Calculus is the hurdle that kills many kids' interest in math. It is the end of the road --- either the last math class children take or the first math class they don't take. In a world where mathematical literacy is an increasingly important gateway to high-skilled, high paying jobs, this could be seen as something of a disaster. Or an opportunity: if this gateway could be made less daunting, it could transform both the personal and perhaps also the communal self-confidence of applicants to this increasingly technical world.
Why exactly is calculus so daunting? It is partly because the subject is inherently harder than anything kids encounter earlier in their mathematical career --- I will discuss exactly what is inherently difficult about the subject in detail later in this essay. But not all the obstacles are inherent; some seem gratuitous. In particular:
1st: It is the first subject where the essential concepts are introduced entirely abstractly. Earlier math subjects, if taught well, introduce concepts first with concrete instantiations and then only later with abstractions. If a kid fails to grasp an abstraction, they can fall back to concrete manipulations. I played with counting blocks before I learned to add; I arranged blocks in rectangles before I learned multiplication; I experimented with dividing pizzas and cakes before I learned fractions; I did word problems before solving equations with unknowns; I might even have played with linear transforms before learning matrix multiplication (actually I didn't, but I could have if my linear algebra teacher had been better.) But where is the concrete thing I can play with before I dive into the abstractions of calculus, and what concrete world can I bail out into if I find the abstraction overwhelming?
2nd: Not only is calculus abstract, but the abstractions are loaded with historical baggage. Why do we teach kids both "x-dot, x-double-dot" and also "dy/dx" at the same time? Isn't it confusing to have two competing notations? Yes, it sure is, but Newton and Leibniz were bitter rivals and couldn't agree to use the same notation, and somehow, centuries later, we are still suffering from the consequences of their rivalry --- and also inflicting it on our kids.
3rd: Not only are we suffering from historical baggage in the notation of calculus, we may also be suffering from historical baggage in its conception. In particular, the main motivating examples in introductory calculus books are essentially one dimensional: the speed of a car on a track, the flight of a projectile, the orbit of a planet. These were the problems that motivated Newton and Leibniz, because they were the new frontier in the seventeenth century, but they aren't the frontier now. Motivating the subject with one dimensional examples is not ideal. As I will explain in detail later, in one dimension it is possible to oversimplify in a way that may seem to make the subject easier, but carries a huge price: it confuses the overall narrative. It isn't fair to kids who are complaining that the subject doesn't make sense if, in fact, the story you are telling them actually doesn't make sense. (More about this later!)
4th: Calculus is taught at an uncomfortable age. It is usually the last course in high school or the first in college, so the people learning it are seventeen or eighteen --- and it is counter to children's natural psychology to still be sitting in a classroom doing purely preparatory work at this age. In olden days, kids became adults at age thirteen. Before thirteen or so, kids are reasonably happy to study just to please adults, and sometimes just for the fun of learning itself. But as teenagers they acquire a longing to participate in the adult world, and become impatient with tasks that shut them out of that world for reasons they do not understand.
The modern world battles this natural transformation, and attempts to prolong childhood for four to six more uncomfortable years in order to pour into children's heads the ideas that are too abstract to teach in elementary school but too general and foundational to motivate with an honest story about their usefulness in adult life. But I think this is disrespectful and unfair. I would like to see the subject reimagined in a way that makes it possible to split it into two age-appropriate phases: a "child's phase" that can be introduced to a child younger than twelve, as a toy or a game that would be amusing to children, and an "adult's phase" that builds on the ideas introduced in the "child's phase" but motivates the extra abstraction and difficulty with an honest narrative about how overcoming these difficulties will empower the teenager in adult life. So I agree with you about wanting to make a toy --- I want to make a toy to give a ten year old, but I also want to have a plan to say to them when they turn fifteen "you know that old toy you played with five years ago? Well, there was more to it than I told you at the time. Now that you are older, I can explain what I was trying to tell you with it. You should care to listen to me, because if you work to really understand this, you will gain skills which will buy you money and respect in the adult world."
In other words, I am envisioning a strategy of teaching that works with rather than against children's developmental urges. Young kids want to play with toys. So give them toys! and let them play without pressure. Older kids want to throw away their toys and move into the adult world. If you try to stop them, they will ask "what good does this do for me? It's a toy and I want to be done with toys." Be ready with an answer, and not just any old answer, but an honest and complete answer. If you can do that, I think you could also get them to learn without pressure, because the pressure would come from inside them, from inside their own will to become an adult.
So... back to the question of calculus. I've explained why I think calculus is often made gratuitously difficult, but I also think it is to some degree inherently difficult. The question is "why?" and also "how could that inherent difficulty be embodied in a toy that small kids would have fun wrapping their minds around, and teenagers could understand as a route into adult life?"