Being poorly versed in R.L. Moore's methods ... other than through some descriptive materials and some conversations with some of his students ... I nonetheless have gathered that the crux of his methods appears to have been to engage his students in their personal development of personal mathematical theories ... rather than in "solving problems" in the usual meanings of that phrase. Their voluminous subsequent contributions to mathematical progress (especially in topology) was through the development of mathematical theories ... which is not the usual meaning of "solving mathematical problems."
Educators have yet to recognize that all humans rely on their own development of functional personal intelligence ... about anything ... in the form of (what amounts to) their own personal theories about "such things". It is as true of pre-schoolers as it is of research mathematicians ... and everyone in between. The essential character of theoristic learning is the same; the differences are in degrees of sophistication ... and before puberty, in developmental maturity. In street language, theoristic learning is commonly called "common sense."
The travesty of American curricular education in mathematics is that it largely fails to guide students to develop strong personal mathematical theories of their own ... much less personal powers of theorizing ... that arm them for effective exploration and decision-making. [That is, mathematics curricula make too little common sense to the students, themselves.]
Epstein is only partly right. The "discovery mode" of instruction (properly done) does, indeed, engage students in theoristic learning ... cultivates their development of personal theories, and nurtures their development of creative, analytic, and rational thinking powers. But discovery instruction is not the only mode for doing so.
In the contrast, didactic modes mostly express theories owned by "the teller." For sure, "I hear" your theory, does not ensure that I grasp it as a theory ... much less buying its validity or reliability. When "I see" that theory, it is through perceiving that, and how, it fits familiar phenomena of the kind it describes. But "I do" when I personally, internally construct a theory ... even if it is essentially a reconstruction of the one that you have expressed. The growing plea for greater "conceptual understanding" ... carefully analyzed ... is an implicit recognition that all humans inherently are vitally dependent on theoristic learning.
Many didactic teachers have mastered the art of telling their own mathematical theories in ways that guide students to internally develop theories that adequately replicate what was transmitted. That scenario is thoroughly described in communications theory. What is special about education is the need for transmitters first to recognize that the receiver needs to assemble "the pictures" into personal theories. Through that recognition, it becomes realistic to deliberate how best to induce "the message" theory.
Discovery is one way ... and it can circumvent many of the communications dilemmas that arise in the encode-transmit-receive-decode process. But the discovery mode is is far too limited for mass communications. In the broader arena, the need is for instructors (teachers, authors, media composers, etc.) to learn how to communicate in ways that induce the development of functional theories within the learners.
However, careful study of the interactive proceedings of discovery instruction ... as can be done through clinical case studies ... can shed much light on how to improve the effectiveness of didactic instruction.
From: Richard Hake Sent: Saturday, February 04, 2012 2:14 PM To: firstname.lastname@example.org ; email@example.com Cc: firstname.lastname@example.org ; PHYSLRNR@LISTSERV.BOISESTATE.EDU Subject: Re: The Moore Method
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A physicist wrote to me privately "What term might be appropriate for the way R. L. Moore taught mathematics at the University of Texas?"
My response and references thereto might be of interest to some subscribers to Math-Learn, Math-Teach, Phys-L, and PhysLnrR.
"Some say that the only possible effect of the Moore method is to produce research mathematicians, but I don't agree. The Moore method is, I am convinced the right way to teach anything and everything. It produces students who can understand and use what they have learned. . . . . . There is an old Chinese proverb that I learned from Moore himself: 'I hear, I forget; I see, I remember. I do, I understand.' " Paul Halmos (1988, p. 258)
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