Is THAT the Best You’ve Got??

A student comes to college, and needs to meet their general education requirement. One of those is in mathematics, and this student actually has some options:

College Algebra (called pre-calculus at their college)
Introductory Statistics
Quantitative Reasoning

Being a typical student, this student wants to avoid the college algebra course; they thought about being an engineer but are too frightened of mathematics. The next choice would be statistics, because everybody seems to think it is the best choice.

In looking in to the course, the student discovers that the statistics course has some nice features. Most of the material is taught by first looking at data from the world around us, and the description says that the quantitative work is somewhat limited. The student becomes worried when they look at the content in the text materials used — it’s got words used in a weird way (normal, deviation, inference, significance); it’s like statistics is a foreign language without any visible culture, so the student feels like much of it is arbitrary.

So, the student tries to find out what “Quantitative Reasoning” means. The course description talks about voting, networks & paths, logic, and ‘proportionality’ (whatever that is). Like the statistics course, it looks like the material often involves data from the world around us; however, it’s not clear how much quantitative work is actually involved. The student is not too worried about any particular topic or phrase in the content descriptions; however, the course does not seem to have any pattern to the topics … it looks like an author’s 15 favorite lessons.

The student thinks about the basic question:

Will any of these courses help me in college courses, in my work, or in my life in general?

Basically, this student will reach the conclusion that none of these three courses will be that helpful. As a mathematician, I would summarize the basic problem this way:

The college algebra course and the statistics course focus on a narrow range of mathematics.
This quantitative reasoning course does not focus on any particular mathematics.

There is a mythology, a story repeated so often that we believe it, that statistics is a better pathway for most students. The rationale is something like “our world is dense with data and decision making” or “making decisions in a world of uncertainty”. I see a basic problem, that remains in spite of what has been written: statistics is an occupational science, with few broad properties or theories. Statistics is about getting helpful results, and for statisticians, this is great. How does it help students when we use “n”, “n – 1”, and “n + 4” for calculations involving sample sizes; the ‘plus 4 rule’ is a typical statistical method for producing the results we want — even when there is no mathematical property to justify the practice. [In a field like topology, we don’t let inconsistent procedures survive.] I think we also over-estimate the value of statistics in occupations; there are limited uses in other college courses, and some nice uses for life in general (for those motivated).

The quantitative reasoning (QR) course has a different problem — we don’t have a shared idea of what this course should accomplish. For some, it’s an update to a liberal arts course (like the example above). For others, QR means applying proportionality and some statistics to life. Still other examples exist.

Is that the best we’ve got? We are giving students options now (a nice thing), but the options are really not that good for the student. For the student above, they really should take the college algebra course — perhaps they will find that mathematics is not their enemy after all; they might become an engineer, an outcome not likely at all with the other two choices described.

As mathematicians, we need to claim the problem and be part of the solution. That college algebra course? Modernize the content and methods so that it actually helps students prepare for further mathematics without becoming a filter that stops students. That QR course? We need professional conversations around this course; MAA and AMATYC should jointly develop a curricular model of some kind. In my view, the QR course is the ideal general education math course; we should include significant mathematics from multiple domains, done in a way that students can discover that they could consider further mathematics. The statistics course? Let’s keep a realistic view of the value of this course; it’s not for everybody, and we tend to think of statistics as the option for people who never need anything else.

No, THAT is NOT the best we have. We have some basic curricular work to do; together we can create better ideas, and help our profession as well as millions of students.

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Math curriculum in general, math reasoning and applications | Jack Rotman | June 6, 2014 12:18 pm

2 Comments

By schremmer, June 7, 2014 @ 12:41 pm

I essentially agree with Rotman except for what is to me a very strange omission.

Back in the old days, we did not learn latin to “help me in college courses, in my work, or in my life in general” but because it was considered to be a means towards “logical thinking”. Eventually of course, latin was abandoned because mathematics was deemed to achieve the same purpose as well as opening other routes but. equally of course, the other routes took over and the purpose of “logical thinking” was forgotten.

What Rotman omits is “logical thinking”. Mathematics being a lot simpler than real life, it makes a lot more sense to learn how to respond logically in a mathematical situation than in a more or less watered down real-life situation. I think that just about any mathematics can be presented in a way that requires the student to develop “logical thinking” and helps her/him learn how to do it.

This purpose of developing “logical thinking”, though, requires that the text itself be carefully developed with a story line meant to help the readier see how each development is called for logically along with, of course, an awareness of the bifurcation points. Etc

Rather than amplify here, I will refer the interested reader to my own current battle with developing algebraic functions in such a direction. (By the way, that the source code is not already posted is due only to my laziness and I will post it should anyone ask.)

Here are the latest versions of Chapter 1 and 2:

Chapter 1(V6-2D)

Chapter 2(V6-2D)http://www.freemathtexts.org/CCP/161.php

but the interested reader might want to compare with the earlier versions also at

Schremmer’s Precalculus I

Regards
–schremmer
By schremmer, June 7, 2014 @ 12:47 pm

I am afraid that the second link is the same as the third. Here is the link to Chapter 2—or so I hope:

Chapter 2(V6-2D)

Apologetic regards
–schremmer

P.S. My “how to do it” referred to “develop logical thinking”.

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