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Someone I know recently took an online intermediate algebra course to preparefor college algebra.

Thus course had 70+ sections, each with 10-30 poblems, beginning with set-builder notation and going on to associative/distributive/commutative laws, etc. and in general proceeding axiomatically.

Most college math courses proceed axiomatically, to maintain rigor.

But in the same high school courses this is intended to replace, the emphasis is on 'learn this useful formula and apply it 30 times until you get it'.

In my experience, the best students, who would actually appreciate the rigor, never take the rigorous college courses, but instead do great in high school and move directly into college-only courses such as linear algebfa and vector calculus. While those who take intermediate or college algebra in college tend to be put off by the overly rigorous approach.

My questions are:

Is there a significant difference in the rigor of these courses as taught in college and high school (i.e., is it not just my imagination)?

If there is a difference, is there any published research supporting such a difference, or statements by those in charge of curriculum at an jnstitution giving an explanation?

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Part of the explanation is just that the first builds on the second... –  vonbrand Apr 15 at 0:08

3 Answers 3

up vote 11 down vote accepted

Although someone else might agree that "difference in the rigor" is the crucial aspect, my own observation is that this is not the issue, although one can argue that there is some sort of "difference of rigor".

Rather, the best students in today's high schools are treated very gently grade-wise, which they have learned is the only truly relevant currency as a measure of success. Thus, they subliminally infer a level of effort, a "good intention", that suffices.

Upon arrival at a substantial university in the U.S., there are several upsets. First, although the students think this is a good thing, the structure to their personal lives created by living at their parents' house is gone, and this makes everything else more volatile. Second, instead of being high-school seniors perhaps at the top of their graduating class, they've become the lowest-status creatures on the whole campus... which has a population 20 times greater than their high school, etc. On top of all of that, suddenly their Pre-Calc instructors don't seem to have their own self-esteem wrapped up in the success of their students... but almost the opposite, in many cases.

In many cases, the use of low-level math courses is not to educate anyone, but to filter, so that otherwise-alarming failure rates are not immediately considered a bad thing.

By this point, seriously, issues of "rigor" are not the critical ones... but general ambience, adversarial relationship of student and instructor, and so on.

(I do not have literal stats, but have been a concerned observer for 30+ years...)

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Similar observations here. –  vonbrand Apr 13 at 3:14
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I'd also like to point out that students who start with college algebra are to some degree playing catchup. Perhaps only one or two percent might desire to become a math major, but these students deserve a chance. A rigorous college algebra course can allow underprepared students to gain "mathematical maturity" as they catch up to speed. If they succeed in Algebra, they can now succeed in there next class, calculus, where many students have probably already taken AP calculus. If Algebra was watered down, those that succeeded may not do very well in future courses. –  MHH Jun 15 at 1:32
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The question is about a specific college math course; almost all of this answer is just about college as opposed to high school in general. In many cases, the use of low-level math courses is not to educate anyone, but to filter, The course being described in the question isn't designed to filter. It's a remedial ("developmental") course covering material that here in California should have been learned in either 8th or 9th grade. –  Ben Crowell Jun 15 at 1:55

High school algebra courses have to cater to both serious and "nonserious" math students (the latter are taking their last course in math). As such, they are not in a position to match college levels of rigor, even for the same class.

It's only beginning with (senior year) calculus, where all the students are "serious," that math is taught a true college level.

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The actual level of rigor is going to depend on the school and the teacher, and has very little to do with the level of rigor claimed in the official course outline or in the textbook. Colleges are required by accrediting bodies to use college-level textbooks, but accrediting bodies can't tell whether teachers are actually applying college-level standards.

It depends on the country we're talking about, but in the US, the material you're talking about is stuff that students are supposed to be exposed to for the first time at an age somewhere between 13 and 15. At this age, they aren't adults intellectually. At age 13, many kids are barely able to read, so they need a textbook pitched to a very low reading level.

The reality is that remedial math courses at the college level have extremely low success rates. This fact has very little to do with the level of rigor of the courses and a lot more to do with the fact that the students who place into these courses are students who have already built up a record of failure in math. Past failure correlates with present failure.

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