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If you're struggling through
a course in Calculus 101 in your tertiary degree right now, wishing you'd paid
attention in high school, we've got some good news: it probably wouldn't have
helped. A study of more than 6,200 freshmen at 133 colleges and universities
across the US has found you'd have been better off mastering the basics than
cramming for that senior level calculus exam.

There are really only two
kinds of human: those few who get calculus the first time, and everybody else.
It's abstract, requires a solid comprehension of numerous fundamental
mathematical principles, and – at first glance – unlikely to be useful.

Most high school mathematics
teachers who haven't been reduced to cynical comedians will do their best to
come up with some creative reason for learning it. Some maintain there is merit, even if it's to
better prepare the few who are destined to go on to further mathematical study.

We largely have the English
polymath Isaac Newton to eventually thank for it, even though his German contemporary Gottfried
Leibniz independently came up with it around the same time.

Like Gottfried,
schoolchildren ever since have muttered under their breath in their contempt
for Newton's ingenious mathematics, despite its invaluable applications in
everything from astrophysics to economics. Of course, if you're studying to be an
astrophysicist, having a solid grasp of integral calculus is essential. What's
up for debate is where that calculus journey really should start.

"We wanted to see if we
could settle that argument," says researcher and physicist Philip Sadler. "Which
is more important, the math that prepares you for calculus, or a first
run-through when you're in high school followed by a more serious course in
college?"

Together with colleague
Gerhard Sonnert, Sadler asked 6,207 students to questions about their family
backgrounds, educational history, and mathematics experience. They combined the
information with mathematics test scores in an anonymised database and analysed
whether having slogged out a course in calculus in high school offered any kind
of boost.

Taking into account
differences in factors such as upbringing and socioeconomics, the results were
pretty surprising. Some students did benefit from calculus – the weaker ones.
But if you're already eyeing off the coveted valedictorian, those lessons in
calculus probably won't do you much good.

To really ensure students
nail calculus at college or university, a good grasp of the basics is a must.
The research found that success in gaining prerequisite skills had twice the
impact than success in an early introduction.

It's hard to say why weaker
students generally got more out of that introduction than their peers, but the
researchers suggest it could come down to a teacher's personal attention, which
isn't like that of a college professor's. "They won't go back and cover
the things that you may be missing like a teacher can do in high school,"
says Sadler.

An overloaded curriculum is
a common complaint across many educational systems across the world. Every
topic jostles for space, and teachers are often left defending lessons with one
eye on moving rapidly onto the next chapter. Dropping calculus could free up
much-needed space to double down on basic principles students just aren't
getting.

"The one thing the
paper says is if your background is strong, if you really know your algebra,
geometry and pre-calculus, you're going to do well in college calculus,"
says Sadler.

It's unlikely a single study
will see high school calculus get left out of text books any time soon, though
it might help ease both teacher and student stress knowing that failing senior
calculus isn't a big deal. This research was published in Journal for Research
in Mathematics Education.

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