Math By Hand—Why?

If you have a child somewhere in our education system, they have probably asked you offhandedly, “why do I need to learn how to do long division by hand when my calculator will do it for me?”  To that you probably said, “well, because it is important to know the basics before you use a machine to do it for you.”  But do you still believe that after a little in-depth thought on the matter?  Have you done long division by hand since finishing high school?  A better question might be: what are the “basics” that we say are so important?  Conrad Wolfram, the strategic director of Wolfram Research, challenges our current approach to math education and is pushing education systems to stop teaching calculating and start teaching math.

It is hard to find a student these days that enjoys math even though it powers some of the world’s most thrilling and/or important things—roller coasters, rockets, the stock market, molecular modeling for drug design, etc.  Much of the reason behind this may be due to a disconnect between how we do computation and why.  Wolfram says that with the focus in schools on difficult and confusing math computation, students are missing out on the bigger picture of how math benefits us every day.    In his view, math is made up of four steps: 1) posing the right questions, 2) turning real-world problems into math formulations, 3) computation, and 4) translating math formations back into verifiable, real world solutions.  But we spend 80% percent of our time teaching step 3 that computers can do instantly instead of putting any weight onto the more important steps of 1, 2 and 4.  “Just today, across the world we spent about 106 average world lifetimes teaching people how to calculate by hand.  That’s an amazing amount of human endeavor.  So we better be damn sure that we know why we’re doing that and [that] it has a real purpose.”

Wolfram is pushing for a computer-based math focus where math can become both more practical and more conceptual simultaneously.  Using computers in education enables us to reorder curriculum to be based on conceptual rather than computational complexity. “Calculus.  Why do we teach it so late? Why don’t we teach calculus to 10-year-olds?  Well, I think because it’s been traditionally quite hard to compute.  Doing integrals by hand is hard, but the concept of finding areas of things isn’t particularly hard.  There’s no reason not to do it in a completely different order when computers do the calculating.” 

Now does anyone seriously think that innate math knowledge is useless and that we should just use computers for everything?  Of course not.  For practicality’s sake, it is important to be able to do mental arithmetic for estimating purposes or for tasks in which using computers is overkill.  But for more complicated math, it makes sense that we would use the tools that we have available to us to simplify the chore so we can focus on the goal.  “Are the basics of learning how to drive a car learning how to service it, or design it, for that matter?   Are the basics of writing learning how to sharpen a quill?  I don’t think so.  I think you need to separate the basics of what you’re trying to do from how it gets done and the machinery of how it gets done.  And automation allows you to make that separation.”

In order to make computer-based math applicable, though, critical reform is needed.  The current paper-based testing system is so reliant on writing out answers to “problems [students] don’t really understand for reasons they don’t get” that we miss opportunities to impart practical knowledge about the benefits of math in everyday living.  This type of fundamental transition in teaching will not be an easy endeavor to be sure, but this may be a powerful way to reinvigorate math education with a new focus on “why” instead of just “how”.

See these resources for what is being done to address this need or a new way of approaching math education:

Stop Teaching Computing; Start Teaching Math

Partnership Institute for Mathematics and Science Education Reform

Mathematically Sane