# Could Calculus Be A Better Way to Introduce Kids to Math Than Arithmetic?

It has long been the assumption that students need to learn the building blocks of math before they can solve more complicated problems. Some educators are beginning to question that assumption, saying that it may be responsible for turning many students off math at an early age. In an article written for the Atlantic, MindShift contributor Luba Vangelova writes about a different approach to math education that focuses on the patterns and structures of mathematics, as opposed to computations.

“‘Calculations kids are forced to do are often so developmentally inappropriate, the experience amounts to torture, she says. They also miss the essential point—that mathematics is fundamentally about patterns and structures, rather than ‘little manipulations of numbers,’ as she puts it. It’s akin to budding filmmakers learning first about costumes, lighting and other technical aspects, rather than about crafting meaningful stories.”

5-Year-Olds Can Learn CalculusThe familiar, hierarchical sequence of math instruction starts with counting, followed by addition and subtraction, then multiplication and division. The computational set expands to include bigger and bigger numbers, and at some point, fractions enter the picture, too. Then in early adolescence, students are introduced to patterns of numbers and letters, in the entirely new subject of algebra.

• marisano

Hmm… Where’s the rest of the article?

• Sarvepalli

The article that the review refers to can be found by clicking on the “Atlantic” link in the above review of the article.

• LocalH
• Keri Lamle

I just showed the article to my 19 year old son. He has always been a whiz at math, taking college level math and science classes as a high school freshman. However, DS found Calculus to be challenging. His comment on the article…. “why would you do that to a kid?” and “that’s just way to StarTrek”. As a parent, I wonder… maybe if he had been introduced to Calculus at a younger age it might not have seemed so foreign.

• http://GrowMap.com Gail Gardner

I agree with your son. If arithmetic is “too hard” what do you think their reactions will be to dumping them into Calculus? Most kids get lost when fractions are introduced which is ridiculous because it can easily be taught visually with props instead of in concept.

What needs to change is the conditioning that tells students “girls are no good at math” or “inner city kids can’t learn Calculus” (proved wrong by Jaime Escalante – see the movie “Stand and Deliver”). Parents and teachers need to stop projecting their challenges onto children.

• YJ

I agree that Marhematics is about establishing a system in real life to quantify values. And there’s no better way to do it than by observing patterns. However, instead of introducing Calculus at an earlier age, I find myself asking Why would you want to do that? To achieve subject mastery? For results to develop intrinsic motivation?

As a high school mathematics teacher from Singapore, we have experimented with introducing calculus at a lower level (14 to 15 year olds). With a few tweaks, students do get it. They can do the calculation, and arrive at the right answers. But at such a superficial level that that’s all there is to it. Their emotional development does not lend itself well to appreciating the concepts of limits and the First Principle. And frankly, there wasn’t much of a “flow” with the other topics, which ended in us abandoning the Calculus portions, to be revisited in the following year.

The fact that you mentioned how “the experience amounts to torture” sheds some light on what could be done instead. Making arithmetic a more gradual learning process by exploring various branches like Geometry and Statistics before branching into abstract math topics like Algebra and Calculus would enable students to see the progression from the known to the unknown, and then to the microscopic level. After all, isn’t Mathematics about seeing patterns and structures in life?

• Don Krieg

Uh I don’t think so. The problem here is that we are forcing the kids into endlessly computing. Though calculus is more close to what math is actually about than arithmetic, calculus is an overly complicated subject whose link to the real world is pretty much limited to engineering. That’s culturally as well, why have your kids do engineer work?
I think it’d be better to introduce kids to eculidean geometry, as it’s much more visual and plastic, and comes embedded with the notions of axiom and proof, along with the showing of patterns.
On the other hand arithmetic IS essential to all math, imagine a 10 year old who can’t sum or multiply two numbers, I mean, if we didn’t have to do that all the time, everyday, it wouldn’t be a big deal but…
anyway I feel the greatest flaw in mathematics lies in the fact that we force the kids to drill over simple algorithms over and over, increasing not even the complexity but the size of the numbers they deal with, while shadowing the underlying principles. Then we force them to memorize a listing of numbers as little drones and have them stand in front of class mindlessly repeating “one by one is one ….”

• Me

When are we allowing little children to actually enjoy their childhood? Everything is deemed an educational marathon.

## Author

### Katrina Schwartz

Katrina Schwartz is a journalist based in San Francisco. She's worked at KPCC public radio in LA and has reported on air and online for KQED since 2010. She's a staff writer for KQED's education blog MindShift.