Thursday, November 05, 2015

Prerequisites

At issue in this post is what should be done when a student has had the appropriate prerequisite courses but remains incompetent in the subject matter that those courses teach.

Let me begin with some recollection of my own incompetence as an undergraduate in select areas of study.  Cornell had a foreign language requirement, which could be satisfied either with proficiency in one language or qualification in two languages, proficiency being a sterner requirement than qualification.  I had 3 years of high school French, which gave me qualification in one foreign language coming in.  My options were either to take another year of French, to achieve proficiency, or take some other language for a year, to achieve qualification in that.  I had pretty low regard for how much French I had retained from high school.  If asked, parlez-vous fran├žais? I could respond, un petit peu. (Or is it une petite peu?  I really don't know.)  This to show I thought I'd get clobbered with another year of French, so I opted for German instead and took what they referred to as a reading course.

I should add here that my mom was a foreign language teacher in high school and ran a tutoring business on the side that was quite lucrative.  She mainly taught French and was a native German speaker.  She and I didn't get along so well during my high school years.  My aversion to foreign languages was a reflection of that.

I did okay in German in the fall semester but the following spring the class met at 8 AM and I blew off many of the class sessions.  At the end of the term when it was time to take the exam to prove sufficient mastery, I ended up coming up short on that.  So I took German again in a 4-week summer session.  I was no genius in the subject after that, but I easily crossed over the bar for earning qualification in the subject.

The thing is, my limitations in foreign language did not impede the rest of my studies one iota.  I did take a course on Kant's Critique of Pure Reason, which had single sentences over a page long.  But it was translated into English and if I recall even native German speakers often read the English translation instead because it was just too hard to make meaning of Kant's original writing.  Other than that, foreign languages were something that every educated person should know, but ignorance would not really be tested in school outside the foreign language class.

What happens when students have gotten through a prerequisite course in the same manner that I got through German, but where the downstream course does expect real knowledge of the prerequisite?

* * * * *

The population of my current class is bifurcated in its math competency.  Here I'm referring to knowledge of high school analytic geometry and algebra as well as a little bit of calculus.  One bit to illustrate this can be seen in the comments to this post, which is where my students pose questions about the Excel homework, this one regarding the simplest possible version of the principal-agent model. The students posting these comments are for the most part perplexed about what they should be doing.  I met with one of them on Tuesday.  He's a good kid, always comes to class, and gets his written work done early.  But he is math phobic.  He told me he memorized his way through calculus.  It is not the first time I've heard students say this.

In contrast, there are other students in the class who said the video they were to watch before doing that Excel homework was very helpful to them in understanding how to do the homework.  These students have the requisite math skills.  I find it comforting that there are at least some students in this category.

I wish that were true for the whole class, because the issue is more than just math.  Microeconomics utilizes math modeling throughout.  If students have at best a shaky understanding of the math, then their understanding of the underlying microeconomics will also be shaky.  Building a structure on a shaky foundation, is a risky proposition.  When a storm comes along the entire edifice may tumble.

* * * * *

I really don't know how particular this issue is to the study of economics.  Might it generalize to a good chunk of undergraduate education, particularly for students who study in the social sciences?

Let me assume for the moment that it does generalize.  What is to be done about it?  In looking for answers, let me suggest two places that campuses offer as solutions but really aren't.  One is pedagogy.  The other is online technology.  Each of these might be useful if there are very specific gaps of knowledge that need to be filled.  But we're talking about here is what is now being called numeracy - quantitative reasoning skills.  It takes enormous amounts of practice to develop these skills.  The kids who got through their math classes by memorization bypassed all that practice.  To expect that these skills can be acquired on the cheap and in short order is an act of denying reality.

The realistic possibilities are (1) take the math parts out of the course as much as possible or (2) force the students do redo the prerequisites but in such a way where memorization won't work for them so that this time around they really learn the stuff.  But (2) will take quite a long time - years probably.  This is what makes (1) so tempting.

I stopped writing for a while after finishing the above paragraph. Then I went into school to help another student out with the homework.  After some coaching, the assignment becomes understandable to her.  I doubt this helps much with teaching the student to make good meaning of such assignments in general, but it does suggest a third possibility, which is to keep doing things as I'm doing them now and simply vigorously market in class and online coming to office hours for those students who are challenged by the Excel homework.

I want to note, however, that as a retiree I'm somewhat time abundant and can schedule these outside of class sessions to meet when the student can make it.  So while this third option is a possibility in my class, it doesn't really cut it as a solution in a generic upper level course.

* * * * *

I want to close here by noting that some of the prerequisites for taking a course like mine are not to be found in prior courses taken, but in what the student learns about markets and particular companies, from their reading and from their hands on experiences as interns.  The students do reasonably well on the intern sort of of experience, but I doubt they do much reading on their own in what I'd term Economics In The News.

Again harking back to my own college experience, I bought the NY Times most days and would read all the articles on the Front Page plus related pieces found inside the paper, the Editorials and Op-Ed pages, and the Sports Section, though not necessarily in that order.  I think that would take the better part of an hour.  At that time, I typically would not read the Business Section of the paper.  So if Economics In The News was part of the general news, then I'd be aware of it, otherwise not.

I really don't know the newspaper reading habits of current students.  The campus distributes paper versions of various newspapers around campus so they are freely available to students.  But I have no sense of the utilization rates.  It's also true that nowadays you can read from a variety of sources online and thereby get writing on current events more in tune with your own interests.  It is impossible to know how much of this sort of thing students do.

I do on occasion reference such pieces on the class site.  Those posts get rather few hits as compared to the posts about the homework, which in turn don't get as many hits as the post giving last year's midterm as practice for this year's exam.  I'd like to appeal to student intrinsic motivation for the subject, if I can.  Yet most of the students don't seem prepared for such an appeal.

When I was an undergrad I took quite a few courses without having the official prerequisites.  This was true both for political science classes, where for the most part that was probably the right decision and philosophy classes where I was in over my head much of the time.  Ultimately, I suppose, it is the student's choice to determine the level of prior preparation for taking a given class.  I just wish that the student makes that choice wisely.

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