Why are high schoolers still learning Cold War math?
Public schools in the US are a living history lesson about social class. Grouping by age teaches kids to be sorted according to birth. Sounding bells teaches kids to become factory workers. Our high school math curricula teaches kids how to win the Cold War.
The goal of high school math is to launch missiles and spaceships.
We tell kids that geometry and algebra are useful only as prerequisites for calculus. And calculus teaches kids how to launch missiles. If you get through calculus and you have more time in high school, you get to take the extra math courses, like statistics. Because you need probability and statistics to take down missiles.
The Cold War permeated daily lives of Americans from the early 1950s, and when the Soviets launched the first satellite into orbit, the Cold War became a race to the moon. Luckily our established math track for launching missiles also taught students to launch space ships.
Our current high school math curricula is what won the Cold War.
In the early 1960s the US budget for NASA increased 500% which explains the full employment of math geniuses during that time. We were so desperate for mathematicians that the government hired women! And in the end, astronauts became war heroes as they shoved six American flags into the surface of the moon.
What do you do with Cold War curriculum after the Cold War?
Today’s measure of success for math geniuses is the Math Olympiad. The original purpose of the Math Olympiad was to improve math skills in the Warsaw Pact, during the Cold War. The US didn’t start sending kids to the Math Olympiad until after the US won the race to space and it was clear that the high school rocket scientists had nowhere to apply their knowledge.
You could look at our high school math curricula as the equivalent of teaching every American kid high school Latin. Another way to look at our math curricula today is like bringing a knife to a gunfight:
Do you know why the French sucked in World War II? They build the incredible Maginot Line so they would never again lose at trench warfare. But the trench warfare of World War I had no place in World War II, so the Germans rolled into France with brand new tanks as if the Maginot Line were a welcome mat.
We make the same mistake as the French when we use Cold War math in the Information Age. Wars today will be fought with data, and we don’t have a shortage of mathematicians, we have a shortage of computer programmers.
When I was a kid the saying “it’s not rocket science” was so common. But I never hear Millennials say that, because rocket science has no context in their Information Age world. Yet rocket science persists as the backbone of high school math today.
The subjects of algebra, geometry and calculus are a tradition that go back far before the Cold War.
They teach programming in high schools now too.
The reason kids have so much trouble with math is that, from algebra on, it’s no longer just memorization. To do a proof in geometry, you actually have to think. Same with creative writing. And kids hate both of those subjects because they haven’t been prepared for thinking at all by the rest of their classes.
Programming also requires thinking, and will be just as unpopular as algebra if they are serious about teaching it.
Now do one on high-school English! My kiddo has been a master in animation and movie story arcs, plotting, genres, common tropes, canon v not-canon, storyboard-to-detail process, script conventions, etc., for years and years. But this “identify some words and phrases that set the *tone* in the assigned story” and “how did the antagonist know that blah-blah-blah” and “how does Hemingway describe goodness” leaves him cold. (He tells me, “I know you like this English stuff, Mom, but I just don’t.”) And I really can’t justify making him plow through it except as practice for college entrance tests, and to check the boxes on the transcript.
Ditto to this. I am a former public school English teacher and one of the many reasons I left is that the curriculum was so pedestrian and outdated. I was preparing kids for tests, but it was really tough to fight the pressure to teach the test. A lot of the reading list is leaden and lacks dynamism. I loved teaching, but I really hated the restraints.
The problem isn’t mathematics per se, it’s that teachers do not allow students to use tools and computers to get the answer. Students still spend a ton of time showing their work and learning how to do math by hand. No one does that in the workforce. NO ONE. Unless you’re a teacher, of course, which is why they teach that way.
Have you heard of Wolfram|Alpha? Link: https://www.wolframalpha.com/
You can do fairly complex calculations for engineering, physics, statistics, and a number of math-related disciplines. All you need to know is how to plug the numbers into the calculation and interpret the result.
Fun fact: I failed calculus and I’m a computer programmer today.
It may be worth pointing out that if you had made it a little farther in calculus, you probably would have begun using specialized math software at that point. For example, at my kids’ school the second year of Calculus uses MatLab.
I sympathize with the teacher perspective that you should know how the math works before you use tools to do the math, because otherwise it’s hard to know whether and why you got the right answer from the tools.
Using existing tools is a perfectly fine strategy- as long as your highest goal is to be a button pusher. There’s someone at the top, making decisions about which buttons need to be pushed. That person needs to understand how things work.
Being a computer programmer after failing calculus isn’t surprising- what’s surprising is that programming is still considered in the math/science field. Computers were originally in that category because there weren’t separate people for hardware and software, and hardware is roughly electrical engineering. 90% of today’s computer programming is really a “foreign” language skill.
The idea that the only thing calculus is good for is ballistics is simply ignorant. Where would the study of electromagnetism be without calculus? And where would we be without electromagnetism? Satellites? AI? Weather prediction? Search engines? All impossible to work with without calculus. Much of what we take for granted during our daily lives – like this thing I’m typing on – wouldn’t be here without calculus.
I agree that not all kids have to learn calculus. Not all will find it interesting or useful, and not all will have success learning it. Not all kids should go to college either, let alone study a branch of science where calculus is useful. But not learning calculus and then going to college expecting to study physics, or engineering, or mathematical modeling, or fluid dynamics, would be as foolish as not learning about evolution and then expecting to study biology.
I can think of about a dozen specific ways in which I found public education to be insufficient for myself and for my children. The inclusion of calculus in the curriculum is nowhere among them; our problem was more that it couldn’t come fast enough.
Oh, this is very well said. I probably could have qualified things more in the post. I think I want to say that how we frame what we do with math and why we do it should be different.
As an aside, Bostonian makes me laugh. He has helped me so much since I moved to Boston, and his son has been so kind to my son. Yet Bostonian has no problem telling me I’m ignorant. Thank you for keeping things real.
Penelope
It sure sounds like you really hate math! Part of me wonders if you didn’t have dyscalculia then perhaps you might have a different perspective.
I do have dyscalculia, and I couldn’t pass a math class. But also as a startup founder, half of my life was running financial projections, which I’m very good at. So I’m always thinking about the different types of math, different ways and reasons to learn, etc.
“So I’m always thinking about the different types of math, different ways and reasons to learn, etc.”
Penelope, I think you would be interested in reading some of the blog posts over at the National Council of Teachers of Mathematics (NCTM). Specifically, the Teaching Children Mathematics (TCM) blog at https://www.nctm.org/tcm-blog/ . Read the latest blog posts (3 part ‘Transforming the Culture of Math’ series) written by a fifth-grade teacher who was an English major and felt very unsure of her math abilities let alone teach them. There are other blog posts on that page and subsequent pages that may interest you also.
The main blog post page at NCTM ( https://www.nctm.org/News-and-Calendar/NCTM-Blog/ ) has links to blog posts for middle and high school teachers for more ideas. Their site has a page that links to numerous (584) publications on math teaching. Here’s one (of many) that should interest you – ‘Deepening Student’s Mathematical Understanding with Children’s Literature’ ( https://www.nctm.org/Store/Products/Deepening-Student-s-Mathematical-Understanding-with-Children-s-Literature/ ). Here’s another book that’s linked to from the three-part series mentioned above – ‘Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners’ – written by researchers at Harvard for educators.
Which gets me back to the idea of ‘different’ in your comment. You say you’re good at pattern recognition. I think you can be good at math. Go back and relearn math your way in the environment, speed, and using the tools that work for you.
I’ll add to Alissa O.’s comment above.
I highly recommend Stephen Wolfram’s blog post ( https://blog.stephenwolfram.com/2016/09/how-to-teach-computational-thinking/ ) on computational thinking. It’s directly aimed at teaching kids how to use the Wolfram language which is knowledge-based and is freely accessible in a web browser. The post is well written and he explains how it stands out above and beyond traditional mathematical thinking. He’s basically been working at and has been the key driving force of the beginnings of this endeavor with his brother Conrad for about 40 years starting with Mathematica.
There are also two TED talks, both given in 2010, by each of the Wolframs. The TED talk ( https://www.youtube.com/watch?v=60OVlfAUPJg ) given by Conrad titled ‘Conrad Wolfram: Teaching kids real math with computers’ is excellent and directly addresses issues that you bring up in this post. The other TED talk ( https://www.ted.com/talks/stephen_wolfram_computing_a_theory_of_everything ) titled ‘Computing a theory of all knowledge’ by Stephen is also very good. It will become evident while reading Stephen’s blog post that Wolfram|Alpha uses a computer to do math and much more (e.g. – history, art, diagramming sentences, make and blend colors, music, sports, literature, geography to name a few) using math. And one more link for educators on their site – https://www.wolframalpha.com/educators/ .
Mark W dude – thanks for the TED links. Fascinating guys.
Couldn’t agree more with the PT opinion need to totally transform education and math. Teachers are still an irritant to me even tho I’ve been out of their hands for decades. Outmoded education is a national economic security issue.
The neurotypical side of my clan (dad’s side) is loaded with conformist teachers who seem dead bent on keeping us all on the plantation and dumbed-down until they collapse the entire system and we finally have equality – where we all have less or nothing. I wish someone could model all of this socialist-leaning education-driven group think and show what the future looks like when they and their millennial offspring finally get their way. Famine, shortage, chaos, and then “revolution”.
Why not just skip those steps? That’s the old school way of change.
Still, I have great hope that some of these brilliant thinkers like the Wolfram bros can start to infect govt. thinking and help create the paradise that the universe wants for us.
You’re welcome, Mark. I’m glad you enjoyed the TED talks.
I watched Conrad’s YouTube talk a few years ago and it very much made an impression and resonated with me. He asks the question – What is math? He then breaks it down into four steps – 1) Posing the right questions, 2) Real world –> math formulation, 3) Computation, and 4) Math formulation –> real world, verification. He then explains that math is not calculating. That math is a much broader subject. We now have computers so math can be thought of as being “liberated” from calculating. He goes on to estimate 80% of math education today is calculating by hand (#3 from above) or calculator. He doesn’t dismiss the need to do rough calculations and estimating without calculators or computers but emphasizes students need to be spending much more time and focus on steps 1, 2, and 4.
When I went to college to take calculus, statistics, differential equations, physics, chemistry, etc. in the mid-70’s, I initially didn’t have a calculator. Calculators were fairly new and expensive. Many other students did have calculators and I had a hard time keeping up with them doing homework and during testing. Halfway into my first semester, I had to ask my Dad to send me a calculator. It was critical I have one as I was doing all the calculations by hand up to that point and I couldn’t keep up. And it wasn’t just solving equations. At the time there was a major push to learn S.I. (system units or commonly referred to as the metric system). Problems to solve were given with both metric and English system values so there were those calculations to do besides. It was maddening to me as I regarded all those calculations to be more busywork than anything else. So Conrad Wolfram in this TED talk described exactly how I felt (even after I got my TI SR-10 calculator which by the way I have to this day and it still works!). Unfortunately, I think the school system is still too focused on the calculating step even though kids today have powerful tablets in the classroom. I need to ask my niece who is in 9th grade and is using one. I cited the Wolfram brothers as they have a good approach and they’ve been working on making math more “high level” and accessible to everybody. When I was in college I took a Fortran IV class. Terminal and punch cards. I learned DOS and some Ubuntu. I’ve taken Visual Basic classes. It doesn’t do much for me. One of my younger brothers has a computer science degree. So the way I look at it now, if I need help programming I’ll ask him. But the truth of the matter is I’m more interested in using a computer to do things with finished apps either on the computer, on a network, or in the “cloud”.
Penelope, I would love to add something to this discussion, but you have teed it up well, and your commenters have hit the ball out of the park. I will say that I loved math, yet I failed at calculus twice. It took a few more years, but I eventually taught myself calculus, and got an MS in applied math.
Yes, calculus remains important; it is actually the theoretical foundation of statistics and data science. But non-math majors don’t need that. I taught business statistics for over a decade, and told my students that statistics represented real life. They laughed at me, but I hope I gave them some quantitative discipline to carry over into the real world.
There’s an article ( http://nautil.us/issue/17/big-bangs/how-i-rewired-my-brain-to-become-fluent-in-math-rd ) by Barbara Oakley I read today that reminded me of this post. It’s titled ‘How I Rewired My Brain to Become Fluent in Math’ with the tagline “Sorry, education reformers, it’s still memorization and repetition we need.” It’s one of the best I’ve read as I could relate to everything she said. Our learning paths, though, are about 180 degrees apart. She says – “After all, I’d flunked my way through elementary, middle, and high school math and science. In fact, I didn’t start studying remedial math until I left the Army at age 26.” Now she has her doctorate and is a professor of engineering at Oakland University, Rochester, Michigan. I concentrated on math and science when I was young but my vocabulary left a lot to be desired. Now to this day, I’m still looking up word definitions which I think I should have learned long ago. Anyways, in this article, she also discusses chunking and fluency with helping her learn both languages and math. She says – “Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success. Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency.” Her story is an interesting one. She makes some good connections to learning to play a sport such as golf or learning to play chess and learning math and science. One sentence that stood out to me – “If there were a textbook example of the potential for adult neural plasticity, I’d be Exhibit A.” I think there’s a lot of people that could say the same thing. Most of us here went to school for our education … and we’ve been unschooling ourselves ever since then in one way or another. Isn’t that adult neural plasticity? Whether you change jobs or stay in the same job, it’s necessary for at least some degree of neural plasticity to be taking place. She discusses other things which I haven’t mentioned here so I recommend reading the article.