Why do we have to only get to calculus or pre-calculus concepts so late and why is it so extreme like it is all or nothing? There is plenty in Applied math in calculus that doesn't hing on algebra. Children natural love pattern recognition and we don't teach anything pattern based till we have beaten them into boring show your work work sheets?

See (A Mathematician’s Lament by Paul Lockhart) http://www.maa.org/external_archive/devlin/LockhartsLament.p...

"In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soulcrushing ideas that constitute contemporary mathematics education."

> Rigor

My trigger word!!! Rigor, the most hatred word in all of education philosophy!!!!

> Three Dirty Words are Killing Education by Deb Jensen

RIGOR VS. RELEVANCE The second problem term is rigor (also known as “high” standards). The term is associated particularly with college readiness. The term might call up images of learned individuals from the 1800s, but today's rigor is imposed artificially — it requires only more algebra or more credits. While the mind needs information to build beyond the concrete to the abstract, much of the random information is actually screened out.

http://journals.sagepub.com/doi/full/10.1177/003172171009200...

Maths is not pattern matching. There's a lot of beauty to be had in playing around with numbers; some of the biggest, deepest unsolved theorems of mathematics can be expressed so that fifth and sixth graders can understand them. Combinatorics and probability can be easily taught to kids, and even the basics of abstract algebra can be expressed in an easily understandable way.

These topics are much more fascinating than mere calculus could ever be, but this requires people to stop viewing mathematics solely as a tool, and start viewing it as a way to reason about the world.

Also lost 20 minutes on this article.

https://betterexplained.com/articles/a-gentle-introduction-t...

A note on rigor (for the math geeks) I can feel the math pedants firing up their keyboards. Just a few words on “rigor”.

Did you know we don’t learn calculus the way Newton and Leibniz discovered it? They used intuitive ideas of “fluxions” and “infinitesimals” which were replaced with limits because “Sure, it works in practice. But does it work in theory?”.

We’ve created complex mechanical constructs to “rigorously” prove calculus, but have lost our intuition in the process.

We’re looking at the sweetness of sugar from the level of brain-chemistry, instead of recognizing it as Nature’s way of saying “This has lots of energy. Eat it.”

A part of the push for rigor in calculus is being able to prove results instead of appealing to intuition. They are both important aspects of mathematics when working together (often intuition guides a slower, rigorous, methodical proof), but we don't want people relying on intuition where a proof is necessary. This kind of critical thinking and logical reasoning are both important cross-disciplinary skills that almost every field requires.

By "any rigor at all", I meant how do you express the concepts of differentiation without knowing how to manipulate symbols?

> Why do we have to only get to calculus or pre-calculus concepts so late and why is it so extreme like it is all or nothing?

I agree. I did some research on teaching the concept of instantaneous speed to 5th graders. Building on their intuitive understanding—from a young age on we are continuously confronted with dynamic systems such as (loco)motion, weather, computer games, cooking, and so on—and connecting to their understanding of a constant speed, I devised a learning trajectory to explore and deepen their understanding of instantaneous speed more mathematically, including quantifying it.

If anyone is interested, you can read more about it here: https://heerdebeer.org/DR/thesis/ch5.html

Wasn't it Randall Monroe who said that most people only need enough math to correctly divide a check for a dinner party where you are covering the bill for the guest of honor?

That's moderately complex math, and goal oriented.

What ends up happening is the people good at math prey on those who are bad at it. You tell a kid "you learn this so people can't take what's yours" and most of them will pay attention.

The basic concepts of calculus (area under a curve, areas inside shapes in 1, 2, 3 dimensions, relationships between forces, etc) don't need anything more than some basic physics experiments and the ability to perceive the world around you.

Calculus can be explained in terms of algebra, sure, but it can also be explained with visualizations and with experiments (and/or you can learn the algebra at the same time).

Explaining the basic concepts of calculus is very different from teaching someone to actually be able to apply them.

Application of calculus to the real world, in its most basic form, is basic physics. The whole point of people who aren't planning on building on calculus with further mathematics taking calculus is to better understand the world and how it works, not to be able to derive stuff, I think.