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.

Questioning 1-1

sign post written in Welsh language

Way back in August, before I took an unplanned five-week blog rest, I wrote a post about attending a community presentation by the overly-large school district that once employed me. The assistant super and his associates wanted to explain their plans for an upcoming 1-1 program.

I ended that post by saying that I have a lot of questions about the project. Let’s start with one of the most basic queries: Why?

Ok, I suppose that’s rather broad. The project page on the district website tries to lay out a rationale so we’ll start there.

Students’ lives have changed considerably in how they live, communicate, work, and interact within a globally connected world. Students need both content and skills outlined in the Portrait of a Graduate in order to be successful in the workforce of the future. FCPSOn can support the development of both content knowledge and Portrait of a Graduate skills. 

FCPSOn increases equitable access to technology and to instructional practices that lead to personalized, meaningful learning experiences. This allows students opportunities for deeper understanding of content and the skills needed by the Portrait of a Graduate. 

FCPSOn will support teachers as they create learner-centered environments that help students learn concepts in meaningful experiences. The technology not only facilitates learning, it also frees time to focus attention in places that makes teaching and learning more rewarding.1

That’s it. Hard to argue with anything in that collection of eduspeak, but it really doesn’t answer my original question. Allow me to expand on it.

Why will giving every student a Windows laptop2 improve their learning?

If every student is carrying a device, does that really lead teachers to create “learner-centered environments” and “meaningful experiences”?

Where is the evidence that continuous access to powerful computing and communication technology will result in students leaving high school with those Portrait skills that are the centerpiece of the superintendent’s goals?

The rest of the page doesn’t really address any of those questions. But whatever committees3 wrote it worked hard to cover as many different educlichés as possible. Anytime/anywhere? Yep. Collaboration? You bet. Digital citizenship? Of course. Too much time on screens? Of course not.

Of course, the simple answer to all these interconnected questions is that technology will not improve learning, make it more meaningful, or improve student skills. Not unless we also make substantial changes to the rest of the learning process.

Missing from this page is the substantial issue of how the curriculum will be rewritten to make best use of these “digital tools”. Access to huge amounts of data and information should allow a shift from students memorizing lots of facts and processes to understanding how to organize, validate, and synthesize that information. But that doesn’t happen automatically.

The page also claims, as a result of this projects, students will work on “authentic projects and real world problems”. So will that change the primary means of assessing student learning? Most instruction is still firmly locked to the state standardized testing program, not to mention the curriculum pacing guides and the district’s expensive, home-grown “electronic” assessment system.

Then there are a few oddities on the page that make me go “huh?”. For example, how students will work on those projects when district policies prevent them from directly connecting with the outside world?

And I certainly don’t understand how adding computers to the classroom relates to this supposed effect of the project: “Supporting planning and reflection of student-created goals and teacher-directed learning outcomes”. How are goals “student-created” if “learning outcomes” are directed by the teacher?

As I said in the previous post, since I’m no longer in the middle of all this, my ranting here is almost entirely based on the small amounts of information provided to the community, like this project page. I could be completely wrong. District leaders may have already addressed all of my questions and have major changes in the works.

I look forward to being shown the errors in my ranting.

But until that happens, I will have more questions…


Image credit: Photo of a multidirectional sign post in Welsh by Dave Clubb was downloaded from Unsplash and is used with permission.

1. For those who are not part of the district, some explanation of terms: FCPSOn is the branding name given to the upcoming 1-1 project. Portrait of a Graduate is a collection of skills, divided into five categories, that a student should have when they leave school. It’s actually not a bad statement. Too bad it doesn’t really connect with what is actually happening in most classrooms.

2. I know it will be a device running Windows. The IT department works very hard to stop any other option.

3. I’m very sure the FCPSOn webpage was wordsmithed by several different offices in the district, probably including the lawyers.

Another Wealthy Education Expert

The latest billionaire who wants to revolutionize education is Jeff Bezos. He says he got the idea from a Twitter “conversation” about where he should put his philanthropy. So you know the idea is well thought out, right?

Amazon CEO Jeff Bezos is launching a $2 billion “Day One Fund” to help homeless families in the US and create a series of innovative preschools.

The Amazon CEO announced his new organization would be “creating a network of new, non-profit, tier-one preschools in low-income communities,” inspired by the Montessori School model, a child-centered educational method that relies on scientific observations of children from birth to adulthood.

Bezos didn’t offer many details on the preschool project, but his words show that he plans on treating these new schools like he does Amazon. He described the students as “customers” and explained that his new organization would ”use the same set of principles that have driven Amazon” to “learn, invent, and improve.”

Describing preschool children as “customers” is rather clueless and somewhat frightening.

And I always thought the principles that have driven Amazon were to grow as fast as possible, crush the competition, and make Bezos very, very rich. I suppose I could have been mistaken.

Anyway, the writer of this particular report at least manages to land on some good reasons why we should not be relying on super rich people to create education policy in this country.

Bezos’ latest announcement comes at a time of heightened criticism of Amazon’s business practices, and some critics say this latest move is savvy PR by the CEO of one of the world’s most profitable companies. But it also illustrates a deeper problem, which arises when private philanthropy fills a gap that the government should be filling, namely, the lack of quality, affordable early education in the United States. The problem lies both in the US government’s lack of investment in early education, and in big tech companies’ success at avoiding paying taxes, thus depriving states of crucial funds they could use to start their own early education programs.

Yep. Maybe if Bezos and his friends just paid their fair share of taxes, we could afford to develop quality educational programs for all kids at all levels.

Sidenote: As always Audrey Watters has an excellent take on this story, adding the historical context that the general media usually misses. Check the URL on the page for her original title. I wish she’d kept it.


Image credit: Wikipedia, used under a Creative Commons license. The Amazon Go stores are completely self-service. Maybe the Bezos schools will be self-learning.


Photo Post – Alaska

One of the reasons for the big gap in posting around here this summer was because during the first half of August, we were off cruising the inside passage of the Alaskan panhandle. Although I’m not a fan of large cruise ships (and the time trapped “at sea”), the scenery was spectacular as advertised.

Below are a few of my favorite shots, and more are in this gallery. I have some 360° images still to be posted.

Golden Gate Bridge

We sailed out of San Francisco and under the Golden Gate Bridge, but just barely since this is a huge ship.

Creek Street

Creek Street in Ketchikan. All of the small towns in which we docked had a Disney-esque tourist feel to them. This felt more genuinely historic than the others.

Lake Mendenhall

Most of the back half of the trip was spent under cold, gray skies. That still made for some interesting images, like these very low hanging clouds around the Mendenhall Glacier near Juneau.

Tracy Arm Fiord 7

One of many incredible views as the ship cruised up the Tracy Arm fjord. Huge mountains with long waterfalls, magical clouds, and, not seen in this shot, large chucks of ice in the water.

Coffee Service

I just found it amusing that, while observing some absolutely spectacular natural beauty, passengers could still buy their expensive coffee from that cart in the lower right.

Observing From The Outside

It has been three years since I left the overly-large school district to set out on a new life as a drain on society.1 Time really does fly when you’re having fun.

But the fact that I’m no longer involved in the day-to-day minutia of instructional technology in the system doesn’t mean I’m not interested anymore. I just have to learn about what’s going on in the school district the same way most of the community does.

There’s the little bit of education-related information that is reported in the local news, although that’s usually only when something bad happens.I can get a little bit of insight from the email newsletter the district sends each week, but that usually reads more like a pile of press releases than any real inside information.

More interesting, and probably more insightful, are the tidbits I get when talking to friends and former colleagues who are still working somewhere in the system. Although, in most of those conversations, we avoid discussing work in favor of more fun topics.

Anyway, out of curiosity about what has been going on, last spring I dropped in on a community meeting about the new one-to-one computing initiative the district is planning to roll out in the fall of 2019 (with the somewhat bland, focus-grouped title FCPSOn).

In my past life I would have been involved with planning this kind of meeting. I was rarely one of the people doing the presentation since my boss knew better than to put me in front of a crowd. I was prone to answer questions honestly instead of sticking to the script.

This particular presentation wasn’t much different from those I remember. Planned and edited by teams in several different offices and led by an assistant superintendent who clearly was working from his briefing notes, rather than a firm understanding of the topic.

In his opening statement, he told us that they wanted very much to hear from the community and we would be spending most of the two hours on discussion and feedback. He then spent the next 90 minutes running through his slide show or having groups of teachers and students talk about their use of technology.

I found those examples especially interesting. They included a mishmash of ideas that provided little or no support for the plan they came to sell. Does each student need a computer for the class to hold a book chat with students in another school? Is publishing an online newspaper innovative if it is directed by the teacher and not seen outside the school?3

The students involved in these segments didn’t help make the case. Many identified as being part of the IB program at the school where the meeting was held, meaning they were certainly not the “average” kid. And their examples of the great use of technology already in their learning included G Suite, Quizlet, Padlet, and even PowerPoint decks posted to Blackboard as.

Missing from the presentations was any discussion about why putting devices in the hands of every student would result in better learning. Nothing about how the district would make changes to the curriculum, pedagogy guides, or assessment as a result of the increased power and capability.

As you might expect, there were many references to “personalizing” or “customizing” learning, but nothing about how students would have a direct say in what they learn or how they learn it. The concept of “flipped” classrooms, in which students watch videos instead of teacher lecture/demos, doesn’t do it. As with most of the other examples, flipped is more about changing teaching rather than changing learning.

On that topic of student input, I found it interesting that the district-created video about “student voices” was dominated by adults taking about giving students voice. The images of 1-1 classrooms showed students in classic rows or groups of four, with everyone working on individual computers. And the students presenters themselves were obviously carefully selected to make the point of the adults who planned the session.

When the assistant super finally finished and asked for discussion from the audience, it was clear the parents and community members (who seemed to be a minority among all the school administrators, teachers, and tech support folks) didn’t want to stick to the script.

Many were concerned about the amount of screen time kids were going to get, especially in elementary school. They wanted to know how taking computers home would increase student stress levels. Is it really necessary to give every kid a device to achieve the district learning goals?

All very good questions. The assistant super and all his assistants in attendance had few answers, and seemed genuinely surprised by the pushback. Maybe if they had done a little reading outside of the bubble, they might have anticipated it.

I have a few questions myself, about 1-1 in general and this particular plan that I never got to ask during this community meeting. But this post has already run too long, so I’ll save them for another rant.

I’ll also be digging a little deeper into what happens with the planning and implementation of FCPSOn over the next year, at least as best I can. It will be interesting to see what this all looks like from the outside.


Image of smiling 1-1 students in a Northern Nevada school district, from an article in the local newspaper.

1. That “drain on society” line is how a former Virginia legislator once referred to the teacher retirement system. Fortunately, he is a “former”.

2. Rule number one for anyone working in Fairfax, and I assume the other area districts, is to avoid making headlines in the Post.

3. I know the IT department still does not allow student work to be published outside the “walled garden” without lots of review and permissions at the district level.