Comment on Alan Kay's Talk at TED by Dom

Thu, 20 Mar 2008 21:00:58 -0700

As I see it, Paul Lockhart’s essay would be much more powerful if it were not written in such a complete historical vacuum. Although Lockhart decries the sterile formalism in which mathematics courses have been and continue to be taught, he makes absolutely no reference to the fact that the traditional mathematics curriculum was demolished by the excessive formalism and abstractions of the SMSG new math, as incorporated in the Houghton Mifflin series of books co-authored by Mary P. Dolciani. This apparent ignorance on Lockhart's part is likely due to the fact that he was educated with Dolciani-type books, and he may not be aware of the preceding textbooks. The manner in which Lockhart ridicules Thales' Theorem (which he does not name), on page 19 of the PDF file, is utterly unacceptable--and it raises serious questions about the rest of his lament about Euclidean Geometry. When I studied 10th-grade Euclidean Geometry in 1963-64, at Everett High School, in the factory city of Everett, MA, we used the textbook by William G. Shute, William W. Shirk, George F. Porter, "Plane and Solid Geometry," American Book Company (1960). On page 25-27, the textbook contains a historical Note about Thales (640-546 B.C.), Thales' demonstration that all vertical angles are equal (considered to be the first theorem ever proved), deductive reasoning, and the components of a proof of a theorem. According to the Note, when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: 1. all straight angles are equal 2. equals added to equals are equal, etc. At the top of page 10 on the PDF file, Lockhart writes: "So put away your lesson plans and overhead projectors, your full-color textbook abominations, your CD-ROMs and the whole rest of the traveling circus freak show of contemporary education, and simply do mathematics with the students!" Although this advice is quite sound, it is unfortunate that Lockhart conveniently makes absolutely no reference to the fact that all this rubbish has been produced and promoted by the self-styled math reformers of the past two decades.

Comment on Alan Kay's Talk at TED by Nicholas Chen

Fri, 21 Mar 2008 13:27:56 -0700

Although this advice is quite sound, it is unfortunate that Lockhart conveniently makes absolutely no reference to the fact that all this rubbish has been produced and promoted by the self-styled math reformers of the past two decades.

I agree that there should be some empirical study about the use of these "self-promoted" reforms in education. My appreciation for these new methods (unfortunately) might come about from the fact that I already know the basis of them and I am viewing them from a different perspective. Viewing things from different perspectives usually helps to solidify understanding. But I am not really sure whether it would help someone who has yet to understand the basic concepts.

And things are usually not as ideal with these new methods as their proponents might claim. Python and Smalltalk:

I knew more than one person who in years past inspired by an Alan Kay presentation have tried Squeak only to encounter lots of bugs and problems with the core tools or trying to duplicate the demos he shows.

Just as a reader is inclined to give up on a book that is poorly written, someone who encounters numerous distractions from a system is also likely to just abandon the system. In this case, since the distractions themselves are not even pertinent to the material being studied, they are nothing but noise. On the other hand, the abstractions and formalisms used in the traditional books -- turgid as they might be -- do pertain to the material that is being studied.

Other interesting points to consider (and I discussed these with my colleagues) are retention and knowledge transfer. Retention: how long does the student retain the main ideas that have been taught. Knowledge transfer: are they able to apply the knowledge they learn to solve other problems? After all, what is the point of just studying something only to pass an exam?

So new methods aren't necessarily better especially if they only have shallow retention and knowledge transfer.

.::output >> /dev/null::. : Alan Kay's Talk at TED

Comment on Alan Kay's Talk at TED by Dom

Comment on Alan Kay's Talk at TED by Nicholas Chen