Arithmetic Commencement Progress Late Improvement in the Art of Teaching
AT the age of twelve, I commenced the study of Arithmetic, that chiefest of sciences in Yankee estimation. No man is willing that his son should be without skill in figures. And if he does not teach him his A B C at home, he will the art of counting, at least. Many a father deems it no hardship to instruct his child to enumerate even up to a hundred, when it would seem beyond his capacity, or certainly beyond the leisure of his rainy days and winter evenings, to sit down with the formality of a book, and teach him to read.
The entering on arithmetic was quite an era in my school-boy life. This was placing me decidedly among the great boys, and within hailing distance of manhood. My feelings were consequently considerably elevated. A new Adams's Arithmetic of the latest edition was bought for my use. It was covered by the maternal hand with stout sheepskin, in the economical expectation, that, after I had done with it, it might help still younger heads to the golden science. A quire of foolscap was made to take the form of a manuscript of the full length of the sheet, with a pasteboard cover, as more suitable to the dignity of such superior dimensions than flimsy brown paper.
I had also a bran new slate, for Ben used father's old one. It was set in a frame wrought by the aforesaid Ben, who prided himself on his knack at tools, considering that he had never served an apprenticeship at their use. There was no lack of timber in the fabrication. Mark Martin said that he could make a better frame with a jack-knife in his left hand, and keep his right in his pocket.
My first exercise was transcribing from my Arithmetic to my manuscript. At the top of the first page I penned ARITHMETIC, in capitals an inch high, and so broad that this one word reached entirely across the page. At a due distance below, I wrote the word ADDITION in large, coarse hand, beginning with a lofty A, which seemed like the drawing of a mountain peak, towering above the level wilderness below. Then came Rule, in a little smaller hand, so that there was a regular gradation from the enormous capitals at the top, down to the fine running no, hobbling hand in which I wrote off the rule.
Now slate and pencil and brain came into use. I met with no difficulty at first; Simple Addition was as easy as counting my fingers. But there was one thing I could not understand that carrying of tens. It was absolutely necessary, I perceived, in order to get the right answer; yet it was a mystery which that arithmetical oracle, our schoolmaster, did not see fit to explain. It is possible that it was a mystery to him. Then came Subtraction. The borrowing of ten was another unaccountable operation. The reason seemed to me then at the very bottom of the well of science; and there it remained for that winter, for no friendly bucket brought it up to my reach.
Every rule was transcribed to my manuscript, and each sum likewise as it stood proposed in the book, and also the whole process of figures by which the answer was found.
Each rule, moreover, was, or rather was to be, committed to memory, word for word, which to me was the most tedious and difficult job of the whole.
I advanced as far as Reduction this first winter, and a third through my manuscript, perhaps. The end of the Arithmetic seemed almost as far off in the future as that end of boyhood and under-age restraint, twenty-one.
The next winter I began at Addition again, to advance just through Interest. My third season I went over the same ground again, and, besides that, ciphered to the very last sum in the Rule of Three. This was deemed quite an achievement for a lad only fourteen years old, according to the ideas prevailing at that period. Indeed, whoever ciphered through the above-mentioned rule was supposed to have arithmetic enough for the common purposes of life. If one proceeded a few rules beyond this, he was considered quite smart. But if he went clear through Miscellaneous Questions and all he was thought to have an extraordinary taste and genius for figures. Now and then, a youth, after having been through Adams, entered upon old Pike, the arithmetical sage who "set the sums" for the preceding generation. Such were called great "arithmeticians."
The fourth winter I advanced but it is not important to the purpose of this work that I should record the minutiζ of my progress in the science of numbers. Suffice it to say, that I was not one of the "great at figures."
The female portion of the school, we may suppose, generally expected to obtain husbands to perform whatever arithmetical operations they might need, beyond the counting of fingers: so the science found no special favor with them. If pursued at all, it was neglected till the last year or two of their schooling. Most were provident enough to cipher as far as through the four simple rules; for although they had no idea of becoming old maids, they might possibly, however, he left widows. Had arithmetic been pursued at the summer school, those who intended to be summer teachers would probably have thought more of the science, and have proceeded further, even perhaps to the Rule of Three. But a schoolmistress would as soon have expected to teach the Arabic language as the numerical science. So, ignorance of it was no dishonor even to the first and best of the sex.