Some Technical Commentaries on Mathematics Education and History

Here is a list of titles of papers dealing with mathematics or science education; just select the highlighted brief title. They are all copyright Ralph A. Raimi unless otherwise indicated. Since some of them are transcriptions from text documents (which I am gradually improving) there are a few accented letters and mathematical symbols that have been replaced here by the best equivalents. This will in general cause no problems, though a couple of words of foreign provenance might look misspelled.

In addition, at the very end of the list of papers will be found two advertisements for myself, or, more accurately, for books written and published by myself. Read all about it.

NCTM Debates the Civilized World, Has the National Council of Teachers of Mathematics really changed its course? A discussion of NCTM's responses to some pointed questions from a newspaper columnist in 2005, and to newspaper commentary on its Focal Points of September 12, 2006. An annotated documentary Appendix is printed separately just below this article. December 11, 2006.

Appendix to the paper, NCTM Debates the Civilized World, Twelve documents in the history of the math wars, 1989-2006, touching on NCTM curriculum visions and their confused interpretations, with notes and bibliographic references.

Recent Events in French Education, A lengthy commentary, all the truth as of 19 April 2006.

Another French Revolution? Statement of Gilles de Robien, Minister of Education. In announcing the publication of the new national standards ("socle") for the primary schools, the Minister charts a new path, in which the actual teaching of such things as French grammar and the algorithms of arithmetic apparently comes first. Posted May 15, 2006.

Why Have Public Schools? (Pourquoi l'Ecole?). Here is the text, translated into English, of a 2006 lecture by Laurent Lafforgue, in which, though his talk is billed as an introduction to a program of technical talks on math and French education, he brilliantly and precisely describes what the schools really can in all modesty accomplish, as against the depressing background of the pretenses of the educational theorists who now govern the curricula in France. Posted January 6, 2008.

The Concept of Conceptual Understanding , A short history of my efforts to understand it. Posted June 16, 2009

An Unfortunate NCTM Textbook Endorsement , Despite subsequent denials, the National Council of Teachers of Mathematics has publicly endorsed certain commercial school mathematics textbooks. Posted November 18, 2006

Newton's Unpublished Calculus Book, a study of compressed misinformation.

Ruth Parker's Chicken Problem, a comment on the lady's road show, and a suggestion for its improvement. Posted here 13 February 2006.

Whatever became of the New Math?, a brief, incomplete and biased account of the school math phenomenon of the 1960s.

Judging State Standards, being Chapter 2 of the symposium volume, What's At Stake in the K-12 Standards Wars (which you ought to buy), edited by Sandra Stotsky. It tells how Braden and I once judged the relative demerits of State math standards, mostly written by the clueless. Posted 2003 by permission of Peter Lang publishers.

My Life With ACHIEVE, an account of some paid labor I did for an organization of some importance, and containing some comments on the organization itself, its purposes and perhaps its influence. Posted here 25 September 2005.

Conference On Teaching Algebra in the Schools,an account of some unpaid labor I did, for nobody in particular, by attending a conference held at the Brookings Institution's Brown Center in September of 2005. Warning: This paper makes no attempt at complete coverage of the talks given, or the comments from the floor. It is entirely unofficial, sometimes a bit cutting, and more a truthful account of my own reactions than of the talks themselves, which I might have represented incorrectly here and there, though not deliberately. Posted here 20 October 2005.

Jerome Bruner and The Wood's Hole Conference of 1959 , a review of Bruner's report on the conclusions of an all-star study of the possibilities of school education, in the days of the "New Math" and other heady designs on the future. (Posted 2003)O

How did it ever come to this?, an expanded version of a talk given at the annual meeting of the National Association of Scholars in New York on 22 May 2004, as part of a symposium on recent sad developments in mathematics education in the schools.

Have we forgotten the value of memory?, a comment on the New York Regents' B-examination in mathematics and its associated crib sheet.

Recent research progress in the teaching of algebra in the schools., a comment on what the National Science Foundation pays mathematics educators to tell each other at conferences on school mathematics (K-12). This essay is intended for mathematicians, mainly.

A letter to Dean Posamentier., responding to a solicitation of advice concerning state standards for school math, but narrowly drawn to address the subject of "proportional reasoning". Posted May 27,2004.

Fair and equal in political mathematics., on the confusion -- probably unintentional -- of a probabilistic idea with a popular moral judgment. Posted June 20, 2004.

How the National Council of Teachers of Mathematics Teaches Children to Lie, , an account of one futile effort to comply with a request for help from a sister organization of the American Mathematical Society. Posted October 8, 2008.

On the circumference of a circle., An anecdote on the popularization of mathematics, which can only be done if one assures the audience there won't be an exam. Posted November 7, 2004.

Recent research progress in the study of the arrogance of mathematicians., a note on a recent paper in the Journal of Research in Mathematics Education. Another essay for mathematicians, who heretofore didn't realize what they were trying to put over on the world.

A Letter to the Editor of JRME concerning their article, commented upon in the link preceding this one, on the alleged arrogance of mathematicians., a letter explaining to the readers of this research journal what "without loss of generality" means in mathematical discourse, and an attempt (futile, I believe) to convince them that its use exhibits the antithesis of the exercise of authority.

Encounter with Steve Leinwand, 1997. (Posted Feb 10, 2001), an account of my first and only visit to a regional meeting of NCTM, where I met and observed Steve Leinwand, Consultant to the Education Department of Connecticut and sometime President of the National Council of Supervisors of Mathematics.

alfie (Posted Dec 14, 2001), an account of my first and only attendance at a local presentation by Alfie Kohn, educational consultant, who spoke to an audience of (mainly) teachers at Fairport, NY on December 5, 2001, in opposition to standardized testing in the schools.

Glenda Lappan (Posted Aug 26, 2004),an account of a talk given by the noted mathematics educator, Glenda Lappan, on the occasion of the inauguration of Raffaele Borasi as Dean of the University of Rochester's Warner Graduate School of Education in 2001. The talk, though directed to an audience of teachers and other education people not particularly expert in mathematics, does contain a good indication of the educational philosophy favored by the National Council of Teachers of Mathematics of that time, with some fairly simple and lucid examples taken from elementary topics in school mathematics teaching.

Stone Age Mathematics, A brief account of the kind of mathematics urged by the National Council of Teachers of Mathematics (USA) upon our schoolchildren, via a ribbon- cutting example. (Posted March 28, 2004, revised December 6, 2005)

High Stakes Examination Problems, An essay on some deficiencies in today's statewide school math exams, and sample textbook problems in general, with examples from New York and Michigan as well as a recent addition to the syllabus for the popular middle school program called CMP. (Posted June 3, 2004)

Basketball Logic and the NAEP, Analysis of a really bad question on the sacred NAEP mathematics exam, the "gold standard" against which our state exams are said to be measured. (Posted November 3, 2009)

Educational Inflation (Posted April 10, 2004, Revised November 2, 2005), a comment on how success in public education is achieved, but with hope for the future anyhow.

Educational Ignorance (Posted April 4, 2004), a description of some of the logical failures in school mathematical teaching on eve of the era of "The New Math.

How polynomials and rectangles illuminate each other(Posted February 4, 2005), an example of how teachers are taught to pretend mathematics can be made exciting, both before and after the era of "The New Math.

Friedrich Engels on the True Meaning of Differentiation, an extract from a letter to his friend Karl Marx.

The absurdity of negative numbers according to Augustus De Morgan., a note on the history of an idea. This essay is intended for teachers of mathematics at levels 7-12, and others.

On using ridiculous answers.. This one is longer than the one on De Morgan's troubles with negative numbers, and actually contains it; but also explains other dark algebraic mysteries, even complex solutions to problems about lengths of sticks. Same audience as above: teachers of algebra in the schools, and their professors. Caution! The square root sign used a number of times near the end looks like a capital V as prefix, e.g. V(z) would mean sqrt(z). Sorry.

Why learn trigonometry?, an answer, so that teachers will know what to say to parents and other practical folks.

Pourquoi la trigo?, the same essay as above, only done into French for those of you who are not strong in English. (Posted November, 2002)

A difficult child, a sad, true story of the consequences of math education in a local school system.

The psychoanalysis of division sums, a curious episode in the history of math education, in which the famous psychoanalyst Melanie Klein uncovers the source of algorithm avoidance.

Calculators in high school linear algebra, how recent NCTM-approved advances in mechanized pedagogy can speed up the process of not learning anything. [The audience for this one must know some linear algebra.]

A Note on Equality, how an imperfect philosophy causes one to misconstrue the meaning of equations and Euclid. [The audience for this comment must understand the use of equivalence classes in algebra.]

A 1958 caution concerning the New Math, being the text of a personal letter from me to Frank Quigley at Yale on the possible fate of the newly-established SMSG and how to prevent it.

Is Mathematics a Foreign Language?, a note on discourse analysis.

Electron shells and Cargo cults, on what passes for successful science education in our schools. (This one is not as long or as good as the next one down this page.)

The Place of Science in a Liberal Education, this one being a longie. Serious.

False Report on the 1999 California Framework for Mathematics, a commentary of a woeful error committed by Zalman Usiskin and not since corrected by him, even after having had it pointed out to him by Wu and others who can read. Posted July 16, 2002.

Review of Israel's Proposed Math Elementary Curriculum 2000, by Raimi and and Braden, posted June 1, 2002.

VESTED INTERESTS, an advertisement for my 1982 book of essays and fantasies. Good book.

THE PHILOMATHIC DEBATING CLUB, an advertisement for my history of a phenomenon of my youth, and before. Also a good book.

Other documents will be added to this list from time to time.