I was a high school calculus teacher (also algebra, geometry, trig) first
job outta university, stuck with it for two years.

Fast forward to almost age 60, and I'm teaching coding to middle schoolers,
thinking it's all still math. [1]

Shouldn't take a "computer scientist" to cover this stuff... Algorithms are
algorithms after all.

Were I to teach calculus today, in light of what I now know, I'd focus on
probability density functions right when we get to integration, as "area
under the probability curve" is precisely how we figure out  chances of
something happening.

We would use Jupyter Notebooks with SciPy, all free & open source.

As I recall, our calc curriculum never did much to bridge to statistics,
but in SciPy / NumPy, every continuous probability distribution function
(PDF) comes with a cumulative distribution function (CDF) that's defined
exactly as a definite integral between A and B, and giving the probability
some x in distribution X falls between A and B.

Forming a bridge twixt calculus and data science would be another strategy
for getting scientific calculators to share the road, with more relevant
free tools (always an ulterior motive for me).  I don't think a TI is able
to do definite integration over a standard normal curve.

Actually, I see I'm wrong:

Oh well, back to the drawing board.  I still think a strong tie-in twixt
calc and data science makes a lot of sense at the high school level. With
or without Jupyter Notebooks.


PS:  right now I'm going through Allen Downey's tutorial on Bayesian stats
using the above mentioned tools, from Pycon 2016:
I attended this conference, but didn't manage to make this tutorial.

[1]  I've shared this before, still relevant:

Also this blog post:
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