March 13, 2013 Leave a Comment

The Mathematics of Storytelling

The question from a couple of posts back was ”When are we ever going to use this?”, something frequently asked by students in my Algebra and Geometry classes.

The Senior Scientist from Pixar offers an answer for kids interested in animation and movie making as he explains how math is used in their storytelling.

The topic of DeRose’s lecture is “Math in the Movies.” This topic is his job: translating principles of arithmetic, geometry, and algebra into software that renders objects or powers physics engines. This process is much the same at Pixar as it is at other computer animation or video game studios, he explains; part of why he’s here is to explain why aspiring animators and game designers need a solid base in mathematics.

And how important is that solid base?

Pixar’s biggest competitive advantage now is its ability to use this math-driven technology not to make better shapes but to tell better stories. DeRose and Pixar aren’t sitting on their laurels. “Somewhere out there, a brilliant kid and their friends are working in their garage” using and improving on tools like Blender, DeRose tells the assembled children and adults at MoMath. “They will be the next Pixar.”

However, there’s a big disconnect between what DeRose is discussing and the reality of the math curriculum in most schools. During their time in K12 classrooms very few kids will get to study the creative applications of math used in animation or be allowed to use any of that “math-driven technology”.

We gotta stick to what’s on the test.

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October 31, 2012 Leave a Comment

Textbook Crisis

We have a textbook crisis here in the overly-large school district.

Ok, “crisis” is probably too hyperbolic for what’s going on but there’s still lots of chatter around the topic of the electronic versions, and most of it isn’t positive. Plus the superintendent has heard from some loud and influential parents on the matter, which in turn makes the situation a “crisis” we get to fix.

The story started a few years ago when our school board decided we needed to begin using digital textbooks with an eye to replacing the paper editions, the price of which is steadily climbing. So, they waved their magic wand and told the super to make it happen.

As a result, last year social studies teachers in upper elementary and middle school got online texts for some of their classes, ones that are little more than enhanced pdf files embedded in a really crappy interface that both teachers and student found difficult to use.  But we moved on anyway and this year we have online math books which include a combination of Flash, pdf, and web-based materials.

So, what’s wrong with that?

I don’t have time or temperament to cover all the problems so let’s just hit the highlights.

First, the books are online and cannot be put on a stand-alone reader, which means they won’t work on the most affordable devices available like Kindles and Nooks. Also making the materials inaccessible in places without an internet connection, like school busses, and difficult to use in homes with multiple people all trying to access a single machine.

Then there’s the matter of the Flash and Java-based content which isn’t playable on iOS devices and, it turns out, is inconsistently supported on Android devices running a variety of different versions of the OS.

I also find it interesting that the publisher’s tech support centers close around 6pm. How many kids do you know that even start their homework before that time?

Then there’s the lack of equipment available for students to use at school, especially during times when it must be dedicated to testing. And that’s becoming all year round with our increasing craving for data (aka practice tests), a rant for another time.

However, the biggest problem has nothing to do with any of the technical problems. Or with the publishers, and the fact that they are far more interested in “protecting” their products than in providing quality instructional materials.

The worst part of this crisis is that our school board and administration are so short sighted that they continue to buy what the publishers are selling: generic, unmodifiable crap that’s written at a slightly higher interest level than most Wikipedia articles, with mediocre graphics and worksheets containing the same rote process problems that have been around for decades, if not centuries.

Math instruction in K12 needs a major overhaul and we should start by throwing out the generic textbooks (adding video and animation is just window dressing) and then take a serious look at what math skills kids need to have when they graduate.

A good chunk of what we do is irrelevant and useless, not to mention boring, just like the textbooks, digital or otherwise.

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August 20, 2012 Leave a Comment

Legislating Ignorance

The headline says it all: Kentucky lawmakers shocked to find evolution in biology tests.

They’re upset that, after mandating a science curriculum “allowing or requiring nonscientific ideas to be taught alongside a standard biology curriculum”, national standardized tests actually expected kids to know the basic facts of evolution, and gave them lower scores when they didn’t.

While it’s the students of Kentucky who are being short changed when it comes to their education, it’s the people running their school system who are truly ignorant when it comes to science.

The same report quotes Representative Ben Waide, who demonstrated his lack of scientific knowledge by saying, “The theory of evolution is a theory, and essentially the theory of evolution is not science—Darwin made it up.” Waide went on to say that “Under the most rudimentary, basic scientific examination, the theory of evolution has never stood up to scientific scrutiny.”

As if this guy has any idea what the term “scientific scrutiny” really means.

Anyway, Kentucky is not the only place pushing ignorance into the curriculum, and not only in science. It appears that some fundamentalists also want to rewrite mathematics.

“Unlike the “modern math” theorists, who believe that mathematics is a creation of man and thus arbitrary and relative, A Beka Book teaches that the laws of mathematics are a creation of God and thus absolute….A Beka Book provides attractive, legible, and workable traditional mathematics texts that are not burdened with modern theories such as set theory.” — ABeka.com

The post at Boing Boing offers both a good overview of set theory and why this is a crazy idea.

And finally, to round out this collection of educational malpractice, enjoy 14 Wacky “Facts” Kids Will Learn in Louisiana’s Voucher Schools, with some historical revisions I’ll bet you didn’t know.

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August 7, 2012 Leave a Comment

Stop Calculating, Start Teaching Math

Although it’s almost two years old, I just ran across this talk from TED Global by Conrad Wolfram this weekend. In it he advocates for teaching kids real math, instead of just calculating, which he says makes up most of our current curriculum.

On the chance that you also have not discovered this presentation (and are interested in math education), here it is, plus a few of my thoughts of course.

According to Wolfram, in math education we’re spending about 80% of the time on what he calls step 3, calculating results by hand. Processes that are done faster and more efficiently using computers, a category that includes smartphones, tablets and those computing devices still called “calculators”.

Of all the subjects in K12, the math curriculum is probably more rooted in the pre-computer age than any other, taught in very much the same way as we did in the past century. And probably the one before that.

Certainly kids need to learn some basic facts and computational processes. But when was the last time you had to divide two fractions? Or did long division of a three digit number into a six digit number? And how did you handle that messy remainder?

I’m willing to bet that for all but the most simple problems, you turned to a computing device of some kind to assist with doing the mathematics.

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July 4, 2012 4 Comments

It’s Not Khan’s Fault

The Chronicle of Higher Education has an excellent critique of Khan Academy by one of the people who inspired the #mtt2k* mini meme now getting its 15 minutes on YouTube.

If you're not a math ed geek, you probably haven't seen the video of two math professors watching one of the Khan videos and offering their comments a la the wonderful 90's cult classic Mystery Science Theater 3000 (look it up, kiddies). Although there are a few snarky remarks about the style, most of their criticism is directed to the pedagogy and mathematics. Dan Meyer has more details.

Anyway, the Chron article hits exactly my greatest problem with Khan Academy: not the quality of the videos, but the over-the-top reaction they get from some high profile education “experts”.

But let’s also be honest about what Khan Academy is not. Khan Academy is not a substitute for an actual course of study in mathematics. It is not a substitute for a live teacher. And it is not a coherent curriculum of study that engages students at all the cognitive levels at which they need to be engaged. It’s OK that it’s not these things. We don’t walk into a Mexican restaurant and fault it for not serving spaghetti. I don’t fault Khan Academy for not being a complete educational resource, because it wasn’t designed for that purpose. Again, Khan Academy is a great resource for the niche in which it was designed to work. But when you try to extend it out of that niche — as Bill Gates and others would very much like to do — all kinds of things go wrong.

One of those things going wrong is the reinforcement of the idea that learning math is all about mastering the process. That if a student just repeats a set of algorithms enough times, we can declared that they have “learned math”. Or whatever subject you like to substitute for “math”.

However, I think the best summary of this kind of video, lecture/tutorial, self-instruction approach to education is this:

Khan Academy is great for learning about lots of different subjects. But it’s not really adequate for learning those subjects on a level that really makes a difference in the world.

For that “makes a difference” kind of learning, students (of all ages) still need direct relationships with teachers, and others who don't necessarily carry that title, as well as an understanding of how to actually use the information.

* mtt2k = mystery teacher theater 2000

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April 23, 2012 Leave a Comment

Change for the Better?

From the front page of today’s Washington Post, is this is what parents think of as an undergraduate college education when they write the big checks to send their kids to Tech?

In the Math Emporium, the computer is king, and instructors are reduced to roving guides. Lessons are self-paced, and help is delivered “on demand” in a vast, windowless lab that is open 24 hours a day because computers never tire. A student in need of human aid plants a red cup atop a monitor.

The Emporium is the Wal-Mart of higher education, a triumph in economy of scale and a glimpse at a possible future of computer-led learning. Eight thousand students a year take introductory math in a space that once housed a discount department store. Four math instructors, none of them professors, lead seven courses with enrollments of 200 to 2,000.

As to those red cups, I remember seeing them sitting next to Apple IIGS machines in more than a few elementary school labs over the years. In those days, students would be asking for help with Math Blaster or Kid Pix.

Anyway, the lab (you need to see the picture) is both cheaper to run than “regular” classes and the students have a higher pass rate for the same introductory math courses than when they opened The Emporium fifteen years ago. Of course, as you might expect, the assessments are multiple choice to make grading faster and easier.

It’s an interesting approach but I have to wonder about this from the math department chair. 

“How could computers not change mathematics?” said Peter Haskell, math department chairman at Virginia Tech. “How could they not change higher education? They’ve changed everything else.”

It’s certainly a change from what I remember of my college math classes (none of which had 200 students), but is it a positive change for the students?

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April 17, 2012 Leave a Comment

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.

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