Geometry: Definition of a Point

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

Monday, March 11, 1912:  I heave a sigh of relief when I think examinations are past for this month. I have my doubts about what I will get in geometry.


Assumption I. If point A, B, C are in the order {ABD} they are distinct.

Assumption II. If points A, B, C are in the order {ABC} they are not in order {BCA}.

Modern Mathematics (1911), Edited by J.W.A. Young

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

I suppose that Grandma had to do some proofs in geometry. Do students do proofs any more in high school? I get a head-ache just thinking about them.

Here’s the definition of a point in a hundred –year-old mathematics book. It was the first term defined in the book. (I assume that Grandma’s examination was on something more complicated—but I enjoyed reading this definition.)

In geometry a great many technical terms are defined, and each is defined in terms of others. Hence at the beginning of a book on geometry at least one term must be undefined; otherwise the book would have no beginning. We have to leave the undefined term point.

This implies that the reader is free to carry in his mind any image of a point which he can reconcile with what is said about it. We may try to import a notion of our image of a point by saying it has no length, breadth, or thickness, or by like phrases, but these are no part of our book on geometry; they have nothing to do with the logical steps by which the theorems are derived.

Modern Mathematics (1911), Edited by J.W.A. Young

Teachers’ Institute

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

Saturday, March 2, 1912:  Well I really think I worked pretty good today. I put things in order and washed up and a lot more that comes under Saturday duties .Ruth was up to Turbotville attending Teachers’ Institute so you see I had to be busy. Tweet is here this evening.

Recent photo of Turbotville Community Hall. The building was once a high school and the Teachers' Institute probably was held here.

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

Grandma’s 20-year-old sister Ruth was a teacher at one of the one-room schoolhouses near McEwensville. Ruth had graduated the previous spring from high school and immediately got a teaching position.

A hundred years ago teachers weren’t required to attend college, though they had to pass tests in various content areas.  The Saturday teachers’ institute would have provided training and professional development.  And, it would have been a wonderful opportunity for the teachers in scattered isolated schools to gather, compare notes, and provide support for one another.

Tweet refers to Helen Wesner. She was a friend of Grandma and Ruth.

1912: Also a Leap Year

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

Thursday, February 29, 1912:  I was quite conscious of the fact that this comes only once in four years. This day I mean. We had a visitor at school today. Two I may say. One was the county superintendent. By good luck he wasn’t there, when we had a hard study to go through.

A hundred years ago the country superintendent probably came down this road with a horse and buggy as he entered the McEwensville. The road wasn't paved back then.

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

It’s interesting that it was also a leap year a hundred years ago. (If I had thought about it, I would have been able to easily figure out that both years were leap years, but somehow I was surprised.)

I wish that I had a better understanding of how school systems were organized in 1912. Then, as now, the state was responsible for public education.

Counties were the intermediary unit between the state and the schools a hundred years ago in Pennsylvania. There were not large school districts back then. Many of the consolidated districts—including the Warrior Run School District that now includes McEwensville— were formed in the 1950s.

The superintendent of schools for the county probably visited McEwensville High School because of the mid-year change in teachers.  McEwensville High School got a new teacher just ten days prior to the writing of this entry. The superintendent probably came to see how the new teacher was doing. I hope that he passed with flying colors!

School Had Financial Problems

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

Sunday, February 18, 1912:  Went to Sunday School this afternoon. The roads are rather muddy. Went over to see Carrie this afternoon. I mean I went to Sunday School this morning. I wonder what will happen tomorrow at school I just wonder if Mr. Forest Dunkel (that’s his name) is going to be stern and terrible.

Grandma would have walked down this road to church--EXCEPT in those days it wasn't paved.

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

Forest Dunkel was going to be the new teacher at McEwensville High School. The previous teacher had quit mid-year.

As I told you several days ago, McEwensville School had a difficult time keeping teachers because of the low teacher salary. Here’s a little more information about the school’s financial problems:

Sometimes the school board was unable to pay the teachers at the appropriate time and could do so only when there was again enough money in the treasury. The McEwensville school board had difficulty collecting tuitions due from the directors for pupils attending from Delaware Township. At one time McEwensville even considered going to court to collect these monies, but concluded that it would not be worth the legal expense involved.

The History of the McEwensville Schools (2000)  by Thomas Kramm

Grandma’s family lived in Delaware Township, so she would have been one of the students that the school was having difficulty getting the township to pay for in a timely manner.

Carrie Stout was a friend of Grandma’s who lived on a nearby farm.

High Teacher Turnover

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

Friday, February 16, 1912: And this is the last day of that wonderful teacher of ours. I wonder how he felt this afternoon. I expected he would give some kind of an address, but he didn’t. Oh well, I don’t think I’ll be sorry of his leaving if the next one comes up to the average.  

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

Grandma wrote the previous Friday that her old teacher was staying for one more week.

I learned a little more about the mid-year change in teachers in the  History of the McEwensville Schools by Thomas Kramm:

. . . The high teacher turnover rate, especially in the high school prior to 1916, resulted in a new teacher almost every year. At least one teacher, and perhaps more, would not return to teach the following school year because the school board refused to increase the teacher’s salary. Although it did not occur often, when a teacher resigned in mid-term it was sometimes a challenge to find a replacement. During the 1911-12 school year, when high school teacher Howard Northrop wanted to resign mid-term, his resignation was not permitted until he personally recruited his own replacement.

Whew, it doesn’t sound like the school board did much vetting of teachers. Hopefully the new teacher will be good.

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.


Get every new post delivered to your Inbox.

Join 823 other followers