and second graders (as well as many kindergartners) are perfectly capable of developing the logic of subtraction, multiplication, and division (Kamii, 2000).”

I’m a proponent of Cognitively Guided Instruction.  I’ve talked about their research in other podcast episodes, but if you aren’t familiar, their research was about letting kids explore and build understanding of the operations through contextual math problems as a path towards fluency.

So many educators see their students struggle with subtraction fluency (or even addition, multiplication, and division fluency) and yet what Kamii, Lewis, and Kirkland are saying here (and is backed up by the CGI research) is that we need to deemphasize the focus on fluency.  They are saying we jump too quickly into trying to develop fluency and kids don’t have a basic understanding of what subtraction actually means. How we do that is a much more in-depth topic. 

We know the reason subtraction is so hard is because they don’t fully understand it because we are focusing too much on making them fluent without building understanding.

To get us started I put together my thoughts about how to make subtraction be NOT so hard for students in a recent video I did.  In that video, I gave three things we can do to make subtraction easier and better understood:

#1: We actually need to de-emphasize subtraction fluency

#2: We need to spend more time building addition fluency (true fluency, not memorization)

#3: Emphasize the relationship between addition and subtraction

I have more videos coming about subtraction over the next few weeks, so if you aren’t already subscribed to my vlog, make sure you sign up at

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As you start off the school year, I want you to keep in mind what is really important as we're trying to teach mathematics to our students.