Digital Conversion

In the last few years, many districts in this area have been promoting a “digital transformation” in their schools, including Fairfax, the system that employed me for many years. It’s a nice phrase and one that is often linked to 1-1 programs. But what does the phrase really mean? What exactly is going to be transformed?

Dig into the plans – posted on websites, presented at conferences, explained in conversations – and you hear a lot of elements not related to learning. The discussion is about technology and support issues: What device should we buy? Do we have enough bandwidth? We need more power outlets. How do we pay for all this? What happens if a student does something wrong with the machine we’re handing them?

Almost completely missing is an explanation of the major changes that will come in curriculum, pedagogy, assessment, or pretty much anything else instructional, as a result of buying all the equipment, software, and infrastructure.

Ok, I know transformations like this take time, especially in a tradition-bound institution like American education. And I’m also sure this kind of external communication doesn’t cover all the pieces districts are considering in their planning.

So, at the risk of covering issues already being addressed, I have a few questions for districts and schools undergoing a digital transformation.

How are you planning to change the curriculum teachers and students will be working with?

Shouldn’t the concept of learning change when information is no longer scarce? When the process of “teaching” is no longer one way from teacher to student? Asking students to recreate the same research papers their parents wrote makes no sense. Plodding through sheets of problems that their phones could solve in seconds, and which add nothing to their understanding of mathematics, wastes everyone’s time.

Are you providing enough support and time for teachers to learn the pedagogy to accompany all the digital?

Managing computers in the classroom is important. Knowing how to work Google Classroom or Office 365 is certainly part of the mix. But using Google is not necessarily transformative. Shifting the standard assignments from paper to digital is not at all transformative. And it’s going to take a lot of time for teachers (measured in years, not semesters) to make the major alterations to their practice that takes complete advantage of the new opportunities available in their classroom.

How will evaluation change to match the transformed expectations for learning?

Certainly there is basic knowledge and fundamental skills that we should expect any educated person in our society to know. Beyond that, digital tools allow for exploring the personal interests and talents that all students bring to school. So how do we assess their learning of both the essential materials and their individual goals? It’s not through standardized tests and we need to figure it out if this transformation is ever going to happen.

And finally, where are the students in your transformational planning?

Educators talk all the time about how the kids are the most important part of school. However, we rarely include them in any of these discussions. Not with surveys. Not by asking their opinion about school rules. Not with a few focus groups once most of the plans are in place. Students need to be at the table when we are finding the answers to all of the questions above. It’s their education. They will benefit most from their work in school (or possibly benefit very little). They need to have an equal voice.

This is just a start. There are many, many other questions that need to be asked, all part of the process of creating real change.

Because if you are using technology to digitize the same old learning process, what you get is a digital conversion, not a transformation.

Why This Math?

A recent, very short post on the NPR Ed blog covers almost 500 years worth of math curriculum.

However, as a Harvard professor explains, the trip doesn’t really require all that many words since not much has changed in that time. After reviewing some very old textbooks, he says, we find “a curriculum that is so similar to the curriculum we have right now it might as well have been written by the good folks who wrote the Common Core”.

That professor is Houman Harouni, who became interested in this topic when his elementary students asked the question all of us who teach math have heard at one point: why do we have to learn this stuff?

But it isn’t just why we teach math that fascinates Harouni. He is particularly interested in why we teach math the way we do: “Why these topics? Why in this order? Why in this way?”

He says history offers the best answer.

Harouni has studied texts dating to ancient Babylonia, ancient Sumer and ancient Egypt, and, he says, he has found three main ways of teaching math, each associated with a different economic group.

The three types of math Harouni identified are “money math”, used by traders and merchants, “artisanal math”, for carpenters, masons and other craftsmen, and “philosophical math”, which was only studied by “elites”. The first two groups arranged for their math to be taught to their children, trainees, and apprentices, solely with the goal of extending their influence and wealth. Relatively few people outside of colleges studied philosophical math until very recently.

Today the math curriculum used in most schools is a mashup of all three, with elementary kids mostly working in money math, because “we live in a world where money matters”, with some artisanal math in the form of Geometry. That’s followed in middle and high schools with most students receiving a heavy dose of that philosophical math in the standard path from Algebra to Calculus.

The bottom line is, the school math we impose on students in most American schools is largely a legacy from centuries long past. Much of it needs to be thrown out (or drastically rewritten) and replaced with concepts and skills that better fit with the way math is applied in the 21st century rather than the 16th.

For most kids in K12 schools, math should be studied as it was 500 years ago, reflecting how it is used in today’s real world: as a tool for solving problems in many different aspects of life. And not as an independent, overemphasized and excessively tested, stand-alone subject.

School Math is the Wrong Subject

Conrad Wolfram, a mathematician and “director of what’s arguably the world’s ‘math company’” (that would be Wolfram Research), believes “today’s educational math is the wrong subject”. Meaning that what we present to students as “mathematics” is not anything like what it is in the real world.

In the real world we use computers for calculating, almost universally; in education we use people for calculating, almost universally.

This growing chasm is a key reason why math is so despised in education and yet so powerful and important in real life. We have confused rigor at hand-calculating with rigor for the wider problem-solving subject of math. We’ve confused the once-necessary hand mechanics of the past with the enduring essence of math.

At its heart, math is the world’s most successful system of problem-solving. The point is to take real things we want to work out and apply, or invent, math to get the answer. The process involves four steps: define the question, translate it to mathematical formulation, calculate or compute the answer in math-speak and then translate it back to answer your original question, verifying that it really does so.

Teachers and textbooks give lip service to math as a tool for problem-solving but do little to help students understand the process Wolfram describes. As a result, the work kids do in “math” class is dry, boring and largely useless. For the most part, students learn to step through algorithms that the real world turned over to computers and calculators many decades ago.

I love how he describes “word problems” (now often euphamistically called “applications”) “as toy problems and largely outside any context most students can relate to”.

But it’s not just about turning the computation part over to computers. Wolfram says we need to completely replace the current mathematics curriculum taught in most schools.

Instead of rote learning long-division procedures, let’s get students applying the power of calculus, picking holes in statistics, designing a traffic system or cracking secret codes. Such challenges train both creativity and conceptual understanding and have practical results. But they need computers to do most of the calculating — just like we do in the real world.

All of us who have taught math in K12 have heard one common question from our students: “when are we ever going to use this?”. The fact that the honest answer is “probably never” should be a clue that something needs to change.

Performing Mathematics

It seems as if there have been a lot of critiques of how we teachmath in the past couple of months. And now the author of a new book that links success in learning math to the “mindset” concept1 weighs in for The Atlantic, explaining the Math-Class Paradox.

If you ask most students what they think their role is in math classrooms, they will tell you it is to get questions right. Students rarely think that they are in math classrooms to appreciate the beauty of mathematics, to ask deep questions, to explore the rich set of connections that make up the subject, or even to learn about the applicability of the subject; they think they are in math classrooms to perform.

Students from an early age realize that math is different from other subjects. In many schools across the U.S., math is less about learning than it is about answering questions and taking tests–performing.

This school view of math as performance comes from their teachers, especially in elementary school, who “boil the subject down to producing short answers to narrow questions under pressure”. Hoping, of course, that this approach will get the kids to produce on the all-important spring standardized tests.

However, you can’t really blame teachers. They are working with the math curriculum, pretty much the same one taught in K12 for a hundred years or more, they have been given.

The fact that a narrow and impoverished version of mathematics is taught in many school classrooms cannot be blamed on teachers. Teachers are usually given long lists of content to teach, with hundreds of topics and no time to go into depth on any ideas. When teachers are given these lists, they see a subject that has been stripped down to its bare parts–like a dismantled bike–a collection of nuts and bolts that students are meant to shine and polish all year. Such lists not only take away the connections that weave all through mathematics, but present math as though the connections do not even exist.

Those connections, not only within mathematics but the applications to many other disciplines, was what I found most interesting when I taught the subject. And I tried hard to convey those connections to my students. But even in the pre-NCLB era when the end-of-course exam did not loom as large, the curriculum was still overloaded with crap. Time for open-ended questioning and exploring the messy world of applied math was still limited.

It Takes More Than an Hour

Last week we celebrated Computer Science Education Week, with many schools offering it’s very popular Hour of Code activities to their students. And we heard from many politicians, business people, and ed leaders calling for all students to study coding as part of their regular school program.

But is that necessary? Or even a good idea?

The Guardian news site evaluated exactly that issue when they asked Should Kids Learn to Code? Their question is prompted by the fact that the UK government has added computer programming to the curriculum for students in all their schools beginning next fall.

In Great Britain, as well as in the US, one of the primary arguments for having kids learn to code is economic. They are trying to grow their tech industries, something, of course, many states on this side of the Atlantic would like to do. New York City has announced that “computer science will be compulsory in the city’s schools within the decade” and other areas are looking seriously at similar requirements.

However, as with the many exaggerated claims for the number of STEM jobs that go unfilled due to a lack of trained graduates, you have to wonder how many programmers will be needed in either country.

Excitable industry claims about creating millions of new jobs by 2020 (tactfully described by one well-placed industry source as “more a campaigning tool” than anything) may not hold water, but the UK Commission for Employment and Skills still estimates that another 300,000 digital jobs could be created by 2020.

Certainly the number of students learning to code in the UK by 2020 will far exceed the number of “digital jobs” available, which is likely an exaggerated number from that “excitable industry” anyway.

Then there is the other major justification to have computer science training for all students: to help them understand how our increasingly software-driven world works (or fails to work in some instances). That is a rationalization I can actually support – but not if the approach taken is the same as for teaching mathematics in most American high schools.

Just as there are no good reasons, academic or economic, for every student to follow the standard path from Algebra I through Calculus, the standard computer programming curriculum is not appropriate for helping future adults understand the digital world.

In any case, I also wonder about the impact of all the Hour of Code events from last week. And last year and the year before. In the schools around here (and I suspect elsewhere), the kids get their hour playing with Scratch or robots or Star Wars-based tutorials and then return to the normal school program.

If the people who believe kids should learn the concepts of code are serious, it’s going to take more than an hour a year. But it also needs to be part of a major overhaul to the standard K12 curriculum.