The usefulness of the three approaches described in the article depends on what the introductory course is trying to accomplish.
One professor taught the subject through a steady diet of mathematical models. If the introductory economics course is aimed at those students who are going to major in economics, then that may make some sense. But most students in most introductory economics courses are not going to become economics majors, much less professional economists.
Among those students for whom a one-year introductory course is likely to be their only exposure to economics, mathematical models that they will probably never use in later life, as they try to understand economic activities and policies in the real world, may be of very limited value to them, if any value at all.
If the purpose of the introductory course is to serve as a recruiting source for economics majors, that serves the interest of the economics department, not the students. It may also serve the interests of the professor, because teaching in the fashion familiar in his own research and scholarship is a lot easier than trying to recast economics in terms more accessible to students who are studying the subject for the first time.
Having written two textbooks on introductory economics -- one full of graphs and equations, and the other with neither -- I know from experience that the second way is a lot harder to write, and is more time-consuming. The first book was written in a year; the second took a decade. The first book quickly went out of print. The second book ("Basic Economics") has gone through 4 editions and has been translated into 6 foreign languages.
Both books taught the same principles, but obviously one approach did so more successfully than the other. The same applies in the classroom.
The opposite extreme from teaching economics with mathematical models was described by a professor who uses an approach she characterized as democratizing the classroom, "so that everybody is a co-teacher and co-learner." This has sometimes been called "discovery learning," where the students discover the underlying principles for themselves while groping their way through problems.
Unfortunately, discovery can take a very long time -- much longer than a course lasts. It took the leading classical economists a hundred years of wrestling with different concepts of supply and demand -- often misunderstanding each other -- before finally arriving at mutually understood concepts that can now be taught to students in the first week of introductory economics.
The Chronicle of Higher Education reported that the discovery learning professor sometimes seemed to be the one doing most of the work in the class, "bringing the students' sometimes fumbling answers back to economic principles."
This course's main focus is said to be not on mastering the principles of economics, but being able to "dialog" and discuss "shades of gray." With such mushy goals and criteria, hard evidence is unlikely to rear its ugly head and spoil the pretty vision of discovery learning.
Discovery learning may not serve the interests of the students, but it may well serve the ego of its advocate. Education may be the only field of human endeavor where experiments always seem to succeed -- as judged by their advocates.
By contrast, the third method of teaching introductory economics, in lectures by Professor Donald Boudreaux of George Mason University, tests the students with objective questions -- which means that it is also producing a test of whether this traditional way of teaching actually works. Apparently it does.
The Chronicle of Higher Education also reported on the students. The feckless behavior of today's students in all three courses makes me glad that I left the classroom long ago, and do my teaching today solely through my writings.