It Works for Me, part 2

Part 2 is riveting. I'm in the middle of it now.

Brownell, spoken well of by NCTM and various luminaries in today's reform movement, was the key reformer of the early twentieth century and promoted what he called meaningful learning; i.e., teaching mathematics as a process, rather than a series of end products of isolated facts and procedures to be committed to memory.If this sounds like what the reformers are talking about today, it is because the complaints levied against how mathematics is taught, like the complaints about education in general through the years, have been perennial.What is often not mentioned when these complaints are "replayed" is that there have also been perennial solutions and some of these solutions have actually been effective.

Brownell led the charge against the isolated, rote-memory type of math teaching that came about in large part through the books and efforts of E. L. Thorndike, another figure of education at that time.The reformers listed above, including Brownell, all wrote math texts that were in use from the 30's through the 60's.The later books were written by Brownell (with Guy T. Buswell and Irene Sauble) starting in the mid-50's in a series called "Arithmetic We Need".I'm familiar with this series because they were the books I used when I was in school.I have copies of these and other books in use by all the authors.All the books give explanations of what is going on with specific mathematical procedures, and topics were presented in a logical sequence that allowed building upon previously learned and mastered material.But what is particularly interesting are the explanations in the teacher's manuals and prefaces to these books:

• From "Making Sure of Arithmetic" (Grade 6):"Each new process is explained in the simplest terms, utilizing every graphic aid possible.From the beginning, meaning and relationship are emphasized.As a result the pupil gains not only skill but skill with understanding." (Morton, et. al., 1946)
• From "The New Curriculum Arithmetics" (Grade 7) "A program of mixed and cumulative practice exercises insures mastery and retention of the processes and topics studied." (Brueckner, et al, 1941)
• From "Growth in Arithmetic" (Grade 3):A comparison chart in the teacher's edition showing the difference between the older (Thorndike-derived) textbooks and this one: "Older: Taught as facts, skills, and habits of procedure; Newer: Taught to emphasize meanings, principles, and relationships. Facts and skills developed after understanding." (Clark, et al, 1952)
• From "Teaching Arithmetic We Need" (Grade 5) "Each book in this series is built upon a conception of arithmetic that involves two aims, the social aim and the mathematical aim.Adherence to the latter aim requires that children see sense in what they learn."(Brownell, et. al.

[snip]

I would therefore add to the list of possible factors influencing the upward trends in achievement scores from the 40's through the mid-60's the textbooks in use, and the implementation of the theories behind them.This is not to say that the traditional math of such time was perfect.If I had to compare the "Arithmetic We Need" texts that I used with Saxon Math, or the math program used in Singapore, I would say the latter two are superior with much more challenging word problems.I can say, however, that the essentials of math were covered well, which would include place value, why a particular algorithm worked, thorough application of fractions and multiplication and division of fractions (similar to Singapore's approach) and application of procedures to solving word problems.Here are two problems from the sixth grade book of "Arithmetic We Need":

• "How many glass containers holding 3/16 quarts can be filled with water from a quart bottle which is ¾ full?"
• "If it takes 1and½hours to drive to the city,what part of the distance will Bill and his father drive in ¾ hour?"

(Brownell, et.al., 1955b)

It Works for Me, Part 1
It Works for Me, Part 2
It Works for Me, Part 3