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.

Teach Me, Seymour

One of the few formal sessions I attended at the ISTE conference was one by Gary Stager. Gary is one of those people with strong opinions, and I don’t always agree with him but he always gets me thinking. Which is a good thing.

His topic this time was a retrospective on the work and ideas of Seymour Papert, who passed away two years ago. If you are an educator and you don’t know about Papert’s work, then there is a big gap in your professional knowledge. Especially if you have anything to do with instructional technology.1

Papert was a pioneering researcher on how kids could use technology to learn. He believed in the idea that children could and should use all kinds of tools create their own learning, leading directly to the current Maker movement. He was also the godfather of today’s “coding for all” efforts, having co-developed the Logo language (Scratch’s grandfather) and advocated in the 80’s for programming as part of the standard curriculum.

During the talk, Gary reminded us of two particular Papert ideas that I believe are very relevant in the techno-rush to “personalize” student learning.

One comes from Papert’s landmark book Mindstorms in which he asks a fundamental question: “Does the computer program the child or does the child program the computer?”

It struck me that the former – the computer programming the child – is exactly the approach taken by many designers of personalized systems. They claim their products are simply offering kids choices, but too often their algorithms are in control of the learning process.

Before buying into the marketing hype of “personalized” learning products, anyone who works with children should be asking the developers Papert’s question. If they can’t offer a satisfactory answer, move on.

Gary also offered another, very simple, observation from Papert that should be quite obvious, but is often ignored: “Learning is not the direct result of being taught.”

Of course, when he uses the term “learning”, Papert was not thinking of standardized test scores. He was concerned with long term understanding and internalizing of knowledge. The kind that only comes from kids constructing their own learning.

It’s an idea that the vendors of “personalized” learning systems seem have missed, since their systems are all about being taught, not learning.

Just a couple of powerful ideas from Seymour Papert that we often forget when surrounded by all the attractive, shiny new toys at ISTE.


The image is a drawing of Seymour being drawn by the LOGO Turtle by Peter H. Reynolds. It is linked from Gary Stager’s Daily Papert website.

1. In addition to Mindstorms, I recommend Papert’s wonderful book from the early 90’s, The Children’s Machine. You can also get much more information about Papert and read many of his papers on Gary’s site, The Daily Papert.

On The Hazards of Free

free stuff

In the past week or so, we have a few more examples of why it may not be a good idea to depend on free.

The first involves Padlet, a service that began about six years ago under the name Wallwisher. Padlet allows users to create a virtual bulletin board and then include others as collaborators. It was enthusiastically adopted by many teachers for instructional use, as well as by many of us who did professional development activities.

The service was attractive because it was relatively easy to use and, of course, the account was free. At least the basic version was free, which means someone had to be paying the server bills.

Padlet is one of many web-based services struggling to succeed using a “freemium” business model. Under that concept, a company makes money (or tries to) from the relatively small part of the user base who are willing to pay for advanced features. It’s a tricky balancing act trying to attract enough “premium” users while not giving away too much value at the free level.

This week Padlet decided they need to rebalance and announced a change to their pricing structure that removes some of that free-level value. The new model severely limits the number of Padlets that could be created by free users and, as you might expect, many of them were not happy.

Then there was another big piece of edtech news that didn’t get the same degree of Twitter coverage but still illustrates the problem with free.

Edmodo, a popular system for building communities founded in 2008 as a “Facebook for education”, was sold to a Chinese company. Their service was also free, at first, and teachers flocked to it, growing to more than 90 million users around the world.

Although Edmodo was able to raise money from investors, they never found a model that could sustain the company for the long term. The question now is how the new owners will change the service to recover their purchase price and provide an income stream. Whatever they decide will likely not be popular with users who have become accustomed to free.

Finally, there was one more reminder about the problem with free that landed in my email box. The message came from the CEO of Noosfeer, letting me know that the service will be “closing its doors to the general public” at the end of the month.

Yeah, I didn’t recognize the name either. Or remember having an account.

According to the website, Noosfeer is (soon to be was) a “content reader and aggregator”, evidently founded around four years ago. It sounds like something I would have wanted to try. I’ve opened a lot of accounts over the years. And forgotten about most when they didn’t fit my needs.

Anyway, this blip, along with the higher profile changes to Padlet and Edmodo are just the latest reminders that free is not a sustainable business model. Just don’t be surprised when “free” changes in a way you may not like. Or disappears.


The photo, by Frank Hebbert, was posted on Flickr and is used under a Creative Commons license.

My Head Hurts

Today I received an ad for a new book titled “How to Teach So Students Remember”. I get lots of similar promotions but there was something about this one that caught my eye. And made my head hurt.

The first line of the description of the publications makes this declaration:

Ensuring that the knowledge teachers impart is appropriately stored in the brain and easily retrieved when necessary is a vital component of instruction.

The copy goes on to promise that the author will provided you with “a proven, research-based, easy-to-follow framework for doing just that”.

There is just so much wrong with everything in the space of one small email, it’s hard to know where to start.

How about the apparent core idea that the goal of good teaching is to have students “remember” all that we “impart” to them? Reflecting the traditional role of the teacher as someone who transfers information in carefully measured clumps from their tightly managed repository to the vessels sitting in the classroom.

And, in the same sentence, is the implication that success is derived from knowledge being “appropriately stored in the brain” and “easily retrieved when necessary”. I can only assume that the most important “necessary” time is the spring standardized tests.

Ok, all that snark is only based on a couple of paragraphs in an email. I haven’t read the actual book, although I did read through the first chapter posted on the web. And just that part certainly lives up to the promotion. Research-based pedagogy right out of a 50’s-era manual for running a traditional teacher-directed classroom.

I just couldn’t believe this is being peddled as a guide for modern teaching by one of the largest professional organizations for educators, the Association for Supervision and Curriculum (ASCD).


An image similar to the one at the top just stuck in my head from the minute I read the ad copy. The picture, taken in 1943, is of a classroom in a UK Catholic school and is used under license from the Wikimedia Commons

Help The Children Lead, Instead of Telling Them Where to Go

From Alexandra Petri, one of the smartest, and often funniest, writers at the Washington Post, some (satirical) thoughts about the students now speaking up against the American love affair with guns.

Now, if you don’t want to hear from any more high schoolers traumatized by gun violence, then you either decide to try to create a world where high schoolers are not traumatized by gun violence, or decide to create a world where you do not have to listen to the high schoolers. It looks like we’re picking the latter!

We are not monsters. This burning shame that keeps us awake is their fault. If they were not there pointing the finger at us — We are being personally victimized! We are the real victims here! They have the audacity to point fingers at people for doing nothing! We haven’t done anything!

You can almost hear that coming out of the mouth of some “regressive”1 commentator on one of the talking heads channels in response to the raw and honest reaction coming from the children.

What these analysts and spokespeople seem to ignore is that the First Amendment doesn’t specify a minimum age and that the right to petition the government belongs to everyone, not just their friends with big bank accounts.

Anyway, I hope that the students from Parkland, now loudly speaking against our absurdly loose gun laws, continue to ignore those calls to shut up and sit down. Even more, I really hope that they, joined by protesting young people from all over the country, have started a movement that can affect major changes.

The adults of my generation have created many, many problems with our current government, and American society in general. Problems that are already severely impacting the lives of these kids beyond the almost-daily gun violence. From climate change to economic disparity and poverty to an increasingly unstable world, they need to be more than just aware. Students must be leaders in the work to the solutions.

But those solutions will not come easily. I agree with a post from a wise friend who writes that such a process will be “incredibly long” and will include many setbacks.

Sustaining the passion for the work is really hard, and you’ll need trusted friends and allies who will listen to you vent and strategize with you and privately call you on your mistakes and tell you when you need to go get some sleep. You will need those people, and I am sure you will be those people for each other as well.

Some of those “trusted friends and allies” must be their teachers.

However, instead of telling them to stay in the classroom, we must listen to our students, to both their concerns and ideas. We, as in all adults who support children, must help them learn how to use their authentic voices and to effectively direct the power of responsible civic engagement.

Guide them into adulthood, instead of always telling them what we think they need to know, what to say, and how to act.


Image is of an editorial cartoon by the wonderful Steve Benson, whose liberal-leaning work always seemed a little out of place at the conservative (but generally responsible) Arizona Republic newspaper (known online as AZCentral).

1. Since “progressive” is often used as an alternate for liberal on the political spectrum, I think we should use a far more accurate synonym for conservative, “regressive”.