Arkady
President
In the New York Times and Slate, I've recently seen a discussion of the idea of scrapping advanced math from the curricula of most students:
http://www.nytimes.com/2016/02/28/opinion/sunday/the-wrong-way-to-teach-math.html?_r=0
The idea would be not to waste time on things like Algebra II, Pre-Cal, Calculus, etc., at least for those not pursuing math or certain sciences as a profession, and instead spend that time on developing greater comfort and facility with the kinds of math that would prove useful in the daily lives of everyday people. That would include some basic geometry and lower-level algebra problems -- the kind of stuff you might use for a back-of-the-envelope calculation during a home improvement project. It would include building a better familiarity with statistics. It would include skills that are practical for balancing a checkbook, running a small business, and managing a retirement plan. And it would include building analytical tools and basic numeracy that citizens need to be savvy about stories involving numbers. For example, it could make news consumers more alert to the idea that just because something triples your risk of a particular kind of cancer doesn't necessarily mean it's a huge health threat, if that type of cancer is incredibly rare to begin with.
The idea is that most of what you learned past the level of geometry and and algebra (or maybe even pre-algebra), you just won't use in real life. So, that's largely wasted time that could have been used teaching you something helpful. And, moreover, those higher-level classes seem to drive drop-out rates for high school and college, as kids grow frustrated with their difficulty learning such abstract topics.
What do people here think about that?
I can certainly see some merit to the arguments, and I'm not sure I have a good argument in the other direction, but I feel like if you steer most people away from higher-level math early on, you'll be screening out some people who could be our future scientists, if they just got a taste for it. I also think there's some kinds of "citizenship science" that really do demand the intellectual rigor that comes from having developed a facility with calculus, not just everyday practical science. For example, even to get a pretty basic grasp on climate science, it's necessary to be able to think in terms of complex systems with dependent inputs and outputs, and equilibrium points, and calculus education gives you the tools for thinking in that way, even long after you've forgotten how to actually work with integrals and matrices.
In my own case, I started out as a physics major, but after two years changed for a variety of reasons (shamefully, one of them is just that I hated getting up before dawn for the undergraduate lab times). As a result of having started on a physics path, I finished AP calculus in high school then took two years of advanced math in college. And I'll quickly admit I don't use it in my day-to-day life. In fact, I can't even remember how to do most of it. A while back a writer friend of mine was writing a sci-fi story and needed someone to calculate a few things for him, regarding the speed a space station of a given radius had to spin to produce 1G, and how long it would take to travel a certain distance accelerating and decelerating to a certain percentage of light speed, and I struggled for an hour remembering how to do that basic math, since I've forgotten most of what I knew. I can't even remember what half the symbols mean at this point. But I still feel like there was something useful in how that advanced math trained my mind. I may not be able to calculate half the stuff I once could, but I know what kinds of things can be calculated, and that makes me savvier about what's knowable and what isn't.
I also just think there's something fun about advanced math. One of the greatest moments I experienced in my education was in pre-cal, the first time I solved for an infinite series. It was a simple word problem where something travels a certain distance, bounces halfway back, travels back, bounces halfway again, etc., forever. The idea that you could calculate total distance traveled even though it would never stop traveling just blew my mind. I had a similar mind-blowing moment in college, the first time I saw a formula for a shape with infinite surface area and finite volume. Those are moments that are spiritual, in the way they open your mind to the possibilities of the universe, and it seems a shame to think that only a small percentage of people would have access to them.
http://www.nytimes.com/2016/02/28/opinion/sunday/the-wrong-way-to-teach-math.html?_r=0
The idea would be not to waste time on things like Algebra II, Pre-Cal, Calculus, etc., at least for those not pursuing math or certain sciences as a profession, and instead spend that time on developing greater comfort and facility with the kinds of math that would prove useful in the daily lives of everyday people. That would include some basic geometry and lower-level algebra problems -- the kind of stuff you might use for a back-of-the-envelope calculation during a home improvement project. It would include building a better familiarity with statistics. It would include skills that are practical for balancing a checkbook, running a small business, and managing a retirement plan. And it would include building analytical tools and basic numeracy that citizens need to be savvy about stories involving numbers. For example, it could make news consumers more alert to the idea that just because something triples your risk of a particular kind of cancer doesn't necessarily mean it's a huge health threat, if that type of cancer is incredibly rare to begin with.
The idea is that most of what you learned past the level of geometry and and algebra (or maybe even pre-algebra), you just won't use in real life. So, that's largely wasted time that could have been used teaching you something helpful. And, moreover, those higher-level classes seem to drive drop-out rates for high school and college, as kids grow frustrated with their difficulty learning such abstract topics.
What do people here think about that?
I can certainly see some merit to the arguments, and I'm not sure I have a good argument in the other direction, but I feel like if you steer most people away from higher-level math early on, you'll be screening out some people who could be our future scientists, if they just got a taste for it. I also think there's some kinds of "citizenship science" that really do demand the intellectual rigor that comes from having developed a facility with calculus, not just everyday practical science. For example, even to get a pretty basic grasp on climate science, it's necessary to be able to think in terms of complex systems with dependent inputs and outputs, and equilibrium points, and calculus education gives you the tools for thinking in that way, even long after you've forgotten how to actually work with integrals and matrices.
In my own case, I started out as a physics major, but after two years changed for a variety of reasons (shamefully, one of them is just that I hated getting up before dawn for the undergraduate lab times). As a result of having started on a physics path, I finished AP calculus in high school then took two years of advanced math in college. And I'll quickly admit I don't use it in my day-to-day life. In fact, I can't even remember how to do most of it. A while back a writer friend of mine was writing a sci-fi story and needed someone to calculate a few things for him, regarding the speed a space station of a given radius had to spin to produce 1G, and how long it would take to travel a certain distance accelerating and decelerating to a certain percentage of light speed, and I struggled for an hour remembering how to do that basic math, since I've forgotten most of what I knew. I can't even remember what half the symbols mean at this point. But I still feel like there was something useful in how that advanced math trained my mind. I may not be able to calculate half the stuff I once could, but I know what kinds of things can be calculated, and that makes me savvier about what's knowable and what isn't.
I also just think there's something fun about advanced math. One of the greatest moments I experienced in my education was in pre-cal, the first time I solved for an infinite series. It was a simple word problem where something travels a certain distance, bounces halfway back, travels back, bounces halfway again, etc., forever. The idea that you could calculate total distance traveled even though it would never stop traveling just blew my mind. I had a similar mind-blowing moment in college, the first time I saw a formula for a shape with infinite surface area and finite volume. Those are moments that are spiritual, in the way they open your mind to the possibilities of the universe, and it seems a shame to think that only a small percentage of people would have access to them.
