Tractor, Slide Rule, Calculator, and The Digital World

Today is the birthday of Heinrich Jung born 1876 in Essen, Germany.  Jung made contributions in the field of algebraic functions.

Today's quote is from Herbert Turnbull.  He quipped, "The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little enquiry into its nature and purpose as a deliberate human activity."

My dad and I were having a discussion about innovation.  He grew up in South Dakota in the 1920's and 30's during the Dust Bowl.  He remarked to me that he remembered the turmoil that a purchase of a tractor caused among neighboring farmers.  I found an article that supported his perspective of that time. There are very few farmers that would subsist without the tractor.

When I was in high school our choice of a calculating device was the slide rule.  I still have my slide rule but am no longer proficient in using it.  The logarithmic concepts on which it is based have stayed with me.  The terms, mantissa and characteristic, have remained a common part of my vocabulary. :-)  I did not use a calculator my high school mathematics classes even though the scientific calculator existed.  I have colleagues that are approximately my age and they did use calculators in their high school math classes. I attributed my lack of technology to my mathematics teacher.  He was an excellent teacher and was a strong influence in my career path, I don't believe he was of the nature to jump to the latest "trend" in teaching.  He explained to me that he was confident that I would do well in college mathematics because the curriculum and instruction I received my K-12 experience built a solid foundation.

My parents purchased my first digital calculator as my high school graduation gift.  The cost was $150 and it was a Hewlett Packard 35s.   This calculator was in lieu of the traditional gift of suitcases.

I started collecting mechanic calculators a few years ago.  The image below is a particular model I purchased at a flea market.  A hardware/lumber yard store in my community has the same model on display.  Their calculator was the original adding machine used when the company was first established.

My current calculator of choice is the Casio Prizm FX-CG10.  This calculator has everything I want in a calculator.  The graphics are in color and has a minimal number of keystrokes needed to accomplish specific tasks.

Our school to transitioning to 1 to 1.  In mathematics, functions that are defined as 1 to 1 are those whose inverses are also functions.  In the classroom, 1 to 1 means that each student is equipped with a digital device.  As with any innovation, whether it is a tractor or a calculator there is a period of struggle to find its proper place.  As with tractors, there were losses and gains as the calculator entered the mathematics classroom.  Some mathematics concepts have fallen to the side while others have been advanced.  I used to teach linear interpolation as a method to approximate nonlinear results.  That topic is no longer applicable.  I am able to give more meaning to the richness of functions in graphic and tabular ways.  There are appropriate times to use the calculator in class but the use of the calculator exists and cannot be denied.  I believe the same will be true in 1 to 1 classrooms.  As educators, we will have our period of struggle, we will find appropriate times to use the devices in our classrooms but there is no denying that we are in a digital world and we must use all means available to us to engage our students.