I’m on a mission. And I invite you to join me.
I’m on a mission to tear calculus down from its ivory tower on the math landscape. Even if you don’t know calculus, you can still join me because this mission is also for you.
Here are a few myths that I would like to dispel on my mission.
Myth #1: Calculus is hard.
My mission is about convincing people that calculus is not hard. The math behind the calculus can be hard to master. If you are not fluent in algebra and trigonometry, then it can be hard to do a lot of calculus by hand, the old fashioned way when we didn’t have computers and watched black and white televisions. But calculus is attainable even if you are not fluent in high school algebra, geometry, and trigonometry.
To believe otherwise does a disservice to calculus and to our work creating the mathematically literate world we are trying to create.
The truth: calculus is joyful, insanely wonderful and powerfully useful. Calculus allows us to divide by zero while also letting us find the sum of an infinite list of numbers. Calculus resolves the tug of war between the infinitesimal (think “zero-ish”) and the infinite with numbers like 6 or 1231 or -7,000,000. Calculus finds the average in the infinite. And that this is just the tip of the iceberg of the awesomeness of calculus.
We don’t need to know a lot of algebra or geometry to appreciate the problems that calculus attempts to solve. It certainly helps, but it’s certainly not necessary.
Leading us to…
Myth #2: You need to study 12 years of math before you can study calculus.
Because calculus is not hard, my mission is also about convincing people that elementary and middle school students (and their teachers) can comprehend and appreciate the problems that calculus solves.
….aaaaaand welcome back!
If you don’t know about integrals, you may not see how this lesson is a gateway for third graders to think about a key calculus concept. Calculus allows us to find the area of odd shapes (like puddles or lakes) and the length of funky curves (like the perimeter or “shorelines” of those puddles and lakes). It does this by dividing up curved area into smaller and smaller polygons and curved lengths into shorter and shorter line segments. This is what integrals are all about. We don’t need to cloud that all up with algebra or geometry.
In Mark’s activity, students can see that smaller shapes lead to more accurate estimates. It’s evidence that you don’t need to know much math to understand the calculus concept of an integral.
Why We Should Dispel these Myths.
Many of us in math education aim to lower “math-phobia” for our students, for our colleagues, and for the regular folks walking around the street who self identify as “not a math person.”
Putting calculus on a high pedestal and keeping it out of reach of the masses only increases this phobia that calculus is something mysterious and dangerous. Furthermore, it also strengthens the resolve of “non-math people” that calculus is certainly not for them.
Calculus is worthy of revering and adoring, but putting it in a sacred space where the worthy can come worship only after 11 (or 12 or 13 or 14) years of suffering through the toils of “lower math” means denying access to many math students, young and old alike, of its joyful beauty.
These myths create an access and equity issue. They create artificial gates that deny access to upper level math thinking for too many students and adults. Dispelling these myths is an act of social justice.
My Mission: Calculus for All
On my mission, I’m asking one key question: How low can we lower the calculus floor to increase access for all?
In other words, to what degree can we remove algebra and geometry and still provide a meaningful entry point in to calculus? How can we shift away from “math fluency” and toward “math intuition” so that all students can play and experience the joy of calculus?
We need to stop thinking about what our students can’t do because they don’t know. Instead, as Mark suggests, only when “we see our students through an asset lens, [do we] believe they are capable, and our students see themselves and the subject in a much more positive light!”
At the very least: Once someone knows area, they can think about integrals; and once someone knows slope, they can think about derivatives. Can we go even lower?
Join me in the cause to bring calculus into the elementary and middle grades. How low can we lower the floor together? This invitation extends to all, regardless of how much calculus you may or may not know.
I’d love some feedback on these Desmos lessons that I created (especially if you don’t know calculus!!). Please play with them. Are there ways I could lower the floor? Are they accessible to students with minimal math fluency knowledge? How early (grade level) could these lessons be taught?
- This lesson asks students to ponder about the area of puddles (much like Mark did but without manipulatives). You can see the teacher dashboard here and try it out as a student here.
- This lesson asks students to ponder about the steepness of a point on a curve (derivatives). You can see the teacher dashboard here. And you can try it out as a student here.
If you do know some calculus, what classroom resources and lessons (like Mark’s) have you used to teach younger students about calculus?
I found this article published by NCTM in 2010 to be a useful read as well about calculus in the middle school grades. What other articles have you found that we should read?
Help further the conversation with me in the comments section or on Twitter @mathgeek76.