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.

I Guess It’s a Start

The title of this post pretty much tells you everything about the current state of digital textbooks: Students Find E-Textbooks ‘Clumsy’ and Don’t Use Their Interactive Features.

The writer is addressing the issue in colleges but that same statement applies to the online Social Studies textbooks we began using last year here in the overly-large school district.

I’ve ranted about this before but the fact of the matter is that the publisher in our case is offering little more than a digital reproduction of the hardcover book, and they still require us to purchase a minimum number of those analog versions.

The math textbooks our students will be using this year are somewhat better in that the material is largely in HTML, includes some video, and adds a few interactive features. However, as with those digital social studies books, the math textbooks are hit or miss when it comes to using them on smartphones and tablets, even those still running Flash.

I suppose you could view this in a glass-half-full manner, as a tentative start to the process of eventually having all classroom materials in a digital form. I’m just not sure that process is going to move very quickly since the publishers seem far more interested in protecting their markets and profits than they do about anything instructional.

If I was running this show, we would be putting some of the large chunk of the money spent every year on dead-tree books into creating online, open-source, accessible on any device instructional materials of our own.

It’s one of those big changes that could have incredible long-term advantages for an educational system accustomed to very short-term thinking.

TED-Ed: A Site Worth Watching

It’s not going to revolutionize education, flip the classroom, or replace teachers, but the new education site from TED looks like it could be a great resource.

TED-Ed (Lessons Worth Sharing), takes presentations from their collection and elsewhere, blends in some animation to give them more context and interest, groups the videos around nine subject areas, and adds some additional instructional resources.

Although many of the articles reporting on their opening this week compare this to the Khan Academy, TED-Ed is very different and much more substantial. For one thing, this new site is more about ideas and concepts rather than providing step-by-step instructions for rote processes.

Like Kahn, TED-Ed tracks your use of the materials. But instead of a self-assessment section based solely on multiple choice questions, the site asks users to do more in-depth thinking about the presentation they’ve just watched and offers additional resources to explore.

However, the more interesting, and potentially more powerful, part of TED-Ed is the ability for teachers to create their own lessons around the material (what they call Flip This Lesson) and share them with the larger community. Even better is the open invitation to submit ideas for lessons and to participate in the creation process. It opens some interesting tools for teachers to enhance and extend their instruction but also intriguing possibilities for student creative involvement as well.

No, it’s too soon to declare that TED-Ed is the catalyst that will forever alter public education (I suspect someone has already made a similar declaration), but it is an excellent start and something worth watching as it grows.

Watch the short tour of the site and see what you think.

Failing Math (Instruction)

By way of KQED’s Mind/Shift blog comes a post asking Does our approach to teaching math fail even the smartest kids?

The answer is most definitely yes, and here’s the fundamental reason why.

Indeed, traditional math curriculum is to teach discrete algorithms, a set of rules that elicit a correct answer, like how to do long division, say, or how to use the Pythagorean theorem. Then students “learn” the material by doing a large quantity of similar problems. The result, says Rusczyk [founder of the online math program Art of Problem Solving], is that students are rarely asked to solve a problem they are not thoroughly familiar with. Instead, they come to think of math as a series of rules to be memorized. The trouble is kids don’t necessarily learn how to attack a new or different kind of equation.

Math instruction, especially in high school, is more about getting the “right” answer to canned problems than it is about understanding the process of mathematics and how it is used to do real work. And those right answers are rarely the messy, not-necessarily-exact, sometimes-ambiguous results found in the real world.

Another major reason why K12 math instruction fails kids (and leads to the high drop out rate from STEM programs in college, the starting point for the post) is the endless repetition throughout the elementary and middle school curriculum. We wring any interest in problem solving using mathematical tools from the kids by boring them with the same material year after year, only with larger numbers.

That includes continuing to cover the many mechanical processes that calculators and computers made unnecessary years ago. Once kids have a grasp on the concept of division, do they really need to do page after page of long division problems? I taught math for eighteen years and still don’t understand why anyone needs to divide fractions.

The math curriculum in most K12 schools in this country has been in need of major overhaul for many years, but it’s not likely to change for a variety of reason, not the least being the standardized tests we use to assess student learning in the subject at the most basic level.

It Kahn Be Done Better

It seems everyone is wild about Khan Academy, offering it up as an example of how to revolutionize education, especially Bill Gates who has contributed a small part of his money to the project.

However, a post that recently popped up in my Delicious network (thanks, Scott), discusses two issues about Salman Khan and his video collection that also bother me.

But what I found was that Khan was just an OK teacher. His examples are not well planned. His pacing is inconsistent. I’d say that at least half the math teachers in this country could do at least as good a job as Khan does. What is ironic about Bill Gates admiration of Khan is that Gates is investing so much energy right now into identifying what makes a great teacher to create better teacher evaluations. Yet the person he considers the best teacher is merely adequate.

Which, of course, also points up the fallacy of allowing someone with a high profile, lots of money, and little understanding of the teaching process to drive education reform.

So, what about that part saying that many teachers could to do a better job than Khan? Maybe instead of funding a collection of canned lessons from one person, this might be the better way for Bill to spend his money.

What we need is a platform where teachers can upload their videos and the ones that are the best can be featured and those teachers can achieve some Khan-like fame. Instead Khan has a monopoly as the one man show.

I’d go even farther and open the platform to students. There are also many kids who could create better instructional materials than Khan, and they often come with better insight than most adults about what it takes to explain complicated topics to their peers.

However, there is one more major reason why the Khan Academy is bad for instruction, especially math, the topic around which his fame was built.

Rote tutorials like this reinforce the concept that math is all about mastering the process, about learning to take select the correct algorithm, plug in a few numbers, and crank through a solution, the one and only correct answer.

Math in the real world is far more interesting, interconnecting not only with science but the social sciences, business, and many other disciplines. We do our students a great disservice by making them think the largely boring work we do in school is “real” math.