It’s called “number sense.”
In mathematics, one of the core numeracy concepts is “number sense,” which is the perception and understanding of numbers and their relation to one another. For example, we know that 10 is different than 1, and 100 is different than 10. In our base-ten (decimal) counting system, we add a “place” to the left of a number once it reaches the next multiple of ten. When we were kids, we called them by name: “the ones place,” “the tens place,” “the hundreds place.”
However, this sense of “tens-ness” gets thoroughly lost when we start doing things like long-form subtraction. Modern mathematics pedagogues have developed new methods of teaching children how to compute algebraically while preserving and reinforcing number sense in a way that older, more traditional methods do not.
I watch meme after social media meme sail by these days, sometimes conflating 2010s-era “New Math” (sometimes called “New New Math”) with the the 1990s-era Reform Mathematics movement (also sometimes called “New New Math”) and the 1960s-era “New Math” movement, illustrated in a humorous half-parody by Tom Lehrer:
I see pictures like this posted all over Facebook all the time:
The picture is idiotic, as is the sentiment. One attempts to illustrate a process (on the right) and one attempts to show the basic idea without process (on the left). If I showed you a picture of a flat tire and a picture of a changed tire beneath it, it would invariably look simpler than a series of step-by-step photographs illustrating the process of changing a tire. But that isn’t “the basics;” it’s a faulty comparison.
See, adults often have trouble realizing that the universe doesn’t revolve around them. They like to see learning as a process that mirrors the way they learned, and to see children as prototypes of them, instead of as the unique, capable individuals that we critical pedagogues insist (and rightly, truly know) that they are. I wouldn’t ask an adult to unlearn 30 years of understanding how to add and subtract and change an efficacious process to a new, foreign process, if the skill mastery is already there. Can you add? Yes. Does it matter how? No, not especially, so long as it works. Did you learn in a way that provided the best opportunities for you to have the best possible conceptual understanding of number sense?
Probably not. I didn’t.
Does that mean I don’t have number sense? No. Does that mean I do not or cannot have ever-better understanding of number sense? No. But modern mathematical pedagogues (who are rooted in good work, at least) don’t accept as a maxim that all mathematical understanding is or must be the same. There are many ways to approach computation and numeracy, and I find it absurd that Badass Teachers and educational revolutionaries would waste one breath of their time trying to fight against sound teaching methodology. I’m not taking a position that one way is better than another way, but I am suggesting that pedantic adherence to “your way” of understanding numeracy and computation may do your children a grave disservice.
I would much rather people who oppose the Common Core State Standards – and make no mistake, I do, because CCSS is irrefutably married to the Standardized Testing Industrial Complex, and is a recipe for the corporatizing of classrooms not the establishment of effective content standards – spend their time and energy fighting against the real problems of CCSS instead of perpetuating this nonsensical distraction.
Just my two cents. Maybe three, ’cause I really do know what I’m talking about. (If you’re a math teacher, you get a nickel’s worth LOL)