Statistical Doors Into Mathematics

That’s really a question — does statistics create a door into mathematics? Or, is statistics (for most students) an alternative off-ramp from the mathematics highway?

The question is perhaps trivial. In terms of the bulk of our work, we are dealing with students required to take specific courses for their program. Every math course becomes a common off-ramp for students. Perhaps we should be satisfied with a curriculum consisting of terminal courses for students interested in everything else but mathematics.

One of my colleagues began her higher education as a fairly typical community college student at our institution. She reports that a turning point for her was a particular computer science course that she decided to take; after this course, she changed her major and got a degree in computer science (and later a masters in math). There was something of beauty in that computer science course that connected with her, and changed her life.

I would be interested in any research on the question:

Do students change their career path to mathematics after taking a statistics course?

I am sure that there are students who change their path to statistics after a statistics course, though I wonder if the rate is equal to that of ‘math program after a math course’.

Like most of us, my students are just interested in passing this math course so they can get their degree or that job. I am fine with helping them along that trail; in fact, I am happy to do so. I teach because I find that rewarding.

However, I am also a professor is in “affirms a faith in something”. I think I have a responsibility to show students in each course something about the beauty of mathematics; something wonderful should show in every class. Partly, this is needed to encourage more positive attitudes about mathematics; partly, this is needed to encourage a more accurate view of the nature of mathematics, that mathematics is much more than processes to generate answers.

To me, however, the largest reason for what I try to do is “opening doors”. A major reason for lowering expectations for a given student is mathematics; lower-skill programs are selected because they require less mathematics (or none). Students even avoid occupations that they would love to be in … just due to mathematics. To me, every mathematics course should be a STEM magnet drawing students towards higher skilled jobs and more security.

I do not think that statistics operates as a STEM magnet. Of course, there are many math courses in our institutions that are not STEM magnets; however, almost all math courses could be strong attractor points drawing students towards mathematical sciences. I think the problem with statistics is that we teach statistics as a practical discipline without a core mathematical structure. We focus on the innate appeal of statistics, on its utility; perhaps we need to show the mathematics supporting statistical methods when possible. If there is no mathematics supporting a method (the ‘plus 4’ rule type of thing), perhaps we should question the presence of that method in a general statistics course.

Clearly, I may be demonstrating levels of ignorance vast and wide. I wonder, though … do we share a view that math courses in the first two years should have a property of ‘STEM magnet’? Can a statistics course be such a magnet?

Before the reader decides that I am far too optimistic about our mathematics courses — yes, I know that we fall far short of a STEM magnet in our current courses. We tend to cede our territory, and deliver service courses; we focus on the practical at one extreme … or the totally useless on the other. In between is the zone needed to be a magnet for students; a magnet can not be unidimensional.

Perhaps the question is more general than statistics; my concern is with the contemporary move towards requiring statistics as the typical general education course. Perhaps the loss is trivial. I do wonder if there is an innate qualitative difference between statistics and mathematics that results in statistics being far less able to contribute towards larger goals such as raising student goals and drawing students towards STEM.

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Learning math, Math curriculum in general | Jack Rotman | December 8, 2014 9:48 am

1 Comment

By Herb Gross, December 8, 2014 @ 4:04 pm

Hi Jack!

I feel a bit like a fraud in the sense that I never even took a statistics course, let alone teach such a course. In my generation (the late 1940’s and ‘50’s), it is my recollection that only people who were interested in becoming statisticians took such courses. The reason was that because there were no hand-held calculators, the great amount of necessary pencil-and-paper computations were overwhelming. In fact the curriculum for statistics majors required calculus-based statistics courses.

Nowadays it is assumed that entry-level statistics courses allow students to use calculators and I sense that students often press keys without giving a thought to the conditions under which the computations are the correct ones to use. I have seen teachers assign grades in an honors course using the computations that apply to normal distributions (that is, to large and random distributions). Yet the students in an honors program are neither a large number nor a randomly selected group. My guess is that most of these entry-level statistic course students are happy just to pass such a course, especially if it is the last math course that stands in their way of graduation!

My above comments are not meant to initiate a debate but rather simply to share my opinion with you. On the other hand, I resonate very strongly with your thoughts about making mathematics courses a more meaningful experience, especially for those students who ask “Why do I have to know this?”. My own feeling (and one that I used as the rational for my first textbook “Mathematics: A Chronicle of Human Endeavor”) is that just as there are courses such as “Art Appreciation” and “Music Appreciation” for students who aren’t interested in working in a “humanities”-oriented career, there should be “Math Appreciation” courses for students who aren’t interested in math/science-oriented professions.

It is a “beautiful love story” to see how scientific notation gradually evolved from the days in which mathematics consisted of drawing pictures on the walls of caves; and how the invention of place value was one of the greatest accomplishments of all time. And how can one not wonder at the awesome imagination of Avogadro who hypothesized that there were approximately 6 x 1023 atoms in a mole (a little over a half ounce of water). The number, known as Avogadro’s number is fundamental to understanding both the makeup of molecules and their interactions and combinations. Yet to write this number in place value notation, at the rate of a billion zeros per second, it would take over 1,000,000 years! Was there ever a poet who had a greater imagination!

And to get students to understand how fractions were treated in the “old” days, ask them how come the first “teen” comes after twelve, even though “teen” means “plus ten”? Or why there are 12, rather than 10, in a dozen? Or why the ancient Greeks divided a circle into 360 equal parts, each of which was called a degree; when 100 would have been a much easier number to work with? Or why they chose to have a mile consist of 5,280 feet even though it would have been an easier computation in converting feet to miles if there had been, say, 5,000 feet per mile instead of 5,280 feet per mile?

In my opinion, teaching math via practical applications tends to make math-phobic students even more “fearful” of math. In my opinion it would be far more effective to present topics then tend to make students say things like “wow! I never thought of that!!”

There is much more that can be said concerning this topic but I hope that what I have written at least gives you the gist of my own thoughts.

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