From Dave ... some thoughts on 1925 .... and the recent lack of data

Related to the issues of math curriculum and pedagogy, I recently saw a math book and thought some of it was highly relevant to the debate.

On page 26, it has a section, “How to Solve a Problem”

“It is important that you develop the ability to analyze problems. Those whose daily work requires the solution of many problems must always think out the analyses, even though they do not write them out. In the problems that follow throughout this book you are asked to think out the analysis of each, and often to write it out. Such work will give you needed practice that will help you to solve the problems that arise when you later enter … your profession.

Other things besides analysis are necessary if you are to solve the problems you meet. Your computations must be rapid and accurate; otherwise your work is of no value. …

Below you will find a suggested method for attacking, that is, analyzing a problem. You should study this carefully and learn how to apply this method to other problems. Although there is no one best form of analysis, the one given here is a very good guide as to what an analysis should be. …”

The book has a great variety of word problems for students and among other things it has a nice section on graphing data, including broken-line graphs, bar graphs, Circle graphs and Picto-graphs. What is the title of this fine book?

The Brown-Eldredge Arithmetics – Book 3

Authors:
Joseph C. Brown, A.B., A.M.
President State Teachers College, St. Cloud, Minnesota
Former Supervisor of Mathematics, Horace Mann School, New York City

Albert C. Eldredge, B.S.
Assistant Superintendent of Schools in Charge of Junior High Schools.
Formerly in charge of Elementary Schools,
Cleveland, Ohio.

Copyright, 1925. Row, Peterson and Company, 12th printing.

It then notes in the introduction:

“In each of the vocations and professions some knowledge of arithmetic is necessary, and one who has not acquired a high degree of accuracy and a reasonable degree of speed in computation is usually at a great disadvantage.

If wisely used, the drill exercises in this book will be of value to you because they will enable you to increase your speed and accuracy. Strive to excel your own best record. Realize that you are working for yourself, and that the knowledge and skill which you acquire will be of great value to you in the years to come.”

Very wise words. This begs the question:

What sort of “science of education” do we have when basic instructional techniques for learning math which worked well for humans in 1925 (written by teacher educators of the day in a book in its 12th printing) are discarded or discredited in the 1990’s only to get revived by those outside the college of education community 10 or 15 years later due to widespread math illiteracy. This should serve as a warning to those looking up to the college of education community for advice and insight into math education. Maintain a healthy skepticism and ask for some hard data, the emperor is not fully dressed and it’s not a pretty sight.