Conrad Wolfram, a mathematician and “director of what’s arguably the world’s ‘math company’” (that would be Wolfram Research), believes “today’s educational math is the wrong subject”. Meaning that what we present to students as “mathematics” is not anything like what it is in the real world.
In the real world we use computers for calculating, almost universally; in education we use people for calculating, almost universally.
This growing chasm is a key reason why math is so despised in education and yet so powerful and important in real life. We have confused rigor at hand-calculating with rigor for
the wider problem-solving subject of math. We’ve confused the once-necessary hand mechanics of the past with the enduring essence of math.
At its heart, math is the world’s most successful system of problem-solving. The point is to take real things we want to work out and apply, or invent, math to get the answer. The process involves four steps: define the question, translate it to mathematical formulation, calculate or compute the answer in math-speak and then translate it back to answer your original question, verifying that it really does so.
Teachers and textbooks give lip service to math as a tool for problem-solving but do little to help students understand the process Wolfram describes. As a result, the work kids do in “math” class is dry, boring and largely useless. For the most part, students learn to step through algorithms that the real world turned over to computers and calculators many decades ago.
I love how he describes “word problems” (now often euphamistically called “applications”) “as toy problems and largely outside any context most students can relate to”.
But it’s not just about turning the computation part over to computers. Wolfram says we need to completely replace the current mathematics curriculum taught in most schools.
Instead of rote learning long-division procedures, let’s get students applying the power of calculus, picking holes in statistics, designing a traffic system or cracking secret codes. Such challenges train both creativity and conceptual understanding and have practical results. But they need computers to do most of the calculating — just like we do in the real world.
All of us who have taught math in K12 have heard one common question from our students: “when are we ever going to use this?”. The fact that the honest answer is “probably never” should be a clue that something needs to change.
On a side note, there is one area that we cannot overlook. Although we might not be teaching future mathematicians we cannot dismiss the beauty of theory and refuse to teach it just because it is not applicable to the larger population. The mysteries that still lie in theory untapped might lead to bigger and better applications of the future world. As a mathematician I feel it is still my responsibility to introduce theory and analysis to those with interest in this area without the intent of them ever using it to build a bridge. It has been my experience that some students end up really loving this content and find that they want to pursue a study of mathematics without an intent of application. To sum it up, if I was an artist teaching students art, I would not say that working with watercolor is obsolete because now we can use digital artwork to imitate the process of watercoloring.
Annie: I agree that there is a great deal of beauty in mathematics, but in most K12 schools we do a lousy job of showing it. I’m not suggesting that students should not study math. However, the curriculum imposed on them is more akin to an art class (to use your connection) in which students do nothing but paint-by-number.
Sure, engagement is a critical issue, but… “When will I need to crack a secret code? When will I need to design a traffic control system?” are just as valid as “When will I need to do (insert boring Maths theory here)?”
Ask a concert pianist about whether they got to “the top” without spending years of “mind-numbing boredom” repeating basic theory and practising it until their hands bled. Listen, with rapt expression, to the best performers, but realise that NOTHING worth doing comes easily and behind the effortless performance is much effort!
Many students today are unprepared to do even minimal groundwork before expecting to become instant experts. Demands for a “hook” to get someone motivated to go through the stages from curious ignoramus to fluent practitioner, technology-assisted or not: is this not merely pandering to instant gratification? Are curiosity and intrinsic motivation really so dead?
Having said all of this, I am a classroom teacher who tries to use technology to both support and “up the ante” of student learning. I just don’t accept, for example, that use of nail-guns has in and of itself made buildings any stronger or better. If the builders themselves are no wiser about their end product despite time savings allowing for more navel-gazing, maybe they need better teachers!!