Math educators have a “split-personality” approach to mathematics. On the one hand, math is the ancient, other-worldly Platonic paragon of Reason, while on the other hand, math is the present-day, natural engine that runs technological optimization and scientific invention.
Neither of these views are wrong–the problem is in attributing one view to the past and the other to the present. Math has always been both language and technology.
In fact, math is one of the earliest technologies of our species, numbers having preceded writing by thousands of years.
When we write out mathematical calculations by hand, all we are doing is using an outdated piece of technology. Calculating by hand is outdated today because computers are much better at it. The difference is comparable to driving a horse and buggy instead of a car. Sure, before calculators were omnipresent, calculating-by-hand was quite a valuable skill. During WWII “computers”–not machines, but humans hired to crunch numbers all day long–were hired by the US military and paid a salary of $1,440, the 2015 equivalent of $20,000. Calculators changed that, but apparently educators were the last ones to notice!
The counter-argument has always been, “we teach math for students to learn logical reasoning.” It’s true that mathematical arguments follow reasoning and a formal logic. But it is dishonest to say that is how math is being taught today. The focus today is on getting students to reproduce the procedures, not be able to logically prove them.
The larger point is that it is a mistake to see Reason as math’s biggest contribution to society. Mathematics does not hold a monopoly on reasoning, despite what Stephen Hawking says. Pascal recognized this almost 400 years ago, writing, “Custom is the source of our strongest and most believed proofs. It bends the automaton, which persuades the mind without its thinking about the matter.” Claiming that mathematics education is primarily about reasoning is like a corporate CEO claiming the advertising division’s primary focus is creating beautiful cinematography or the military claiming that marksmanship training is primarily for the Olympics skeet shooting competition.
Mathematics as language is about Reasoning. Mathematics as calculation is about technological progress.
Our society has no problems letting computers determine our economics (which in turn runs our politics)–but for a student to use a computer to solve a quadratic equation is cheating. Rather than calculation-by-hand, we might as well be teaching students to use slide rules or, better yet, play video games.
Even the Common Core’s math standards, while a useful idea in principle, are hopelessly stuck in the calculation-by-hand philosophy. And they could not have been implemented at a worse time. Teachers are increasingly teaching to the test at a time when they should be experimenting within the new digital world to cultivate students’ curiosities into interests and passions. This is especially true of math, which lends itself to digital learning more than other subjects.
Isaac Asimov wonderfully named the split-personality mindset that mathematicians (and many others in our society) have historically suffered from: Spacer ideology.
– “Space-out” when discussing the downsides to a technology.
– Outsource as much human labor to machines as possible.
– Blindly trust that technological progress is the same as social progress.
So what about education, specifically, has prevented this outsourcing of computational labor to computers in math classrooms? Mark Weston identifies the “lack of school-level support” for helpful educational technologies, combined with the entire field of education “ignoring its own research” and “failing to investigate and build consensus about how to take what works to scale.”
Math teachers across the world, take action before it’s too late! As math teachers, we have to learn to coexist with digital technology. The organization Computer-Based Math laid this information out years ago, but it’s calls have largely gone unheeded. Don’t resist it any longer!
Strive to find the balance between the two extremes. Don’t fall for the promise of easy technological fixes, but also don’t refuse technology altogether. Instead, collaborate. Seek out other educators to figure out what works. Move into the networked reality of our “Spacer” global economy, while keeping a critical awareness of the potential downsides to technology, and not abandoning the logical, linguistic foundations of math.