A few years ago I was teaching some teenaged young men and women how to measure. Why they didn’t know how to measure is grist for another mill; for the purposes here, they did not know. The utility of inches and feet were compared to the efficiency of centimeters and decimeters. The importance of creating a sense of the unit sizes, various mnemonics suggested, was emphasized; and historical differences offered. I rather naively assumed that we could go on from there to measuring with the various units; practice would develop for each person their own route to discovery of measurement as tool.
After a few minutes of measuring common classroom objects – notebooks, books, pencils – the numbers were disturbingly inconsistent. I was prepared for confusing millimeters with centimeters and even metric with imperial units, but 3 people sitting at the same table getting 10 mm, even 20 mm, differences when measuring the same book surprised me.
I then observed a most remarkable thing. Students were often taking great care reading the number intended to represent the length of the object, but giving the most casual attention to setting the origin point of the measurement. Some were setting the starting point at the ‘one’ position on the scale. Others were beginning the measurement at zero, though without much concern about it being well aligned or it remaining aligned when their attention was turned to the ‘reading end’ of the measuring stick.
Since it is my style not to point too directly at errors, preferring that they be discovered, I would only say when given a measurement that it was incorrect and to do and think through the process from the beginning again. Many times students became frustrated telling me in detail of their monumental efforts to read the numbers accurately from the scale; saying these things while the origin end of the measuring tool was flopping around in 5 mms of limbo.
Some of the more aggressive students tried to defend their numbers with argument rather than measuring several times, collecting the numbers and looking for the sources of the inconsistency. Leaving aside the purely defiant, most students were reluctant to test the situation and take responsibility for the numbers – the ruler was giving the answers and therefore taking a single measure with a single ruler was all that was necessary; and that answer would just have to do.
Again, what led these poor, misguided students to these deeply held attitudes is a topic for another time; what I began to think about was the metaphor to so much else in our lives. I often hear people argue politics and economics with great attention to the ‘end points:’ “Communism is a failed system, just look what happened to Eastern Europe.” “No, no! It is Capitalism that is the failed system, just look at the destruction of climate stability.” “Oh triple no! Capitalism is the greatest source of growth and only growth can save the poor – rising tides and boats, etc. – so we must grow faster and faster to catch up with the increasing rates of poverty.”
In these arguments I hear the students saying: “The edge of the book is exactly on the line at 243 mm and that has to be the measurement.” Another (while looking from an angle of 45 degrees) says: “Looks like 245 mm to me.” A measurement from another table comes in at 237 mm and yet another is certain that the length is 9 1/2 ‘cm.’
This makes an obvious argument for learning history as a way to set our “zero” points when measuring the present or extrapolating the future, but that is not where I am going. I am more concerned with habits of thought, and not just of students, but of people in general.
If education does not result in it being either obvious or readily discoverable that the zero end of a scale must be set with same attention and accuracy as the reading end of the scale is read, then the basis of all other thought is compromised. We are a creature of metaphor: understand a physical lever and understand the “levers” of political power; understand conversions of inches to centimeters and understand ratios of all kinds; understand the concept of the limit and understand ecological complexities.
If a person cannot measure the length of a line, find the area of a complex space or figure out how to estimate the volume of a solid, then how in the world are they to think through the complexities of even honestly presented social, economic or political concerns?