Building a New Math Curriculum

Chalkboard with math symbols

Conrad Wolfram, probably the only modern mathematician that anyone outside the field might have heard of, wants to build a new math curriculum. One that actually assumes computational devices exist.

Today, computation now gets done fantastically well by computers—better than anyone could ever have imagined 1,500 years ago. But what we’re doing in education right now is making people learn how to calculate by hand, but not learn how to do problem solving at a high level. They’re learning how to do computation, and not leaving that to the machines. Until we fix that fundamental issue, we’re not going to have the subject of math converging with what we need in the real world.

Think about how most of the math problems presented to students are structured. They are required to remember the right algorithmic process, stick in the numbers, and grind the wheels until the “right” answer pops out. And repeat with the next one in the set. That has changed very little since I was in high school and I have the textbook on my shelf to prove it.

The way mathematics is actually used, is very different. In reality, math is a tool used to help solve problems in a variety of fields from business to social science, science to the arts, engineering to even linguistics. About the only place math is studied independently is in pure research. And K12 schools.

So, what about the hot new topic of coding? Everybody needs to learn that, right?

Today we need people to learn how to code. It’s what I call step two of the problem-solving process. The first is trying to define the problem. Step two is extract to the language of math, which today is usually code. You want to write it so the computer can understand it, but so you can also communicate it. Step three is calculating, what we’ve been discussing, and hopefully you get a computer to do that.

Coding is crucial. If you think about coding as learning how to abstract a problem, which I think is really hard especially the fuzzier and more complex the problem gets, then I think it’s good we’re seeing this being encouraged.

I think that tying math together with computational thinking and other subjects, and combining it with code, would be the absolutely ideal direction for the future.

Learning to code, like math, is not an independent course of study. It is also a tool that must be learned in context.

There’s more to this interview and it’s worth a read.

Wolfram is right that we need to completely revise the K12 math curriculum to focus on “computational thinking” instead of having students crank through processes better done by machine. I’m just not as confident that the change will happen as quickly as he seems to believe.


Image of a chalkboard with math symbols I might have written when I was teaching the subject is a free download from Pixabay and is used under a Creative Commons license.

The Real Meaning of Pi

Chalkboard with Pi

Today is Pi Day. Because the 14th of March could be written as 3.14, the first three digits for the irrational number we all learned something about in elementary mathematics.

Of course, this little bit of trivia only works if you’re writing the date as we do in the US. The whole exercise falls apart in most of the rest of the world where they traditionally write the day before the month. 14.3 makes no sense.

Anyway, beyond the fluff of memorizing lots of the digits and serving actual pies to math teachers (which we do appreciate), pi is a core mathematical concept with a long history and many important applications.

In this New Yorker article from three years ago, a math professor at Cornell University briefly offers a few reasons Why Pi Matters.

So it’s fair to ask: Why do mathematicians care so much about pi? Is it some kind of weird circle fixation? Hardly. The beauty of pi, in part, is that it puts infinity within reach. Even young children get this. The digits of pi never end and never show a pattern. They go on forever, seemingly at random—except that they can’t possibly be random, because they embody the order inherent in a perfect circle. This tension between order and randomness is one of the most tantalizing aspects of pi.

A little knowledge makes for a better Pi Day.


The image is from the header of the New Yorker article.

What’s Your Attitude Towards Science?

Word cloud based on question

3M, the US-based conglomerate probably best known for their Post-It notes, recently released a report called the State of Science Index. They call it “one of the largest, most global studies” done in recent years to gain some understanding of the public attitude towards scientists and their work, surveying more than 14,000 people in 14 countries.

Overall, the general attitudes expressed were positive:

  • 87% said that their general attitude towards science was one of fascination, rather than boring.
  • The same percentage thought “the world is a better place today because of science” and were “hopeful” when they heard the word mentioned.
  • Two-thirds said they were “excited when thinking about the future impact of science on society” and that “science is very important to society in general”.

However, when you dig down into the responses, there is much to be worried about.

I don’t mind the 32% who said they were “skeptical” of science. Questioning claims made in scientific reports is a healthy approach to understanding complex ideas. Especially since most people get their science news from a TV news reader who likely doesn’t understand beyond the summary statement in their script.

Far more troubling than skeptics is the 27% of respondents who “do not see the point of needing to understand science as adults”. Plus the relatively large percentage of people who agree with statements like “If science didn’t exist, my everyday life would not be all that different.” and who fail to see a link between scientific research and “technology”.

In the US, these numbers parallel the around-30% in political poll after poll who refuse to accept basic scientific findings like the existence of climate change as major problem facing society. Or who believe that childhood vaccinations are some kind of conspiracy between doctors and drug companies.

These kinds of attitude surveys can be interesting, although they should also be read with some skepticism. But if you teach middle or high school students, you may want to give them the executive summary and ask them to reflect on the findings. How do their attitudes compare to those of the adults in this survey?

Of course, the 3M Index is looking at current opinions and only tangentially addresses the state of science education. However, how children are taught science during their years in K12 directly affects their understanding of science as adults.

There is a direct link between classroom science instruction that involves memorizing lots of facts and little direct interaction with scientific concepts and the 86% of respondents who say they know “little or nothing” about science. And the large percentage of those people who have no interest in learning more as adults.

Unfortunately, we tend to elect far too many of those people to leadership positions.


I learned of this survey through a discussion with former astronaut Scott Kelly on Marketplace Tech, a daily podcast about how technology affects our lives.

The image is from the executive summary of this report and shows the word cloud created when people were asked to complete this task: “Please fill in what you think science is in no more than two to three sentences. Science is…”.

ET Probably Isn’t Coming

In an excerpt from a book of essays by scientists discussing the search for extraterrestrial life, an astrobiologist wonders why aliens would even bother with Earth.

To make the point, he runs through a list of common sci-fi alien invasion movie plots. Like when the monsters come to Earth looking for slaves. Or lunch.

Alien races enslaving each other is a common trope of many science fiction universes. While enslavement of defeated enemies or other vulnerable populations has regrettably been a common feature of our history on Earth, it’s hard to see why a species with the capability of voyaging between the stars, and therefore having already demonstrated the mastery of a highly advanced level of machinery and of marshaling energy resources, would have any need for slaves. Constructing robots, or other forms of automation or mechanization, would be a far more effective solution for labor — people are feeble in comparison, harder to fix, and need to be fed.

Maybe they will arrive looking to steal the Earth’s water or other raw materials.

The problem with this supposition is that there are loads of far better sources of water in space… you’d have access to a far greater amount of water in the icy moons and cometary halo of the outer solar system. You’d also find it much more practical to operate in deep space, rather than trying to suck up the oceans against the gravitational pull of the planet Earth. And as with the water, it’s hard to see why aliens would bother extracting material against the gravity of the Earth when the asteroids are composed of the same basic rocky stuff.

Of course the process of just getting here in the first place is a major physics problem. Instead of sending bulky, fragile life forms, our first extraterrestrial visitors would more likely be “sentient robots as emissaries”.

Although alien invasion films like “Independence Day” often do huge box office,1 thought exercises like this that address the science (and pseudo-science) behind them are actually more fun. I even enjoy it when people like Neil deGrasse Tyson take a science poop all over big sci-fi movies.

But then, I’m strange. Possibly alien?

What To Do When ET’s Phone Call Arrives

While life continues chaotically forward (sorta) here on Earth, there are still people looking upward and outward for signs of life, intelligent or otherwise. They’re also trying to figure out what we will do when, and they do believe it’s when, not if, a message arrives.

Within the International Academy of Astronautics, a group has drawn up the “SETI2 post-detection protocol”, a set of guidelines of how scientists should address the issue.

Including, how to tell the rest of us.

My SI

It’s that part that worries them most since any message received is likely not going to come from a spaceship we can see hanging over New York City. Or say something particularly intelligible.

“In this day and age of social media, it’s almost impossible to keep anything under wraps for more than a few hours,” said Davies. “[The veracity of a signal] will take a long time to check, I don’t think you’re ever going to have an absolutely clear cut signal, but instead something that’s just on the edge of detectability. It will be a long drawn out process, and possibly take decades to resolve.”

But even if SETI scientists keep mum on the discovery until it has been verified–whether this process takes a few months or a few years–there’s no guarantee about how people will react to the news. As pointed out in a report from a NASA workshop in 1993, “reactions to a detection can range from indifference…through millennial enthusiasm or catastrophist anxiety, to full scale paranoia…a few reactions would probably be irrationally extreme or even violent.”

I would bet on that “irrationally extreme” reaction from far too many people, especially those currently running the show who wallow in rumor, paranoia, and conspiracy theories.

Anyway, I find this aspect of scientific preparation very interesting, even though I only know enough about the science to understand that direct, meaningful contact with another species is extremely unlikely at this point.

It’s not that I believe we’re alone in the universe. Only that the universe is a really, really, REALLY big place and all of us are subject to the laws of physics.