Many people know the story of Archimedes and his discovery of a crime that would result in a goldsmith’s life. Archimedes, the great Greek scientist, was given the task by King Hiero to determine whether the golden wreath dedicated to the gods was truly made out of gold or just an ulterior alloy that looked like gold.
Unable to melt the golden wreath into a small cube to determine its volume, it is said that he sat in a warm bath to think of a way to determine its density. As the water rose, he quickly concluded that the volume of water displaced is equal to an objects volumetric density.
Upon the discovery of this new and improved way of measuring density, Archimedes went running through the streets yelling “Eureka! Eureka!” or the Greek Εύρηκα! “I found it!” Result: Angry king…dead blacksmith…story told millennium later…and a problem almost none of my students can figure it out.
It is quite a conundrum that we live in a society in which more information and knowledge is at the tip of your fingertips (literally) and milliseconds away (literally again) and yet our students in school can not problem solve. They have been taught over their elementary, middle, and high school public education to memorize facts, listen to teachers, and regurgitate information on tests…and yet a man over 2200 years ago was able to logically problem solve much more effectively.
The end of the second week of school, I conduct a laboratory where my students determine the density of 5 objects. They are given only five things to accomplish this task – one large beaker, one small beaker, one measuring tape, one digital balance, and one graduated cylinder. One rule is given – they can only measure the volume of liquids out of the graduated cylinder (not the beakers)!
And I give them these 5 objects to measure and calculate their density:
- A small piece of aluminum
- 10 copper pennies (pre-1982)
- A small piece of lead
- A baseball
- A 200 g mass too big to fit in the graduated cylinder
They instantly are able to get the densities of aluminum and lead as well as the pennies – with some difficulty of whether they should divide by 10 or not (another discussion for another day, math teachers). The baseball gives them some trouble (it is too big to fit down the graduated cylinder) but they eventually feel the need to ask me for the equations for volume of a sphere and circumference of a circle.
But then the 200 g mass. It seems impossible to them. It won’t fit down the graduated cylinder, they keep wanted to use the imprecise (and against the rules) volumes on the beakers, and are about to give up 2 minutes into trying. Absolutely great problem solvers that we are building here in America – our students have become entitled to instant gratification rather than excited to solve a problem that is bigger than them and takes some outside-the-box, logical thought process.
For the ones that persevere, it is as if their faces say “Eureka! I found it!” And for a teacher, that is the greatest look in the world.