Over 70 years ago in Manchester, New Hampshire, children learnt no formal arithmetic until grade 6 (about age 11). The program's creator, Superintendent Louis Benezet, describes it like this:

The paragraph above is from the first part of his classic three-part paper:In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite - my new Three R's. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language. I picked out five rooms - three third grades, one combining the third and fourth grades, and one fifth grade.

L. P. Benezet, "The Teaching of Arithmetic I, II, III: The Story of an Experiment," Journal of the National Education Association The articles were reprinted in the Humanistic Mathematics Newsletter #6: 2-14 (May 1991).

Here is a single PDF or html file with all three parts. Here are scanned-in GIF images of the articles (as reprinted in the Humanistic Mathematics Newsletter).

Here are JPEG images of Louis P. Benezet.

### Rote learning

Here is problem 5 from Benezet's list of problems:

The distance from Boston to Portland by water is 120 miles. Three steamers leave Boston, simultaneously, for Portland. One makes the trip in 10 hours, one in 12, and one in 15. How long will it be before all 3 reach Portland?

In the ninth-grade students in Manchester, traditionaly taught, 6 out of 29 gave the right answer; the experimental second grade "had an almost perfect score." Probably many of the ninth graders gave 37 as the answer. At least, that is the result of arithmetic teaching today, as these extracts from current research indicates.### Hassler Whitney

Whitney (now deceased), a research mathematician at the Institute for Advanced Study, got interested in elementary education and saw great value in Benezet's approach.- F. M. Hechinger, "Learning Math by Thinking," New York Times, 10 June 1986. Reports on the article by Hassler Whitney (the next item in this list).
- Hassler Whitney, "Coming Alive in School Math and Beyond,"
Journal of Mathematical Behavior, 5(2): 129-40 (Aug 1986).
Abstract:
The status of mathematics instruction, especially in the elementary school, is discussed. A meaningful, holistic approach is advocated, rather than an emphasis on rules and procedures.

- A. Lax, "Hassler Whitney 1907-1989 - Some recollections 1979-1989," Humanistic Mathematics Newsletter #4:2-7 (1989).

- Andrew Gleason of Harvard wrote a short, unpublished article (html |pdf) arguing that we should try Benezet's experiment today. (The article is based on a talk he gave at the University of Illinois.) We agree, and hope that people will consider its relevance to other subjects. Physics teaching, for example, suffers from the same rote learning that Benezet abolished in his mathematics reform. What would a Benezet-style physics or science curriculum look like? What about history or languages?
- D. Hammer, "Physics for first-graders?" To appear in Science Education ("Comments and Criticism"). Preprint available (html | pdf). Very interesting article about rote-learning in physics.
- John Clement, Jack Lochhead, George S. Monk. Translation Difficulties in Learning Mathematics. American Mathematical Monthly 88(4):286-290 (Apr 1981). In PDF: high resolution (574k) or fax resolution (167k).
- Mahajan, S. & Hake R.R. 2000. Is It Time for a Science Counterpart of the Benezet-Berman Mathematics Teaching Experiment of the 1930's? Physics Education Research Conference 2000: Teacher Education.
- Material at http://www.whimbey.com. Just as calculators can turn mathematics into button pushing, algebra can turn it into symbol pushing. Solving problems without algebra encourages graphical, visual methods of solution -- methods that require thought.
- National Research Council, Reshaping School Mathematics: A
Philosophy and Framework for Curriculum (Mathematical Sciences
Education Board, 1990); pp. 30-31:
Mastery of subject matter has for years been the predominant focus of mathematics education research...Contrary to much present practice, it is generally most effective to engage students in meaningful, complex activities focusing on conceptual issues rather than to establish all building blocks at one level before going on to the next level (Hatano, 1982; Romberg and Carpenter, 1986; Collins et al., 1989)

...

There is some evidence to suggest that paper and pencil calculation involving fractions, decimal long division, and possibly multiplication are introduced far too soon in the present curriculum. Under currently prevalent teaching practice, a very high percentage of high school students worldwide never masters these topics - just what one would expect in a case where routinized skills are blocking semantic learning (e.g.,**Benezet, 1935**). The challenge for curriculum development (and research) is to determine when routinized rules should come first and when they should not, as well as to investigate newer whole-language strategies for teaching that may be more effective than traditional methods.**this is an area where more research needs to be done.**[Our**empahsis**.]

Send comments and contributions to:

Sanjoy Mahajan <sanjoy@mrao.cam.ac.uk> Richard Hake <rrhake@earthlink.net>We thank:

- Jerry Becker, of Southern Illinois University, for sending the plain text of Benezet's and Gleason's articles.
- Alvin White, of Harvey Mudd College, for reprinting Benezet's paper in the Humanistic Mathematics Newsletter.
- The authors of HTMLDOC, the free-software program used to convert HTML to PDF.