Professor Kolstoe in [Kol75] observes:
It has been contended quite properly that one person does not teach another. A teacher can do little other than set the conditions for allowing others to learn. A more eloquent statement of the same thing is that ``nobody can't teach nobody nothing.'' The consequence of this observation attests to the functioning of a teacher as a manipulator of the learning environment. When a person shows a change in behavior, learning is inferred to have occurred.

There are, at least, two approaches to education: the mimetic approach and the mathetic approach. The mimetic approach emphasizes memorization and drill exercises and is most efficient in inculcating facts and developing basic skills [Gar89, p. 6]. The mathetic approach stresses learning by doing and self exploration; it encourages independent and creative thinking [Pap80, p. 120]. In the mimetic framework, creativity comes after the mastery of basic skills. On the other hand, proponents of the mathetic school believe that self discovery is the best, if not the only, way to learn:

``There is a strong temptation,'' Dewey wrote, ``to assume that presenting subject matter in its perfected form provides the royal road to learning. What is more natural than to suppose that the immature can be saved time and energy, and be protected from needless error, by commencing where competent inquiries have left off? No matter how true what is learned to those who found it out and in whose experience it functioned, there is nothing which makes it knowledge to the pupils'' . . . . Piaget echoes: ``A truth is never truly assimilated except insofar as it has first been reconstituted or rediscovered by some activity,'' which ``may begin with physical motions'' but grows to ``the most completely interiorized operations.''
Or to cite Papert [Pap80]:
Educators sometimes hold up an ideal of knowledge as having the kind of coherence defined by formal logic. But these ideals bear little resemblance to the way in which most people experience themselves. The subjective experience of knowledge is more similar to the chaos and controversy of competing agents than to the certitude and orderliness of p's implying q's. The discrepancy between our experience of ourselves and our idealizations of knowledge has an effect: It intimidates us, it lessens the sense of our own competence, and it leads us into counterproductive strategies for learning and thinking.

I think there is a need to balance encouragement for creative thinking with efficient development of basic skills. After all, one must assume that college students are capable of abstract thinking and that they already have some analytical foundation to build on. Hence I have adopted the mimetic approach in giving lectures, utilizing homework assignments for drill exercises; at the same time I try to provide a framework and opportunities for students to engage in self exploration and knowledge discovery through course projects and independent projects.

I use lectures to set up and motivate problems, to place each problem within the context of the field. Lectures are also useful as synchronization points to summarize and relate materials learned over the semester. I agree with the authors of [DW84] that, ``Lectures provide the scaffolding without which the course would collapse.'' Some experts in education suggest that lectures can be made more mathetic by adopting the ``Socratic questioning'' method [Gar89, p. 6]:

[T]he teacher is more of a coach, attempting to elicit certain qualities in her students. The teacher engages the student actively in the learning process, posing questions and directing attention to new phenomena, in the hope that the student's understanding will thereby be enhanced . . . . Socratic questioning is the best-known classical instance of a ``transformative approach.''
While I do use Socratic questioning to enliven my lectures, and I do believe that it can help students understand various approaches to a problem by discussing the advantages and disadvantages of each approach, I do not consider transformative teaching to be distincly different from mimetic teaching in that it doesn't facilitate internalization of knowledge intended by mathetic learning. As Papert puts it [Pap93, p. 13]:
[A] teacher leading a class of students by ``Socratic questions'' to ``discover for themselves'' some formula in mathematics . . . is not significantly different than a good explanation of the formula.

The mathetic balance I seek lies not in Socratic dialogs but in requiring students to be intimately involved with the problems on hand, that they approach a problem from different angles and observe how each approach does or does not lead to a solution. This is my interpretation of what Papert calls syntonic learning, a.k.a. learning by doing [Pap80, p. 63]. Carl Rogers, as cited in [Kra78], said, ``The only learning which significantly influences behavior is self-discovered, self-appropriated learning. Such learning, . . . assimilated in experience, cannot be directly communicated to another . . . . Significant learning is acquired through doing.'' One can effectively practice syntonic learning in the mind, or with the help of pencil and paper, to explore the properties of analytical formulae that describe static or simple dynamic systems. To practice syntonic learning for complex dynamic systems, such as multi-node computer networks, however, requires prolonged observation of the system, with the help of computer simulation and visualization tools. Not only does the nature of syntonic learning require students' intimate involvement with the dynamics of a problem in the process of knowledge discovery, the fundamental goal of the mathetic approach to encourage creative thinking also requires long-term involvement in a research project. Here's a nice long quote from [Gar89, p. 113] on creativity:

Intelligence involves the ability to solve problems, or to fashion products, which are valued in one or more cultural settings. [Creativity is an ability to] regularly solve problems or fashion products . . . in a domain which are initially considered novel or unusual but ultimately come to be accepted in one or more cultural settings.

Most psychologists have considered creativity a trait, which individuals possess to greater or lesser extent, which can be applied equally to any content, and which can be assessed reliably with short paper-and-pencil tests. The typical item on such instruments asks individuals to list all the uses of a brick which they can think of; or to indicate all the objects a given geometric configuration could depict. Those individuals who can come up with many responses, and particularly responses that are deemed unusual, are considered more creative "in general" than those who come up with few, or with banal, associations.

While this definition--and its operationalization in a test-- may ferret out individuals who are inventive in a "cocktail party setting," I contend that this standard way of thinking has little to do with the heights of creative achievement of a Mozart, an Einstein, a Leonardo, or even the more modest achievements of the leading artists or scientists of the day. The creative achievements to which I refer occur only at the hands (or in the minds) of individuals who have worked for years within a domain and are capable of fashioning--often over significant periods of time--products or projects that actually change the ways in which other individuals apprehend the world. Verbal cleverness or disparate associations have little to do with what is distinctive about these creative titans.

It is often said that college education is that which remains after one has forgotten what one has learned. Scientific breakthroughs and technological advances make obsolete, at a faster and faster pace, skills and knowledge one learns in college. To function at all in today's society, one must constantly acquire new sets of skills and ``brush up'' on one's knowledge. This is a totally delightful proposition, actually, if one loves learning. To put it more somberly, [Tea66]:

The desirable end [of learning] is a self-starting, self-propelling eagerness for more learning as helpful to a more abundant and intelligent responsiveness to the individual's life encounters . . . . [W]ith the practical mandate that each student should continue into adult life his drive to acquire a larger body of operational knowledge as well as to handle his leisure with productive resourcefulness, this problem of self-motivation assumes greater importance than ever . . . . To learn to want to keep on learning is one of the priceless assets of the right kind of collegiate experience.
So what motivates one to want to learn and to keep on learning? Roger Kraft in [Kra78] says:
[N]o real discovery and no learning take place unless the student is genuinely absorbed. He must feel a need to do and to know, and it cannot be for what Bruner calls extrinsic reasons, like passing courses, getting grades and degrees, or pleasing someone else. If such are his only purposes, then how to get high grades, degrees, and approval will be all he will permanently learn . . . .
This ``need to do and to know'' is what propels one to want to know, to want to learn, more. This ``need'' is called ``curiosity.'' Wilkinson in [Wil84] says, ``Basic to any intellectual achievement is curiosity--variously described as the `desire to know,' or the `urge for discovery.'''


H. Dubrow and J. Wilkinson. ``The Theory and Practice of Lectures''. In M.M. Gullette, editor, The Art and Craft of Teaching, pages 25-37. Cambridge: Harvard University Press, 1984.

H. Gardner. To Open Minds. New York: Basic Books, 1989.

O.P. Kolstoe. College Professoring: or, through Academia with Gun and Camera. Southern Illinois University Press, 1975.

R.G. Kraft. ``Bike Riding and the Art of Learning''. Change, X(6):36,40-42, Jun./Jul. 1978.

S. Papert. Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books, 1980.

S. Papert. The Children's Machine: Rethinking School in the Age of the Computer. New York: Basic Books, 1993.

O. Tead. ``The Need for Significant Learning''. In N.T. Bell, R.W. Burkhardt, and V.B. Lawhead, editors, Introduction to College Life, pages 133-138. Boston: Houghton Mifflin Co., 1966.

J. Wilkinson. ``Varieties of Teaching''. In M.M. Gullette, editor, The Art and Craft of Teaching, pages 1-9. Cambridge: Harvard University Press, 1984.