Teaching Calculus To 5-Year-Olds

Doofus writes "The Atlantic has an interesting story about opening up what we routinely consider 'advanced' areas of mathematics to younger learners. The goals here are to use complex but easy tasks as introductions to more advanced topics in math, rather than the standard, sequential process of counting, arithmetic, sets, geometry, then eventually algebra and finally calculus. Quoting: 'Examples of activities that fall into the "simple but hard" quadrant: Building a trench with a spoon (a military punishment that involves many small, repetitive tasks, akin to doing 100 two-digit addition problems on a typical worksheet, as Droujkova points out), or memorizing multiplication tables as individual facts rather than patterns. Far better, she says, to start by creating rich and social mathematical experiences that are complex (allowing them to be taken in many different directions) yet easy (making them conducive to immediate play). Activities that fall into this quadrant: building a house with LEGO blocks, doing origami or snowflake cut-outs, or using a pretend "function box" that transforms objects (and can also be used in combination with a second machine to compose functions, or backwards to invert a function, and so on).' I plan to get my children learning the 'advanced' topics as soon as possible. How about you?"

Mischaracterization of problem

[Anonymous Coward]

Doing the same thing 100x is only "simple but hard" if you can actually do it accurately. The point of that sort of practice is to make it easy.

Any teacher handing that out to someone who can already do it isn't doing their job properly. However, handing it out to someone who can't do it and needs to practice is perfectly reasonable.

How about me?

[kruach aum]

I plan to make sure my children understand what they're taught, and are taught new things based on what they already know. If that means teaching them complex ideas earlier than they would normally learn them then that's fine, but to make that a goal in itself is nonsensical.

I agree with all of the things.

[dicobalt]

I remember being in grade school and being irritated that for the 3rd year in the row I was learning how to do basic math. Then when I got to high school I was pissed off that I was rushed though from algebra to trig in 4 years. I don't think they understood that basic math is easy and higher math is hard and your math level has nothing to do with your grade level.

Re:I had something similar as a kid

[ackthpt]

The trick is getting to kids before their idiot peers who casually go around saying things like "Math is hard", "I can't do math, it's difficult", "Math is only for really super smart people."

Math is actually pretty easy, but once you've convinced yourself it's hard it becomes twice the battle, first to get past that mental barrier about how impossible it is.

Same applies to many areas of study. I was coding like a coding fool on National Coding Day and my High School counselor wouldn't let me into the programming classes because my math grades needed to be higher. Pfft, like math is more prevailing than logic. Anyway, plenty of misconceptions on what people are really capable of, particularly at a very young age.

I think there's a growing culture of morons who think you should molly coddle kids rather than get those little brains working during the time in their lives when they are capable of learning the fastest.

father of 4 year old, align with interest is key

[trybywrench]

In my experience, with young children your best chance at teaching them these things is to relate it to their current interest. My 4 year old is really into maps right now, he draws me one every day at his preschool. I've been showing him different maps and trying to relate the concept of directions etc. With his interest in drawing hopefully I can work in the alphabet at some point too. It's a tricky task to put things in terms a 4 year old mind and attention span can digest without overwhelming them.

Re:I had something similar as a kid

[lgw]

Calculus, taught properly, is incredibly easy and intuitive because it's all geometry - you can teach it visually, with no numbers.

Area under a curve? No harder to understand qualitatively than the area of any other shape. Slope of a curve at a point? Again, quite easy to understand with construction paper cut-outs of curves, and a ruler.

And there are plenty of real physics problems that can be solved with simple geometry! Make a drawing of velocity over time that tells a story of a trip. With constant acceleration, all the shapes will be triangles and rectangles. Find the area to find the distance travelled.

For actual curves, you can make them from wood and weigh them to find the integral. Awesome hands-on fun that completely de-mystifies calculus. Not sure a kid would be ready for it by 5, but 8-10, no problem.

People are missing the point

[rabtech]

The article didn't make this terribly clear, but people seem to be missing the point.

If you teach the concepts through hands-on interactive play, kids as young as five can understand the concepts underlying Calculus without too much difficulty. This also happens to be one of the best times in your life for learning, when the brain is rapidly forming new connections.

Her point is teach the concepts, teach the patterns, teach kids how to find patterns, and how to internalize mathematical knowledge.

The mechanical drudgery of formal language, writing out and solving equations, etc comes later on but builds on the fundamental understanding developed much earlier in life.