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.

CS for All? Where Are We Going to Fit It In?

Last November, Virginia became the first state in the US to require computer science instruction – specifically “computer science and computational thinking, including computer coding” – at all levels K-12. For elementary students, teachers will be expected to integrate the concepts into the rest of their instruction. In middle and high school, students can choose elective courses in computer science but will not be required to take one.

Is this a good thing?

Lots of politicians, business folks, and other education “experts” have declared that CS for all students is necessary. Some say that the economic future of the country depends on training many more computer programmers, although the case for that is rather shaky (like that for the emphasis on STEM). Others seem to believe that CS would be beneficial to every high school graduate for a variety of rather murky reasons.

I certainly believe that everyone should have a fundamental understanding of how the hardware and software they use every day works. If we’re going to depend on computers to run our lives and the rest of the world, we should at least know a little about what’s happening.

However, I’m not sure these new requirements from the department of education will ever get that job done.

For one thing, these new Standards of Learning will not be tested which means it’s quite likely that, in most classrooms, the content will be added in when time allows. I also suspect that many teachers will be given the requirements with little or no help implementing them. Professional development of any kind is not given a big priority in most districts, especially for something not tested.

All of which points to a larger problem for not only CS for all, but also for STEM, the maker movement, design thinking, project-based learning, and the other “reform” ideas we have been pouring into schools in the past decade or two: there’s no room for them in the “normal” school day.

Coding is done in an hour. STEM lessons are done in after-school programs. Students go to maker spaces for special activities, in they same way they used to go to the computer lab. We bring out the projects after the “regular” work is complete.

If computer science and the rest of this is really important, it needs to be part of the standard curriculum. Every day for all students, not just on special occasions for the kids we know will pass the standardized tests.

Fitting it in shouldn’t be hard since much of the mathematics and science curriculums used in schools is crap and could easily be trashed (or at least minimized).

Replacing the classical, college-prep academic training that begins early in elementary grades with curiosity-driven, hands-on activities would not only allow plenty of time for CS and the rest, it would also make school more meaningful and interesting for students.

A win for everyone.

Digital Citizenship Was So Last Week

Last week was Digital Citizenship Week. My Twitter and RSS feed was full of posts about activities teachers were doing with students around the topics related to working responsibly online. Lots of pictures of kids doing digital citizenship stuff.

But what about this week? Will Internet safety, validating information, and fair use of copyrighted content continue to be front and center in classrooms?

In most schools, the answer, of course, is no.

As with Hour of Code, Digital Learning Day, and many other education-related special events, these topics are highlighted for a specific amount of time and then we go back to “normal”. There’s a reason why none of them are scheduled in the spring during testing season.

Certainly there are some teachers who keep these important topics in front of their classes every day. Better yet, they continually model best practices for working on and learning with the web in full view of their students.

However, if any of these topics and issues were really important, they would not be optional, distinctive occasions. Digital citizenship, coding, and the rest would be a core part of the standard curriculum, essential learning for every student.

Instead of one-and-done annual diversions from “real” learning. After all, none of this stuff is on the test.

The Mathematical Obstacle Course

In a Medium post, a “research mathematician turned educator” discusses how extremely talented students are often disillusioned by high powered mathematics competitions like the International Math Olympiad.

Of course, extremely few high school students will ever be involved in this kind of “cheap competition that brutalises the subject into a performance act”, and this piece is of very limited interest to even most math teachers.

However, this observation accurately describe the high school math experience for most students.

School maths is engineered as a relentless competition, where students are ranked and judged according to the narrowest measures of aptitude. The spoils go to those who can mercilessly commit facts and procedures to memory (irrespective, and often at the expense, of understanding), and recall them in the arbitrary confines of exams.

In most high schools, the math curriculum imposed on students is a complex obstacle course aimed directly at Calculus, a class few of them need or will ever use.

Your New Curriculum?

I listen to a lot of podcasts. Most take the format of an intelligent conversation between two or more people, or someone telling a good story.

icon for tell me something i don't know podcast

Then there’s the program called Tell Me Something I Don’t Know, which the producers (who also do the more conventional but also excellent Freakonomics) describe as journalism wrapped in a game show package.

On most segments, they have a panel of three very smart people and a general theme. Audience members (often experts in a specific field of study) are then invited on stage to tell the panel about something they may not know related to the theme. The panel gets to ask any questions they might have and, after all the stories have been told, they decide who did the best job.

It’s all simple, very nerdish fun.

However, as I was listening to a recent episode, it struck me that this is very much what school should be.

Stay with me.

Currently, in most classrooms, a teacher stands in front of a group of students dispensing information. Or at least they direct the distribution of that knowledge in some way.

So, what happens if the teacher walks into the classroom and instead challenges the kids to tell me something I don’t know?

There would have to be some structure, of course. I’m pretty sure teenagers could reel off a whole lot of trivia they consider interesting that would baffle most adults. But the show itself provides some of that organization.

The rules of the game are that the IDK (short for the “I don’t know”) presented must be something we truly don’t know, something that is actually worth knowing (which may eliminate everything on the E! channel), and something that is demonstrably true.

Ok, there are probably more than a few details that need to be worked out before anyone puts this idea into practice.

But what better way to get students to look at learning in a different way than to ask them to choose a topic they find interesting, immerse themselves in the details, and then put the material they find into a compelling form for a live audience?