Thursday, February 25, 2016

Robo Versus the Subtraction Algorithm

Lately, I've seen many of postings on social media about using the following method to solve subtraction exercises:

Well, parents are outraged. And rightly so, but I feel for the wrong reasons.

Many of parents feel this is Common Core's fault. That the new standards are forcing this obscure form of subtraction onto their students and it doesn't allow parents to help with their students' homework. On the contrary, it has very little to do with Common Core. The Common Core State Standards (CCSS) don't necessarily ever state the WAY something should be taught, rather it promotes conceptual understanding; which is exactly what this model is trying to do!

This model of subtraction clearly shows what subtraction is really about: the distance between two numbers. This is vastly different from what most American students learned back in their elementary school years:

The wonderful (or dreaded) subtraction algorithm!
And don't get CCSS wrong, it does actually promote it! In fact, it's a standard! (Check for yourself!)
The problem with the traditional algorithm is that many people don't know exactly how it works. They just know that it does work. And as a budding mathematician and high school teacher, this bothers me. But now it has become an epic battle!

Maths is about recognizing patterns and understanding how they work. All the way from arithmetic to category theory. We want UNDERSTANDING! But how can understanding be promoted if...well...we don't understand how things work!

I see the flaw in the "new way"s design. It seems to promote algebraic thinking before students even know what Algebra is (Is that such a bad thing?). It's not necessarily that the "new way" is hard to understand, it's just represented in the wrong fashion. There are definitely other ways to represent subtraction. For instance:

This diagram shows exactly what the "new way" is trying to get at except it uses a number line, which is always more mathematically viable than any algorithm...right? Also, I firmly believe any parent, despite the fact that they may not have seen it this way, would understand exactly what the problem is asking of them. It's a win-win! Theoretically, of course.

Also, there are plenty of other way to understand how subtraction works! We aren't just limited to algorithms. In fact, algorithms make math uninteresting and, in many cases which I've seen, deter the students' understanding of what is going on mathematically.

And not to be limited to only two ways to subtract, here are a few more representations of what subtraction could look like!

Subtract the same large quantity from each to get smaller quantities!

Think of subtraction as the inverse of addition. So 24 plus what number is 43? DANGER: still a promotion of algebraic thinking! But students do seem more comfortable with addition than subtraction.

Use base ten to your advantage! This is actually the more visual representation of how the standard algorithm works. And perhaps could be more effective than the algorithm! Given that your child knows how negative numbers work, of course.

Happy maths!



  1. Well said! Can't wait to see you tackle the infamous division/fractions algorithm!

  2. I'll do my best for ya, Ben! We'll see how it goes.

  3. Always crunching times I question the purpose myself if students don't understand the concept behind any algorithm displayed. Thus, we have the shifts to keep in mind. I agree that algorithms are necessary, but students need support as to why they work. Isn't math supposed to be flexible?

  4. Exactly. One thing I have noticed in my short tenure is that the definition of many terms are being thrown to the wayside. Even the most elementary of ideas, such as subtraction. I don't want to make math a game of vocabulary but the CCSS shouldn't be the reason why students now know how subtraction works! It's ludicrous!