Leading Korean Mathematician Advises: Read Novels, Watch Movies

Hwang Jun-muk
Korea Herald

The prominent Korean mathematician Hwang Jun-muk -- interviewed by Oh Kyu-wook -- offers some unusual advice in "Mathematicians must be storytellers" (Korea Herald, August 28, 2013):

A good mathematician requires not only techniques but also creativity . . . . [Hwang Jun-muk] perhaps inherited his creative side from his parents. His father is traditional Korean music composer and "gayageum" master Hwang Byung-ki and his mother is one of the country's leading authors, Han Mal-sook.

"Thanks to my parents, I read a lot of books at home in my childhood. That may help me now when I present my ideas to others."

"I had a chance to talk to high school students, and I told them read novels as well as watch movies a lot to practice and improve their skills to present their ideas well in a simple and interesting way . . . . [This is] important to be a good mathematician," he added.

Why such advice?

The ability to tell stories is needed among mathematicians in Korea where the subject is still deemed boring and learned by rote, said the nation's top academic in the field.

Korean students are among the top performers in international mathematics contests, but they lag far behind in terms of interest and passion, which may account for the relatively modest performances by professional Korean researchers in the world . . . . "When I prepare for a presentation, I think hard to put my ideas into a good, interesting story. If you put all mathematical proofs just in order and present it to your audience, it will be extremely boring . . . . Korean mathematicians have good techniques and knowledge and made progress in research, but they are still not good at making a story (in comparison to Western powerhouses for advanced mathematics)."

Mathematics taught through stories! That's an unexpected reply to my query! Here's the crux of the problem:

A key stumbling block is the current educational curriculum, which has traditionally emphasized only problem-solving techniques. Also, many Korean mathematicians do not learn how to present their ideas.

In short, Hwang says that the Korean pedagogical system does not encourage creativity and the inspiration that comes with good teaching, and that means, even for mathematicians, telling stories. Is he right? Well, he surely knows more about this than I do.

But I wish the article had given an example of a story Hwang might use to teach mathematics . . .

Professor Ricardo Duchesne: On Pedagogy

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Wicked-Paideia

I noticed this pedagogical statement on Professor Ricardo Duchesne's faculty page, and found it worth reflecting upon, so I quote it here:

Dr. Duchesne believes that the reading of great books, from cover-to-cover, is essential to a university education. The term 'lecture' was originally applied to the exercise of reading -- and correcting -- the language of handwritten texts. The task of the student was to follow the reading, and make the necessary corrections in the manuscripts. Since the texts were difficult, the teacher would concentrate on explaining and interpreting the manuscripts, line by line, word by word. 'Resources' such as handouts, power-points, and WebCT lectures promote the erroneous notion that knowledge comes ready-to-wear. Knowledge is actually produced through continual reading, note-taking, dialogue, and rewriting. Duchesne upholds the traditional spirit of broad learning for the BA degree with a multidisciplinary core curriculum taught by generalists with a strong grounding in the Western intellectual tradition.

I wonder how many of those Medieval 'lectures' involved real dialogue. I reckon much of what went on was strongly hierarchical, with the lecturer doing most of the talking and the students listening in silence.

But I see value in Duchesne's own approach, and have even followed that method from time to time. One of the highlights of my graduate studies was reading Hans Blumenberg's Legitimacy of the Modern Age in a reading group with Lionel Jensen, Tom Long, and a couple of other brilliant individuals -- each of them towering over me intellectually -- and we read the text closely, aloud to each other, slowly, discussing each point, with each participant bringing his particular expertise to bear. I learned more from that year-long reading group than from any other single learning experience ever.

Duchesne's own book, The Uniqueness of Western Civilization, should probably be approached similarly . . .

Student Evaluations of Faculty (SEF)

Schoolboy

Receiving

Bare Bottom Birching

Medieval Source

(Medieval! Should I update my pedagogical methods?)

(Image from Wikipedia)

Readers will recall my previous two posts on student evaluations of teaching, both in response to Professor Stanley Fish's two columns on the topic. In the latter of these two posts, I noted Professor Fish's reference to "the preponderance of studies document[ing] . . . [the] non-correlation" . . . "between student evaluations and effective teaching ," and I wondered:

Professor Fish's column is nonacademic and thus cites no sources, but I'm curious about the studies alluded to, for I would like to have cited such studies in previous years when issues of this sort arose in discussions over good teaching.

Well, in response to my query, an instructor who read my post emailed me some studies and papers. I've only had time to skim most of them (one is 50 pages long!), but a couple caught my attention. A paper titled "Student Evaluations: A Critical Review," written by philosophy professor Michael Huemer (University of Colorado, Boulder), states the following concerning student evaluations of faculty (SEF) -- and I've also included his sources cited in the passage:

The most common criticism of SEF seems to be that SEF are biased, in that students tend to give higher ratings when they expect higher grades in the course. This correlation is well-established, and is of comparable magnitude, perhaps larger, to the magnitude of the correlation between student ratings and student learning (as measured by tests) . . . . Thus, SEF seem to be as much a measure of an instructor's leniency in grading as they are of teaching effectiveness. The correlation holds both between students in a given class and between classes. It also holds between classes taught by the same instructor, when the instructor varies the grade distribution. And it affects ratings of all aspects of the instructor and the course. (6) Many believe that this causes rampant grade inflation. (7)

6. See Rice, 335-6; Wilson; Greenwald and Gillmore, 1214.

7. See Goldman; Sacks.

Goldman, Louis. "The Betrayal of the Gatekeepers: Grade Inflation," Journal of General Education 37 (1985): 97-121.

Greenwald, Anthony G. and Gerald M. Gillmore. "Grading Leniency Is a Removable Contaminant of Student Ratings," American Psychologist 11 (1997): 1209-17.

Rice, Lee. "Student Evaluation of Teaching: Problems and Prospects," Teaching Philosophy 11 (1988): 329-44.

Sacks, Peter. Generation X Goes to College (LaSalle, IL: Open Court, 1986).

I'm not sure whether or not Professor Heumer has published this paper, but it can be read online via his website.

The other article that caught my attention is a published paper, "No pain, no gain? The importance of measuring course workload in student ratings of instruction," Journal of Educational Psychology, Volume 89, Nr. 4 (1997), pages 743-751, by Anthony G. Greenwald and Gerald M. Gillmore. Here's the abstract:

Samples of about 200 undergraduate courses were investigated in each of 3 consecutive academic terms. Course survey forms assessed evaluative ratings, expected grades, and course workloads. A covariance structure model was developed in exploratory fashion for the 1st term's data, and then successfully cross-validated in each of the next 2 terms. The 2 major features of the successful model were that (a) courses that gave higher grades were better liked (a positive path from expected grades to evaluative ratings), and (b) courses that gave higher grades had lighter workloads (a negative relation between expected grades and workload). These findings support the conclusion that instructors ' grading leniency influences ratings. This effect of grading leniency also importantly qualifies the standard interpretation that student ratings are relatively pure indicators of instructional quality.

Both papers confirm something that I've long wondered about and also help me to analyze a set of course evaluations that I received yesterday from students in a particular department where the students are generally quite good in English due to having attended international schools or having been educated overseas. This set of evaluations was lower than I would ever have wanted. Indeed, I had expected outstandingly high marks based on classroom rapport and the depth of what I had taught the students about researched essay composition. I received, however, surprisingly low marks. When I checked the written comments, I found complaints that they, as students of their particular department, should be required to take essay composition courses since they are already good in English and had already learned how to write essays in high school.

Think about that. The set of evaluations that I received for that course were low because the students thought that they had nothing to learn, didn't want to take the course, and were annoyed by the requirement.

Such an attitude might be more acceptable to discover if these students of a particular department really did have nothing to gain from the course, but their view of their own abilities was grossly exaggerated. All of them had difficulties in reasoning soundly and using evidence effectively, and all of them needed to learn how to do research well and cite sources properly. The grades that they expected to receive reflected these weaknesses.

Let me explain that last point. During the semester, and in every course, I grade on an absolute scale based on what I consider to be rigorous standards. The grades that students receive during the semester are thus significantly lower than what they are accustomed to receiving, based on many other courses that they have taken in their major fields. Students often come to see me and say that they have never received such low grades before . . . and they are generally skeptical that they deserve such grades. This is especially the case with students in the particular department noted above.

Based on the two scholarly papers cited in today's post, I infer that my undeservedly low evaluations by students of this particular department were due to their expectation of low final grades for the course. The students' comments didn't mention this expectation, but such is unsurprising since that would be to acknowledge that they weren't as good as they thought themselves to be.

The irony is that despite their expectations, these students received good grades. Why? Because while I grade on the absolute scale during the semester, I adjust to a high curve for the final grades. I do this adjustment because we are required to grade on this sort of curve. I would prefer to assign grades on an absolute scale, but I can't. Nevertheless, because I have always felt that students should have a more realistic appraisal of their actual performance, I've chosen to rank them on an absolute scale up until I finally assign course grades.

I guess I'd better stop that pedagogical practice and grade on a relative scale throughout the semester unless I want to keep getting low evaluations from students in that particular department.

For the record, I was reasonably satisfied with the other three course evaluations that I saw yesterday. One of them was lower than I wanted but about what I had expected. The students of that course had very low English skills, and I never quite figured out the best way to help them . . . but I'll keep working on finding a way.

"A Shift" in gear this academic year

Okay, here's the battle plan...

(Image from schoolmarm.org)

Gord Sellar -- published author, fellow expat, and innovative teacher -- has articulated an idea for a different approach to teaching this semester, and I think that it might work.

Let me explain.

Aside from incompetent teaching, perhaps the biggest barrier to having a successful class in Korea lies in the refusal of Korean students to speak up. Many if not most Korean students here in Korea have a tendency to remain silent during discussions or to parrot something that they've memorized beforehand.

In an effort to overcome student reticence, Gord plans to try something that he has seen at science fiction conventions:

I'm going to introduce a variation on "presentations." This might fly, it might crash, I'm not sure, but I think it's worth a try. The idea is simply stolen from SF conventions, where "panels" discuss some subject at length. Whether a panelist is an SF author, a fan, an editor, or some technical expert, everyone ends up on an even ground because the task of the panel is to come together, contribute individual thoughts and ideas to a discussion, entertain the listeners, answer questions in a thoughtful, interesting, or entertaining fashion, and fill up one hour semi-spontaneously.

This allows students to prepare in the way they're used to -- scouring Wikipedia, memorizing random bits of useful information -- but also makes it impossible for them to follow a prearranged script, since besides preparing a few questions or discussion topics individually, they'll have to grapple with questions put forth by the "moderator" (me) and the students, who will be expected to think up a few interesting questions as well. (And this kind of participation as an audience member will be tracked, too, for grades.) Since panelists will be competing, they'll all be trying hard to entertain their classmates and me, and to say something interesting, which will reduce the likelihood of them coming together and forcing through some kind of prepared presentation. And I'll be assigning the topics, so I can set the breadth to allow for focused discussion as well as general thoughts on the topic.

I've been toying with something like this myself, albeit not quite so well-thought out as what Gord suggests. I've tried lecturing to Korean students (though not for a long time), I've tried open discussion sessions (periodically, but not recently), I've tried assigning presentations (but long abandoned), and I've tried reading through a paper together with students in the classroom (more recently relinquished), but nothing seems to work very well consistently.

I'm not familiar with the method that Gord has experienced at science fiction conventions, but I think that I envision how it works, and I think that it might also prove effective in my cultural studies classes, so I may test it as the course moves along.

Before doing so, however, I'm resurrecting the discussion method for a couple of courses. At Kyung Hee University, I'm again teaching British and American culture, where I focus on the issue of multiculturalism, and at Yonsei University, I'm teaching a course on Islam, where I focus on Islamism. In both classes, I'm having the student spatially arrange themselves in a circle that includes me so that we can all face each other.

However, I'm dealing with the two courses somewhat differently.

For the Kyung Hee course, I'm assigning a text that we all read and bring to class to discuss. I've told students to come prepared to ask at least one question and to make at least one statement. They might not each have the opportunity in each discussion to ask or state what they've prepared, but at least, they'll be ready. This has sometimes worked, and I'll soon see if the students are self-motivated enough. If not, I'll move more toward what Gord is trying in assigning 'panels'.

My Yonsei students are more self-motivated, and I'm trying something radically different there in my Islamism course. Except for the first week, when we read and discussed the article "Manual for a 'Raid'" on 9/11, by Hassan Mneimneh and Kanan Makiya, I won't be assigning readings. I will offer suggestions from week to week, but I've told the students that we will define the course as we proceed. In effect, we're modeling our course on an organizational principle employed by the Islamists themselves, namely, "open-source" operations. Rather than the hierarchical classroom where I choose topics and assign readings, I'm letting the students follow up their interests within the context of Islamism. We will depend upon one another to fill in each other's gaps in knowledge, as we branch out on our own, by returning each week to report on what we've found out about ideas, personalities, movements, organizations, and so on -- and we'll make suggestions on things that others could read. I think that the students' self-motivation will enable this to succeed.

In both courses, students will be writing research papers, so these should contribute to the discussions as the course proceeds. Additionally, I intend to open a webpage for the two courses where students can post links to useful articles and ask each other questions about particular issues. My aim is to get the students more intimately involved.

I'll see how these two approaches work, though I may have to structure the coursework more if the students are not performing as I hope that they will.