Comparison: 1912 and 2012 Algebra Textbooks

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Tuesday, January 23, 1912:  Sleigh rides are a thing of the past now. There is no danger of freezing yourself now. I’m at a standstill in Algebra.

Her middle-aged granddaughter’s comments 100 years later:

Maybe Grandma was struggling in algebra because the textbook was confusing.

To get a sense of how algebra textbooks have changed over the past 100 years. I compared the promotional materials for an algebra textbook published in 2012 with the information in the preface of an algebra textbook published in 1912.

The Books

2012 Book

Beginning & Intermediate Algebra, (4th Edition) by John Tobey, Jr., Jeffrey Slater,  Jamie Blair, and Jennifer Crawford (Pearson)

1912 book

Durrell’s School Algebra by Fletcher Durrell (Charles E. Merrill Company)

Comparison

Of course the book published in 2012 is brightly colored with lots of pictures and figures (and there are numerous supplemental online resources). The 1912 book is black and white with only a few pictures.

The 1912 book looks denser than then new one. However, the chapter titles are similar. For example both books had a chapter called Factoring.

Purpose

2012:  “. . . builds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical “building block” organization makes it easy for students to understand each topic and gain confidence as they move through each section.”

1912:  “The main object in writing this School Algebra has been to simplify principles and give them interest, by showing more plainly, if possible, than has been done heretofore, the practical or common-sense reason for each step or process.”

Problems

2012:  “Student Practice problems are paired with every example in the text . . .”

1912: “A large number of problems. . . .”

Review and Reinforce

2012:  “Students will find many opportunities to check and reinforce their understanding of concepts throughout the text . . .”

1912: “Numerous and thorough reviews of the portion of the Algebra already studied are also called for.”

Cube Root Word Problems

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Monday, January 8, 1912: A regular snow storm set in this afternoon. How beautiful the snowflakes looked as they descended to ground. Am now able to extract the cube root without difficulty. Pa came for Jimmie and me this evening.

Her middle-aged granddaughter’s comments 100 years later:

The teacher must have clarified how to do cube roots. Grandma was struggling with cube roots the previous Friday.

As a parent who had strong opinions during the “math wars” of the 1990’s about what should be included in (and, perhaps more importantly, what should be excluded from) the math curriculum, I’m fascinated by early 20th century math text books.

In textbooks from a hundred years ago, there is more focus on calculation than there is today but they also contain some cool word problems —Cube roots are a great example of this.

Here are some cube root word problems from a 1911 textbook called Kimball’s Commercial Arithmetic:

1. If a cubical block contains 21,952 cubic inches, how many square feet of paper will be required to cover the entire surface?

2. The entire surface of a cubic block is 384 square feet. How many 1-foot cubes can be cut from the block, allowing nothing for waste?

3. A cubical cistern holds 400 bbl. of water. How deep is it?

4. What are the dimensions of a cube that has the same volume as a box 2 ft. 8 in. long, 2 ft. 3 in. wide, and 1 ft. 4 in. deep?

The texts also contained lots of “tricks” and principles.

Principles

1. The cube of a number cannot have more than three times as many figures as its root, nor but two less.

2. If a number is separated into periods of three figures each beginning at the units’ place, the number of figures in the cube root will be the same as the number of periods.

I thought of several easy cube roots (100 is the cube root of 1.000.000. and 5 is the cube root of 125.), and decided that the principles are correct. (Of course they were correct—but somehow I felt better after I thought of a few problems to confirm it.)

If you’re a math geek, here are some previous posts that explored the math curriculum and problems from a hundred years ago.

Odd, Unusual, and Strange Math Problems

More Odd, Unusual, and Strange Math Problems

1911 Algebra Problems: The Lusitania and Molasses

Old Math Problems

An Old Mental Math Trick

Lowest Common Multiples and Highest Common Factors

Fractions in 1911 Algebra Book

Has the Math Curriculum Been Dumbed Down?

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Friday, January 5, 1912: It’s so cold now. How quickly the weather has changed. I didn’t mind it at all in school for the stove sent forth a regular shower of heat. Was rather freezy coming home and the wind a blowing. We’ve come to the extracting of the cube root in arithmetic and I can’t see very good the way it’s done. But suppose I can after I get some kind of an explanation from somebody and not from the book alone. We had these things several years ago, but my idea of them is now rather hazy.

Cube root example from Kimballs Commercial Arithmetic (1911). If you want to read the example, click on the picture to make larger.

Her middle-aged granddaughter’s comments 100 years later:

Whew, math has changed a lot over the years.

I never learned how to do cube roots when I took math in the 1960’s and 70’s, but I can remember struggling with square roots. My children can manually calculate neither square roots nor cube roots, but they do know how to calculate them using a calculator.

Has the curriculum been dumbed down over the years? . . . or has the tedium been removed so that students have time to grapple with more complex problems?

One Hundred Year Old December School Bulletin Board Ideas

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Wednesday, November 29, 1911: Had sort of a little entertainment this afternoon. We got out of school early. Jake was going away so that was the whole reason. I can not give my myself up to a vacation of two days.

 

Bulletin Board Directions

Going Home. This takes three rolls of white crepe paper, one roll each of yellow, lavender and green, with ten sheets of gray matboard for the trees and fence, which are touched up with black tinting fluid. Orange tissue paper will furnish the hospitable glow seen through the windows. Pink tissue paper over yellow crepe paper is used to produce the flesh tint for the lad’s face. (Ladies Home Journal, December, 1911)

Her middle-aged granddaughter’s comments 100 years later:

In 1911, Thanksgiving was on November 30, and apparently the high school students were let out of school early on the day before the holiday.

I wonder if primary students on the first floor of the school building were also left out early.  Grandma’s friend Rachel Oakes was the primary teacher.  Might Rachel have stayed after school to prepare for the following week? Maybe she took down a Thanksgiving-themed bulletin board picture and put a winter one up.

The December, 1911 issue of Ladies Home Journal had an article titled “Christmas Scenes to be Made of Paper: A Suggestion for the Schoolroom Bulletin Board” that had some great examples.

Bulletin Board Directions

The Sleighride. This requires two rolls of gray crepe paper, three of white, and a roll each of red and green, together with four sheets of gray matboard, two bolts of narrow red ribbon for the sun’s rays, black tinting fluid and a little white cotton. The horse is cut from the matboard and tinted with color obtained by wetting a sheet of brown tissue paper.

Bulletin Board Directions

Christmas Carolers. Black and gray matboard, crepe paper, yellow, and orange tissue.

Fractions in Old Algebra Book

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Thursday, November 23, 1911: Am working at my algebra in the evening so I can make a better mark than I did last month. If it isn’t any better I will be beyond all hope.

 Her middle-aged granddaughter’s comments 100 years later:

In October Grandma struggled mightily with algebra—the topic was least common multiples (L.C.M.) and highest common factors (H.C.F.)—and she ended up getting a 68% on the exam.

I’m not sure what Grandma was working on in November—but in one early 20th century algebra book—Durrell’s School Algebra, the chapter after L.C.M. and H.C.F. was Fractions.

The book says:

In algebra, a fraction is often useful in expressing a general formula

Here are a couple of exercises from the book:

1. If three boys weigh a, b, c pounds respectively, what is their average weight?

2. If sugar is worth a cents a pound, how many pounds can be obtained in exchange for b pounds of butter worth c cents a pound?

3. If coal is worth c dollars a ton, how many tons can be obtained in exchange for f bushels of wheat worth h cents a bushel and for w bushels of corn worth y cents a bushel?

Colleges and Public Service a Hundred Years Ago

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Friday, November 3, 1911: Nothing very much doing today. Didn’t get any of my lessons out this evening. I wasn’t in a very studious mood.

Her middle-aged granddaughter’s comments 100 years later:

Grandma  so often worried about school—though she often seemed to not quite get around to studying. I wonder if Grandma ever considered going to college after she graduated from high school.

I suppose college seemed beyond the realm of possibilities to a farm girl in rural central Pennsylvania a hundred years ago. Less than 3% of the people were college graduates back then—and the rate would have been much lower than that for women.

There was an article in the November 6, 1911 issue of Youth’s Companion about why men—the article didn’t mention women—attended college.

Excerpts from

The College in the Service of the Nation

by

Arthur Twining Hadley (President of Yale University)

The American college serves the nation in three conspicuous ways: first, by training men for public office; second by establishing standards of professional success in private business which lead men to do what the public needs, instead of trying merely to make money for themselves; third, by promoting the search for the truth and the spirit of discovery and invention that are necessary for national progress. . .

When we think of public service, we naturally think of these meanings. So did the founders who established the earliest colleges. The founders of the collegiate school at New Haven [Yale] stated in the charter of 1701, that it was the purpose of their institution to fit youth for employment in church and state. . .

Every man, whatever his business can conduct it in such a way as to serve the public. The lawyer who pleads in the courts ought to be doing the same sort of service to the public as the judge who decides the cases. The physician can render and ought to render the same service in providing for public health that the watchman or the signalman provides for public security against accidents.

Any business however simple in its character, where a man thinks first of the work that he is doing and only secondarily of the pay that he is going to get deserves the name of profession.

One of the most valuable things that our colleges can do is to emphasize this ideal of public service, so that the professional element will count for more in men’s lives and the trade element will county for less.

A third way in which our colleges can render public service is by keeping alive the spirit of exploration and discovery-the spirit which leads men to test new methods of action and to pursue new lines of truth. I believe that this is the most important and necessary service of all.

So far as our colleges teach their students the love of pursuing truth for truth’s sake, without regard to the material reward, they fulfill their highest and most necessary duty in the service of the nation.

What Is Rhetoric?

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Thursday, November 2, 1911: Am now taking up the study of Rhetoric, so if my English is not all together proper now is the time to expect a change for the better.

Recent photo of building that once housed McEwensville High School.

Her middle-aged granddaughter’s comments 100 years later:

Rhetoric is the art of writing and speaking. It includes the study of writing rules. I found a 1911 Rhetoric textbook and it includes sections on proper sentence structure (no dangling participles!) and punctuation (sentence structure must be understood to punctuate correctly!).

Oh dear—my English probably is not all together proper . . .

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