Are you a math person? Are you a creative person? Or, perhaps, you are one of those rare individuals who are both?
Have you ever wondered what education was like in the days of not
so long ago?
In the fall of 1953, when I was in the 3rd grade, my grandfather sat down
each evening to teach me the multiplication tables. He also used this
time to reminisce by relating stories about his childhood adventures.
One day back in the early 1980’s, I happened to be in Mr. Russell M. Weaver’s office in Harrisonburg, when out of the blue, Mr. Weaver turned to me
and said, “My one regret in life is that I could never hit a baseball like
your grandfather.” Without a moment’s hesitation, I turned to see if
someone else had entered the room while I had been absorb in examining the old documents
Mr. Weaver had recently found. Finding no one, I realized that I was
about to learn something very special about my grandfather’s life. Mr.
Weaver went on to say that, “everyone
held their breath when C.A. came up to bat as they all knew that the ball was
going to be hit so hard that it would go out of bounds.” A smile spread
across his face as he relived old forgotten memories. Then, he proceeded to
tell me a few other things about my grandfather and his family that I did not know.
Our conversation reminded me that I had several leather bound
school books in my collection. Even today, I vividly remember unpacking
each of those old volumes when I returned home that day and I still treasure
each of those wonderful, old books. But on that day, one book in
particular caused my eyes to midst over with unshed tears. It was a math
book which had been originally published in Philadelphia in 1801. This
book had been revised many times as I held a copy of the 1834 edition in my hands. As I
opened the cover, I was surprised to find that it stated on the first page that
it was written in “Federal Money.”
As I thumbed through the book, I could not help but wonder what in
the dickens was “Federal Money.” When I looked closer, I
found that each math problem was followed by the correct answer. I
could not help but smile as I realized that this was a teacher’s edition. Now, there were two questions which ran through my mind: “Who would have used this
sort of book?” and “How did it compare with today’s educational
standards?”
If such a volume was printed and used in Philadelphia as was stated
on the front page and was also used this early in our own Shenandoah Valley, it
must have been a basic educational tool of its day…sort of like the “Dick
and Jane” series of books which were used to teach reading from the 1930’s
through the early 1960’s or perhaps like the earlier McGuffey Readers.
By checking internet sources I discovered that this was a revision
of a book which had been written ca. 1801 and had stayed in print until ca. 1900.
Obviously it had a wide circulation and had influenced many young people during
the ninety-nine years it was in print.
What a crucial time in our nation’s history for such a book to be
in print. The printed reviews indicated that men such as Abraham Lincoln
[whose grandparents lived in Rockingham County], Thomas Jonathan “Stonewall”
Jackson, Robert E. Lee, Turner Ashby, Nathan B. Forrest as well as most
all of the men of that era would have been taught mathematics from this one
basic source of knowledge. Add to this, the men who mapped the
frontier like Jedediah Hotchkiss, the men who opened the west by using what
they had learned from this book in computing the dimensions for forts, the
length and widths of bridges, and men such as my own grandfather who more than
likely had received his mathematical education from this particular
volume. He and many of his family members and friends had worked on the railroad
while maintaining their own farms within our Shenandoah Valley.
A lot of useful information is found in this little [4” x 6 ½ “]
leather volume which opens by explaining that, “Arithmetic is the art of
computing by numbers. It has five principal rules for its operations;
viz. numerations, addition, subtraction, multiplication, and division. It
further states that Numeration teaches to write or express numbers by figures,
and to read numbers thus written or expressed.”
It continues to explain the following:
“ A unit is a single one.
A ten is ten units
A hundred is ten tens.
A thousand is ten hundreds
A million is ten hundred thousand”
It also states in a note on the same page “that as it takes ten
hundred thousand to make a million, when a number is expressed greater than a
thousand, and less than a million, we use tens of thousands, or hundred of
thousands, or both, as the care requires. Likewise to express a number,
greater than a million, we employ tens of millions, or hundreds of millions,
etc.”
An example of a problem of addition is found on page 11 and is as
follows:
“The distance from Philadelphia to Bristol is 20 miles; from
Bristol to Trenton, 10 miles, from Trenton to Princeton, 12 miles, from
Princeton to Brunswick, 13 miles, from Brunswick to New York, 30 miles.
How many miles from Philadelphia to New York? Answer: 90”
An example of simple subtraction is found on page 13 and is as
follows:
“A person had in his desk 1000 dollars. He took out 120
dollars to pay a debt. He afterwards put in 75 dollars. How much
was there then in the desk? Answer: 955 dollars”
Page 13 states that, “multiplication teaches to find what a number
amounts to when repeated a given number of times. The number to be
multiplied is called the multiplicand. The number to multiple by is
called the multiplier. The number produced by multiplying is called the
product. The multiplies and multiplicand are also called factors.”
Page 14 cautions, “that the scholar should commit the following
Tables to memory before he proceeds further.” The multiplication table to
the 12th power is then cited for immediate memorization.
An example of simple multiplication is found on page seventeen and
is as follows:
“There are fifteen bags of coffee, each of which weighs 112
pounds. The bags which contain the coffee weigh 22 pounds. How much
would the coffee weigh without the bags?” Answer: 1658 pounds
Page 17: “By division we ascertain how often one number is
contained in another. The number to be divided is called the
dividend. The number to divide by is called the divisor. The number
of times the dividend contains the divisor is called the quotient. If on
dividing a number, there be any overplus, it is called the remainder.”
 |
| Federal Money |
“Federal Money, or Money of the United States.
The denominations of Federal Money are: Eagle, Dollar, Dime, Cent,
and Mill.
10 mills (m.) make 1 cent, cts.
10 cents 1
dime
10 dimes (or 100cts.) 1 dollar, D. or $
10
dollars 1 eagle”
Page 34:
“Apothecaries Weight
By this weight
apothecaries mix their medicines, but buy and sell by avoirdupois weight.
The denominations of Apothecaries weight are pounds, ounce, dram, scruple, and
grain.”
Page 35:
“Cloth Measure
By this measure,
cloth, tapes & c. are measured;
Land Measure or Square
Measurer:
This measure shows the
quantity of lands. The denominations of Land Measurer are acre, rood,
square perch, square yard, and square foot.
Liquid Measurer
This measurer is used for
beer, cider, wine & C. The denominations of Liquid Measure are tun, pips,
or butt, hogshead, gallon, quart, and pint.
Dry Measurer
This measure is used
for grain, fruit, salt, & c. The denominations of Dry Measurer are
bushel, peck, quart and pint.”
Page 37:
“The following is a
statement of the number of days in each of the twelve months, as they stand in
the calendar or almanac:
The fourth, eleventh,
ninth, and sixth,
Have thirty days to each
affix’d:
And every other
thirty-one,
Except the second month
alone,
Which has but twenty-eight
in fine,
Till leap year gives it
twenty-nine.”
Now that we know most of
the rules and have investigated some of the frills of mathematics, let’s
examine some of the more common math problems.
Page 196:
“There is a cellar dug
that is 12 feet every way in length, breadth, and depth: how many solid feet of
earth were taken out of it? Answer: 1728
How many brick 9 inches
long and 4 inches wide will pave a yard that is 20 feet square? Answer: 1600”
Page 195:
“A person said he had twenty children, and that it happened there was a year and a half between their ages; his eldest son was born when he was 24 years old, and the age of his youngest is 21; what was the father’s age? Ans.73 ½ years."
And to end this delightful excursion into long ago mathematics:
Page 197:
"A line 35 yards long will exactly reach from the top of a fort, standing on the brink of a river, to the opposite bank, known to be 27 yards from the foot of the wall: what is the height of the wall? Ans. 22 yards 9 3/4 inches."
Would you believe that this was a 5th Grade math book?
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