Thursday, July 20, 2017
Algebra or Stats?
That said, the solution in Florida was to create classes called Math for Liberal Arts that have almost no algebra but lots of applications. (They have been around for many decades, replacing College Algebra for, say, History majors. Students don't have to memorize formulas, but they do have to know how to apply them.) These classes are forbidden to STEM and Business majors, but they do a great job with mortgage rates and basic statistics, things that are really useful for people in fields that don't even require a knowledge of "real" statistics.
By the way, the assumption is that they have all taken and "passed" algebra in high school so it isn't like they have never seen algebra. They just hate it.
The statistics that bioinformatics and bioengineering students are required to take at my university requires fairly heavy-duty integral calculus. (They refer to the algebra-based statistics course that the biology students take as "baby stats" or "high-school stats".) So what I regard as bare minimum statistics may be far beyond what people are envisioning in a "stats for all" course.
If people wanted to remove a mostly useless math course from the high school curriculum, I'd argue that dropping geometry would be of more use than dropping algebra. Not that geometry isn't useful and even fun for some people, but it has very little transference to other subjects. Statistics would be a better core for teaching reasoning than geometry is, and teaching logic directly would be better for the cultural role of mathematical proofs. The main reason for enshrining geometry is the medieval quadrivium (arithmetic, geometry, music, and astronomy) and most schools have dropped astronomy and made music an extra option. I think that we'd be better off nowadays concentrating on the trivium (logic, rhetoric, and grammar), which seem to be getting short shrift in the schools.
Why can we have a course that's some combo of algebra lite and real world stats. There would be transfer issues, of course. But aside from STEM fields, I can see that being the exact amount of math most college students need.
The author of the NPR story described "intermediate algebra" (which is functionally equivalent to high school algebra 1, where using the quadratic formula is its highest-level skill) as "abstract algebra". I had all I could do to stay in my chair.
Yes, they are talking about dropping "intermediate algebra", which is something that colleges and universities in Florida did in response to a legislative mandate to assume that all PUBLIC HS graduates were qualified to take college level reading, composition, and math classes. Someone needs to look at the data, but this move can only be positive. Many students despise algebra but find formal logic interesting and fun. It can also help in the STEM areas, because it makes intermediate algebra (which only earns college credit at a CC, but does not count as "college level") into a class that is required for only two classes: College Algebra and Real Statistics. (Our stats class does not require College Algebra, for the few majors that require statistics but don't mandate algebra, but Business majors usually take College Algebra and Business Calculus before Stats. You don't use logarithms and factor cubics in a soft-ware driven statistics class.) Intermediate Algebra is no longer required for the two Liberal Arts math classes, so its rigor can be increased to help students get ready for a pre-calculus sequence.
GSwoPumps: the stats they are talking about are quite basic, what might be in a HS statistics class, if it is what is in one of our Liberal Arts math classes. Just enough to be helpful to a crimial justice or social work major.
Johan: I was puzzled by your statement about "no math", because our state requires TWO "college level" math classes for all state universities and colleges, but the NPR article confirms that only 60% of college students are required to take any math in college. That might reflect high admission standardsat some places or football-driven universities that don't have an option like Liberal Arts math to keep athletes eligible for competition.
Correlations and standard deviations also rely on some knowledge of algebra.
I'm not sure what DD's getting at here. The formula for the standard deviation requires no algebra, just basic arithmetic functions (e.g., square root, addition). You don't need to know a lick of algebra to calculate and meaningfully interpret standard deviations. I'll go as far as to say that I can't think of any of the essential concepts in an intro stats class that require any algebra skills. I know it probably makes the mathematicians cringe that students in a stats class are not able to derive the formula for the least squares regression line using differential calculus, but the calculation and interpretation of a regression line only requires arithmetic skills and some logical reasoning.
I have a solid undergrad stats background (4 or 5 stats-related classes with calculus as a pre-req), and work with math people daily. I tend to think that college-level math begins with Calculus (although I had never taken even an algebra class when I started college.)
I think that a class in "Statistical Reasoning" could be done well without algebra; it wouldn't prepare someone to generate statistics, but would prepare someone to read them. I think that it would be more valuable for most non-math majors than algebra, or even calculus.
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