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.

When Do Kids Have Time For Failure?

We hear a lot from politicians and education reformers about teaching kids to be creative. Learn to be innovative. Helping them develop an entrepreneurial spirit. Teaching them “how to fail”.

However, in the real world creative results come from experimentation. Innovators are those who do something different with familiar parts and processes. Failure results when trying something other than a prescribed recipe, then learning how to fix it.

And these are all things schools largely discourage in students, even punish them for on occasion.

If kids ask questions in class, we expect them to ask the right ones, or at least the ones we anticipated in the lesson plans.

In the world of school math there’s one “right” answer. Science classroom experiments have one established conclusion. The writings of Shakespeare, as presented in English texts, have a single set of interpretations. In music everyone sings from the same score.

Since the over-riding goal of most schools is the highest passing rate possible on the annual standardized tests, when are students allowed to be creative or innovative (something I think is a natural instinct, not learned)? How can they experiment in the learning process if everything is prescribed for them?

When do they learn “how to fail” when we have already decided on the “intervention” process if they do?

Prioritizing on Irrelevance Has Real Consequences

Following up on my math rant from yesterday, an opinion piece from the Post’s Answer Sheet blog adds some thoughts to the idea that our traditional math curriculum, as well as how math is taught in most schools, needs a major overhaul.

Now, calculus sounds essential to pre-eminence in science and engineering. It sounds like a gateway to the enticing “jobs of the future.” But here’s the reality. Other than high-school calculus teachers, adults no longer perform the low-level mechanics (months studying various integration techniques) that comprise high-school calculus. The tiny number of adults who do use Calculus in their careers compute integrals and derivatives … with computers.  Online resources like Wolfram|Alpha handle these tasks instantly — everywhere except in our classrooms. When it comes to calculus, a strong case can be made that we should do less.

Calculus reflects our true dichotomy in education. In a very different world where all of us have ready access to content and computational resource, we can have kids study things whose importance has faded or disappeared, or we can re-think what’s essential. To be specific, kids who take Calculus, generally forego statistics – a discipline that’s essential for citizenship and immensely valuable for careers. Organizations don’t need employees who can do integrals by hand using trig identities, but they’d love to hire young adults who can analyze data. With over 50 percent of recent college graduates under- or flat-out unemployed, prioritizing on irrelevance has real consequences. [emphasis is mine]

That rational thinking comes from Ted Dintersmith, a venture capitalist who organized, funded and produced the well-received documentary “Most Likely to Succeed,” and co-authored a book titled “Most Likely to Succeed:  Preparing Our Kids for the Innovation Era” (one I need to add to my reading list).

I also loved his description of the place given to actual educators and students at last month’s White House Summit on Next Generation High Schools in which he participated.

After the big-footprint speakers departed from the summit, we heard from compelling teachers, students, school leaders, district superintendents, and non-profit heads. They brought vision and bold ideas to the White House, despite being allocated just 120 seconds to describe their life’s work. The irony of a rapid-fire sequence of “talk at you lectures” on the topic of re-imagined learning wasn’t lost on this crowd.

Read the whole post for more fresh thinking on math in American schools.

Rethinking the Math

A tweet from Scott pointed me to an article from his local paper which discusses how community colleges in the Seattle area are rethinking the types of math courses required of their students. Currently about half of their incoming students must take remedial classes, and few of them even pass those.

About the same time a former student left me a comment on Facebook: “Today was day 10585 in a row that I didn’t use algebra.” I suppose that was his way of praising my skills as a math teacher. :-)

Anyway, the leaders of Washington’s community colleges are asking some fundamental questions about how much math, and what subjects, should be required, both to be admitted and to earn a degree. Their answer is that there is no one answer.

However, there are some bigger issues underlying that discussion, as well as the remark from my former student. The problem with the mathematics curriculum in our schools has less to do with the subjects taught than it does with how we teach the subjects.

For the most part, we teach mathematics as a mechanical process. For each problem, student build a machine, usually replicating the same machines created centuries ago, toss in some raw materials, and crank out the “right” answer. Now repeat the process twenty more times for homework and please don’t mention how bored you are.

Sometimes we dress them up the machine as an “authentic” problem (which is largely what Common Core tries to do). But kids realize pretty quickly that the extra words and faux “real world” language are nothing but diversions. Eventually we’ll determine the correct machine and necessary numbers, and crank away.

On top of that, we still for the most part ask kids to perform these mechanical processes on paper (show your work, and it better follow the same steps in my answer key). Rather than passing those tasks off to computers (including the one in their pocket) and instead spend the time on investigating real problems using mathematics as a tool to find solutions.

Solutions that are messy, often with the right answer being “it depends”, problems that are interesting, possibly personal to the kids, and which very often lead to even more questions.