State of Pennsylvania Responsible for Provision of Public Education

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

Tuesday, February 13, 1912:  We had an inspector up at school this morning. You can bet I was glad when he had gone. Ruth and I went up to Oakes this evening. I took my Algebra along and Rachel helped me with it some.

Click on the picture to enlarge the words.

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

The previous Friday Grandma wrote that this would be the last week for her teacher and that she’d then get a new teacher.

I suppose that the school inspector visited McEwensville High School to make sure that all was on-course and to prepare for the transition to the new teacher.

A hundred years ago there were many schools scattered across the county. A county superintendent was responsible for making sure that they followed state requirements.

The state, then as now, was responsible for providing public education.  In a 1912 book I found the language in the Pennsylvania constitution:

The General Assembly shall provide for the maintenance and support of a thorough and efficient system of public schools, wherein all the children of this Commonwealth above the age of six years may be educated, and shall appropriate at least one million dollars each year for that purpose.

Source: Pennsylvania Constitution as quoted in The Status of the Teacher by Arthur Perry, Jr.  (1912)

Over the years this provision has been shortened. It now says:

Public School System

Section 14

The General Assembly shall provide for the maintenance and support of a thorough and efficient system of public education to serve the needs of the Commonwealth.

I guess there no longer is a need to indicate that at least a million dollars of state money will be spent on public education. According to Wikipedia the state of Pennsylvania allocated more than $11.4 billion for education-related programs for the 2008-2009 fiscal year. :)

Do Students Cheat More Now?

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

Thursday, January 25, 1912:  Gave my ear to a free-for-all lecture this afternoon. It was delivered by Mr. Teacher, the chief part of which was about cheating on examinations. I’ve been so worked up at this, although Conscience tells me not to.  Anyway I believe it is time to stop, and do better in the future. So now, I will try to bid adieu to all ways of crookedness and get the things in my head instead of having them on paper.

Recent photo of the building that once housed the McEwensville school.

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

My grandmother cheating on tests!! . . . .Grandma, what were you thinking?

Sometimes it’s hard to interpret what Grandma wrote without judging her.  Grandma was 16 and about 40 years younger than me when she wrote this diary entry. I’m looking at this entry through the lens of a mother and I can’t completely wrap my head around why a teen would decide to cheat.

I want to think that the world was a simpler place a hundred years ago—and that students were less likely to cheat back then. But I’m not sure. This is the second time Grandma’s mentioned cheating in the diary.

On February 7, 1911 Grandma wrote:

Some of the boys at school found the teacher’s Latin questions in examination, and we all expect to make a good mark. I do at least, but I might be fooled as some cheats are.

And, the next day, her diary entry said:

Had some of our exams today. Came out all right in Latin. Our arithmetic wasn’t so easy though.

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?

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