Math Without Computation?

Everyday professionals, who are not mathematicians, solve difficult mathematical problems without ever making a single calculation.  From calculating trends in the stock market to predicting population changes, these professionals find mathematical answers to interesting questions without spending hours or days making calculations by hand.

According to Conrad Wolfram, head of the mathematical lab at Wolfram Research (the developers of the computational engine, WolframAlpha) as computers become more and more sophisticated at prediction models and complex calculations, the professional's work becomes more about asking the right questions and understanding the answers provided by the mathematical computations, than actually performing calculations.

In this TED Talk, Conrad Wolfram explores the idea that we should be teaching students to think like mathematicians instead of teaching them to be computers.



Although this idea seems extreme on the surface, I think there are valid reasons for focusing our educational energies on thinking skills rather than computational skills.  It is true that understanding the basic computations and mathematical relationships is important for mathematicians who will continue advancing mathematical research.  However, most students will not become mathematicians; they will become professionals who use math to answer complicated questions everyday. And for those students who do wish to become mathematicians, many university mathematics programs begin with the basic skills and math theory.  Knowing how to approach a problem and knowing what questions might provide answers to a problem are the skills needed by most professionals.

I think that it is vitally important that students know how to use the tools available to find the answers to their questions, and how to understand the answers provided by those tools.  If even students in the elementary grades with the use of computer models, can analyze complex calculus problems, why wouldn't we want to give them that opportunity?  Isn't our goal as educators to prepare students to be effective, productive, contributing members of society?  I propose that we will not meet that goal if we do not teach our students how to search out the answers to their questions using the technology available to them, rather than asking them to spend valuable time making calculations that an effective, productive professional currently would handle with a computer.


Image Source: Marcus Mo