Why Do Students Have to Take Math in College?

The multiple-measures and co-requisite trends (fads, if you will) continue to gain share in the market.  Results are generally positive, and more laws are passed limiting (or eliminating) remedial mathematics in colleges.  Given the talk on these issues, I have to wonder … why do we require students to take a mathematics course in college?

Clearly, I am not raising this question relative to STEM or STEM-ish programs that some students follow; their need for mathematics is clearly logical (though that experience needs to be more modern than they usually experience).  These students normally proceed through some sequence of mathematics, whether 2 courses or 10.  No, the question is relative to programs or institutions which require one math course, usually a general education course.

Those general education math courses are often very close in rigor to high school courses common in the United States at this time; I’ll provide a specific rubric for that statement below.  “College Algebra”, the disaster that it is, happens to be pretty close to the algebra expectations in the Common Core standards; the details differ, but the level of expectations are very similar.  “Statistics”, at the intro level, is again similar to those expectations; even some of the intro stat outcomes are in the Common Core.  Liberal Arts math has topics not normally found in K-12 mathematics, but the level of rigor is generally quite low.  Quantitative Reasoning (QR) has some potential for exceeding the high school level, but most of our QR implementations are very low on rigor.  See https://dcmathpathways.org/resources/what-is-rigor-in-mathematics-really for a good discussion of ‘rigor’ as I use the word in this post.

Do we require a math course in college as a means to remediate the K-12 mathematics students “should have had”?  Or, do we require a math course in college in order to advance the student’s education beyond high school?

Those questions seem central to the process of considering those current trends.  The high school GPA, the cornerstone of most multiple measures, has a trivial correlation with mathematical abilities but a meaningful correlation to college success; if the college math course is essentially at the high school level, then using the GPA for placement is reasonable.  Co-requisite remediation can address missing skills but not a lack of rigor (in general); if the college math course is essentially at the high school level, there is little risk involved from using co-requisite remediation.

On the other hand, if we require a math course in order to extend the student’s education beyond high school, neither multiple measures nor co-requisite remediation will dramatically decrease the need for stand-alone remediation.  K-12 education does not work that effectively; prohibiting stand-alone remediation in college will punish students for a system failure.  Our ‘traditional’ math remediation involving three or more levels is also a punishment for students, and can not be justified.

I would like to believe that we are committed to a college education, not just a college credential.

Before we conclude that multiple-measures and/or co-requisite remediation “work”, we need to validate the rationale for requiring a math course in college for non-STEM students.  A key part of this rationale, in my view, is our community developing a deeper appreciation of the quantitative needs of all disciplines.  Few disciplines have been exempt from the radical increase in the use of quantitative methods, and this is a starting point for ‘why’ require a college math course — as well as the design of such courses.  Most of our current courses fail to meet the needs of our partner disciplines, which means getting more students to complete their math course will have a trivial impact on college success and on occupational success for our students.

If it is important to extend a student’s education beyond the K-12 level, then the ‘rigor’ of the learning is more important than the quantity of topics squeezed in to a given course.  The discussion of rigor cited above is helpful but a bit vague.  Take a look at this taxonomy of learning outcomes:

This grid is adapted from a document at “CELT” (Iowa State University; http://www.celt.iastate.edu/teaching/effective-teaching-practices/revised-blooms-taxonomy/), and is based on the “revised Bloom taxonomy”.  The revised taxonomy is a significant update published in 2001; one of the authors (Krathwohl) has an article explaining the update (see https://www.depauw.edu/files/resources/krathwohl.pdf ).  The verbs in each cell are meant to provide a basic understanding of what is intended.  [Note that the word “differentiate” is not the mathematical term :).]

Within the learning taxonomy, the columns represent process (as opposed to knowledge).  Those 6 categories are frequently clustered in to “Low” (Remember, Understand, Apply) and “High level” (Analyze, Evaluate, Create); the order of abstraction is clear.  For the knowledge dimension (rows), the sequence is not as clear — though we know that ‘metacognitive’ is higher than the others, and ‘factual’ is the lowest.

In both K-12 mathematics, and the college math courses listed above, most learning is clustered in the first 3 columns with an emphasis on “interpret” and “calculate”.  A direct measure of rigor (“education”) is the proportion of learning outcomes in the high level columns, with possible bonus points for outcomes in Metacognitive.   Too often, we have mistaken “problem complexity” for “rigor”; surviving 20 steps in a problem does not mean that the level of learning is any higher than simple problems.  We need to focus on a system to ‘measure’ rigor, one that can justify the requirement of passing a math course in college.

1 Comment

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  By Larry Stone, February 26, 2019 @ 3:55 pm

  Not to say whether this is good or bad, but doesn’t it seem, on the non-STEM side (and probably for “light STEM” as well), that the purpose of college math reform really is to address what K12 neglects? We need citizens who can analyze their own budgets, who can critically evaluate numerical claims in the media, and so on — so if they can’t do it upon graduating high school, let’s at least make sure they can do it upon graduating college?

  I mean, K12 has long been neglecting “real math” for the sake of pushing students onwards and upwards into algebra and beyond — so that now, in MN, algebra 1 is a middle school subject and functions are introduced (conceptually) in about third grade. The mission is to get as many students as possible into IB-this and AP-that, whether their numerical common sense is developed or not. So, no big surprise, we’ve been getting graduates who can give you a few ideas how to get x by itself but have no respect for what compound interest can really do to them.

  My hope is the “QR revolution” will actually begin to make a difference in how educated adults view math. That way, when I tell other professionals that I’m a math teacher, I won’t have to keep hearing “Oh I’m terrible at math.”

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