[kaiwetzel]

I've taken an introduction to statistics course with social science students and based on that experience, I can relate to what you are saying, 100%.

However, I think there is a broad group of students[1] for which a significantly earlier exposure to calculus would be beneficial and make learning statistics (and physics) a lot easier or at least faster.

When I took introduction to statistics as a math major, I found the subject extremely confusing because the discrete and continuous case where taught completely disconnected and useful anchors for understanding such as basic measure theory and Lebesgue integration where left out. That's certainly a good way to teach for many but for some it doesn't work.

A similar case was physics for me (classical mechanics in particular). From grade 5 to 10 (after which I avoided the subject) there was little insight gained (e.g. heavy things fall down, there may be some friction, memorize all those seemingly random formulas and if you use a long lever, make sure you pick a strong material). Then I was exposed to an introduction to physics course at university (for non-majors) and the revelation that all those random formulas have a strong grounding in just 3 general principles and can then be developed with some help from calculus was liberating. Just too late in my case. Maybe I would have loved physics and actually study it, had they told me in 7th grade that there is something tying all of it together, and the ultimate goal of the class was to reach that summit. Just trying to show the other side of the coin which should be integrated into the way math and science is taught in schools in my opinion :-)

[1] Say, the top 5-10% of middle school students.

[Steuard]

Oh, don't get me wrong: I was served very well by today's standard math sequence. I learned fascinating stuff in precalc, and calculus was a revelation and a profound joy. Prof. Benjamin's argument favoring statistics instead was a tough sell for me.

But I'm a theoretical physicist. As much as I hate to say it, structuring the entire standard math curriculum so it works best for kids like me (or even for the top 10% of students) just isn't reasonable. (Ideally, a solid gifted program could fill that gap.) I think that we agree on that.

I'd like to think that there are ways of introducing concepts from physics or statistics that do highlight the underlying structure of the field, even if the students don't yet know all of the math they'd need to work through the details themselves. If I find a perfect way to do it, I'll let you know!

[bunderbunder]

One approach I've seen and thought was interesting is the course schedule offered at the Illinois Math and Science Academy.

Their pre-calculus courses have been somewhat radically reorganized into a curriculum called "mathematical investigations" which orders the topics according to more of a practical progression. So, for example, bits of linear algebra are pulled all the way up into precalc because they're useful in geometry, and will also work better with the science curriculum. Perhaps physics teachers inheriting students who already understand vectors, for example.

Then the calculus curriculum is split into two tracks, one more basic, and a more intensive one for students who anticipate going into fields that require more calculus.