20160728 PAPER TEACHING

Why educators hate counting?

The picture is from "The Book of Trades". It was created by Jost Amman and published in 1568.

One of the first observations I made trying to understand US elementary school was that the teachers not only sow and nurture what they were told is right - they aggressively prosecute and eradicate what they told is wrong. Weirdly, their major enemy is dactylonomy or finger reckoning.

For this column, I picked a recent article from The Atlantic. The authors try to convince educators to change their attitude. No doubt, school will not listen.

I made several half-hearted attempts to find out exactly when and how finger reckoning became so unwelcome. During antiquity and in the Middle ages it was perfectly fine. It fell out of grace somewhere between 15th and 20th centuries AD.

The obvious reason for expelling finger reckoning from classrooms could be the raise of the Hindu-Arabic numeral system, which we use today. Popularly, it's importation is credited to Leonardo Fibonacci. Apparently, long before him, the wizards of Europe were reading the Latin translations of the works of Muhammad ibn Musa al-Khwarizmi and wondering who could have written them.

Like book printing, calculations in Hindu-Arabic system became popular due to an unsung innovation: Europeans had learned Chinese art of paper making. I heard they started producing paper because they were drowning under rags, and the reason they suddenly faced such an abundance of linen and hemp was the plague.

The next critical change occurred only in 1840s. Industrialists in Germany and Canada learned to make paper out of wood pulp. Their product quickly became cheap enough for disposable news, but schools at that time and and well into the 20th century were using even cheaper substitute: slates.

Their numeracy was about traditional units of money and measurement. Only the numerals were decimal. The technology, however, was modern because calculations were performed in writing. Before writable arithmetic, people had to rely on their fingers and abaci.

The modern school was quite new back then. The king of Prussia Friedrich the Great kick-started the famous Prussian education system in 1763, but only after Napoleonic Wars Europeans took mass education seriously. Napoleon, by the way, promoted decimalisation.

The man behing the Prussian reform was Johann Julius Hecker. He could have been the first to teach teachers. Wikipedia says that the Prussian system "was adopted by all American K-12 public schools and major universities as early as the late 18th century". Did Hecker's seminary teach teachers to root out finger reckoning?

By the middle of the 19th century, elementary education was becoming mandatory. Could this entice educators to crack down on out-of-school knowledge to solidify their emerging monopoly?

Literacy and numeracy, dilapidating cornerstones of US elementary school, are inextricably tied to paper. Even teaching reading using computers, they teach to read from paper. Apparently, at some moment, the teachers decried the shnumber methods and devices like calculi, fingers and abaci to concentrate on selling the only truly scientific technology. Whatever benefits for themselves they saw in it, they cling to paper, pencils and erasers even today, when devices made such a spectacular comeback.

From my American kids, I learned that the teachers secretly told them to use a number line if they can't remember a "math fact". I suspect this device is allowed due to the reasons discussed in this post. School favors stakes: They are more difficult to understand and to use. Devices use sticks. It is unlikely that this school will relearn arithmetic from devices anytime soon. Meanwhile, it's students live in the age of machine computations.

You may think that calculi, fingers, abaci and mechanical calculators were left in the dust. Well, so am I. I use calculi to teach quantity and even algorithms. My and my students' fingers are always with us. The method of positional addition and subtraction in Shnumbers was adapted from decimal abaci, and it does teach numeracy, while elementary school scares students off it. Our Original-Odhner is indispensable for learning multiplication.

Outdated is the whole idea of arithmetic as of elementary math. Outside of schools, this business is called computing.

Meanwhile, paper teachers are struggling with silicon.