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Happy Pi Day!

How are you celebrating this once in a century event?

Chances are that unless you teach math, the last time you thought about the number pi was about the same time you stopped crushing on the hot guy in AP English.

But it’s time to renew acquaintance with this elegant number because this Saturday is not only the annual Pi Day (3.14 – get it?) but the best Pi Day of this century, 3.14.15, the date corresponding to the first five digits of pi.

And it’s about to get raucous, or as raucous as a date commemorating a mathematical constant gets. Both the University of Houston and Texas A&M University will have parties. The Children’s Museum of Houston will celebrate its sixth annual Shaving Cream Pi(e) Fight at 1:59 p.m. Saturday, 9 being the next digit in pi.

What’s all the fuss? Isn’t pi about, like, circles or something?

Sit back, grasshopper, and listen to the professors.

Pi, often depicted as the Greek letter π, is the ratio of a circle’s circumference to its diameter. It was discovered independently by many cultures over the centuries, probably starting with the Babylonians about 4,000 years ago, says Bernhard Bodmann, professor of mathematics at the University of Houston. The Babylonians, though, weren’t terribly accurate and put its value at about 3.

The real early hero of pi is the Greek Archimedes in the third century B.C., says Frank Sottile, math professor at Texas A&M. The Greeks knew, as you learned in school, that the circumference of a circle is 2 πr, and that the area of a circle is πr², but they didn’t get that the two pis were the same thing. “Archimedes showed that π=π,” he says.

Another cool thing? The volume of a sphere such as the Earth is 4/3 πr³.

Pi’s true beauty is its simplicity, says Scott Chapman, a math professor at Sam Houston State University and editor of the American Mathematical Monthly.

“It’s the best example of a nonsimple number that a person on the street can understand,” he says. School kids know it. Contrast that to e, or Euler’s number, another constant of note. “To understand e, you’d have to remember what a natural logarithm is,” Chapman says. That’s calculus. Ahem.

True enough, but as the great Leonhard Euler taught us, e^(πI) + 1 = 0. It’s all connected somehow. If you’d like to know more about this magical number, I recommend the book A History of Pi. Originally published in 1970 by Petr Beckmann, it’s a little dated, especially when Beckmann goes off on the occasional historical/political rant (executive summary: he did not like the Germans or the Roman Empire), but it’s a great overview how we learned what we know about pi. It doesn’t skimp on the math, so be prepared to exercise those parts of your brain, but it’s well worth the effort. Happy Pi Day!

UPDATE: Some awesome visual representations of pi.

No calculators for you!

I’m OK with this.

Texas schoolchildren should not use calculators until they learn to work through math problems the old-fashioned way — on paper, State Board of Education members said Thursday.

The board on Thursday tentatively approved new math curriculum standards designed to add rigor while encouraging students from kindergarten through fifth grade to learn basic math without the aid of calculators.

“We hear more and more from parents that their kids in school are being allowed to rely on calculators without actually memorizing their math facts and building that firm foundation,” board Chairwoman Barbara Cargill, R-The Woodlands, said.

Member Mavis Knight, D-Dallas, cast the only dissenting vote against removing calculators from the early elementary grades. The board is expected to take final action on the new math standards Friday.

[…]

“Our objective today is that our kids are required to memorize their math tables and their basic math,” said David Bradley, R-Beaumont, who pushed for the restriction on calculators. “That will then lead to success.”

The board, he said, wants to send a message in the new standards that “calculators are not to be an instructional tool in K-through-5.”

Knight said she believes teachers need flexibility and should be allowed to use calculators as “an enrichment activity.”

“I think it’s nonsensical in this 21st century that we are not having students use the tools at the appropriate time and at the appropriate level because these are the tools that they will be using as they advance through school and in the work world,” she said.

The new math curriculum standards will not ban calculators in the early elementary classes as there is no way to enforce such a prohibition, but Knight said teachers “will interpret the standards as ‘we cannot use calculators.'”

The Board gave its final approval to this and the new math standards on Friday. I don’t really want to invoke the “back in my day” argument, but I did get a degree in math and never once used a calculator in any of those classes. I do think there’s value in using calculators for higher level math, mostly for graphing, and I don’t have a problem with using them in other classes where math is part of what you do – physics, for instance – but I have to agree with Cargill and Bradley here. There’s no substitute for knowing your multiplication tables. I’ve seen people whip out a calculator to multiply something by ten, or to add two two-digit numbers together. That’s crazy, and to my mind represents a failure of that person’s elementary education. Calculators have their place, and I agree with Knight that students do need to know how to use tools to help them do more things more efficiently, but knowing the times tables is a tool, too. Save the calculators till you’re at least in algebra.

The SBOE can even make math controversial

The State Board of Education is gearing up to revise math standards, and as is always the case someone is pushing back.

The Texas Association of Business is urging the state board of education to go back to the drawing board on the standards, which the 15-member state panel is expected to take up next week.

The proposed math standards are “far from in-line with Texas’ goal of raising educational standards; in fact, the currently proposed standards are actually worse and less rigorous than the Common Core Standards,” the group’s president and CEO Bill Hammond wrote in an April 9 letter to board members.

[…]

In an interview, Hammond said his group hopes the state board will “stop the process” for debating (and possibly approving) the new math standards, arguing that they require “massive revisions.”

“Obviously, the leadership in Texas decided we’re not going to go with the common-core standards, and we don’t have an issue with that as long as we have excellent standards, well-written, rigorous standards,” said Hammond, whose organization represents more than 3,000 business members across Texas, as well as more than 200 local chambers of commerce.

Hammond added that his organization’s main concern is “about creating a workforce that will meet the needs of our employers.”

The Texas board of education gave preliminary approval to the revised math standards in January, then put them out for public comment. A press release from the Texas Education Agency said that the revised standards drew from the state’s existing standards “as well as math standards from Massachusetts, Minnesota, and international standards from places such as Singapore, which are all believed to have some of the world’s best math curriculum standards.”

The Texas business group asked Ze’ev Wurman, a vocal critic of the common math standards, to analyze the proposed Texas standards. Wurman, a Silicon Valley executive and former education official under President George W. Bush, recently served on a California commission that evaluated the suitability of the common standards for that state. (I recently blogged about a forum in which Wurman debated the common standards with a math professor.)

Wurman’s analysis concludes that the Texas draft “picks many nice ideas from the common core, yet it also introduces errors and clumsiness. … The draft creates a wordy, sometimes incoherent, and often garbled document, particularly in K-8, that shows the disparate fingerprints of the various groups and committees that influenced it through its development.”

Ultimately, Wurman contends that the math document is inferior, in terms of “coherence and rigor,” to both the common-core standards as well as “many of the better state standards. I am hard-pressed, indeed, to say that it represents an improvement over the existing [Texas standards].”

Hammond, of course, doesn’t want to actually pay for a public education system that will meet the needs of a growing workforce, but that’s a topic of another blog post. He is correct to note, as he does at the end of the story, that this is only controversial in a very limited sense because no one gets all that riled up about math standards. That EdWeek post from last week (the SBOE review begins today) was the only story I saw on this until the Trib wrote about it yesterday. The Texas Freedom Network, which is usually all over everything the SBOE does, has no mention of this, which should tell you something. Anyway, I haven’t spent a whole lot of time on this, but you can read the review and grade by grade analysis, which seem reasonable enough. I don’t have any strong feelings about this, but I do think all curriculum revisions the SBOE undertakes deserve to be scrutinized and publicized. This one may not be particularly political, but it’s still worthy of our attention. EdWeek link via Political Animal.

More algebra, please

I applaud HISD for doing this.

A handful of campuses in the Houston Independent School District are experimenting with placing their best math students in algebra in seventh grade – two years before most take the class.

The earlier they pass algebra, the thinking goes, the more time they have to take advanced math courses in high school that could lead to college credit.

Over the last decade, policy-makers across the nation have pushed for algebra to become the standard for eighth grade, while some educators argue against the rush.

HISD’s move to teach algebra to an even younger set gives the students – many from poor, minority families – a head start in the course, considered a stepping stone to college and 21st century careers.

Time will tell whether the effort produces a crop of math brainiacs who take college-level calculus and statistics in high school or burnouts who ditch the subject after earning the four credits needed to graduate.

“Certainly we don’t want to push kids into something they’re not ready for,” said Monica Kendall, HISD’s manager of secondary math. “But I would like to challenge what people think kids are ready for. A lot of people think economically disadvantaged students can’t do upper-level math. My whole perspective has been, ‘Let’s find out what they can do.’ ”

Little research exists on seventh-graders taking algebra, although HISD isn’t breaking entirely new ground.

Locally, the Spring Branch and Alvin school districts are among those that have been enrolling their top seventh-graders in algebra for years.

I have no opinion on whether algebra should be the standard in eighth grade, but I can tell you from personal experience that seventh graders have been taking algebra successfully for many years. I know because I took it in the seventh grade, which was in 1978-79. My intermediate school (that’s what they call “middle school” in New York) offered algebra for its gifted & talented seventh and eighth graders; it was done as a two-year course, and enabled you to go straight to geometry in high school. By doing so, you were on track to be able to complete a year of calculus in high school, which needless to say gave you an advantage going into college.

Obviously, this isn’t for everybody; the story says that about two percent of HISD’s seventh graders are enrolled, which almost surely means there’s room for growth. It should be fairly easy to identify the kids who are bored with grade-level math and are ready for a greater challenge. It should be the goal to make algebra available in every middle school for all seventh graders who would like to take it.

The future of textbooks

I figure the traditional textbook is eventually going to go away, but how and when it will be replaced is not yet clear.

The average college student spent $702 on books in 2006-07, according to the National Association of College Stores — a figure that has continued to grow and is speeding the transition to electronic textbooks and other digital class materials.

“At some point, we’re going to price ourselves out of the marketplace,” said Anthony Martin, director of the campus bookstore at Houston Baptist University. “Kids are going to figure out a way of getting through school without books at all.”

Relief has been sporadic, at best. Plans to exempt textbooks from the state sales tax fizzled in the Legislature this spring. But an increasing number of faculty members are paying attention to the price of the books they assign, and a few are using electronic textbooks — about half the price of a print book — or materials that can be downloaded free.

Rice University is one of the leading players in the latter movement, which has the potential to reshape the textbook industry.

“This is the generation that grew up with the Internet and TV,” said R.H. Richardson, a biology professor at the University of Texas at Austin, who will use an electronic textbook for the first time this fall. “I think the e-book will evolve far beyond its present state. You can stick in a video if you want to. I’m sure there will be video games built into a textbook some day.”

Thinking back to my experience in college, back when dinosaurs roamed the earth, I’d say that you could replace the bulk of the dead-tree books for the problem solving classes – calculus, linear algebra, differential equations – with computer-based training and texts pretty easily. Classes that are about doing proofs, maybe not. But taking derivatives, solving integrals, that sort of thing, I don’t see why it couldn’t be done on the computer. If a company like Reasoning Mind, which is delivering math curricula at the grade school level here in Houston among other places, can do it for grade schoolers, surely someone can do it for college kids.

Beyond that, it seems to me that a lot of the books I bought in college were plain old ordinary books, not textbooks. I see no reason why you couldn’t just get them on your Kindle or whatever digital-book device you have. At least that would create competition for the campus bookstore, and would make it easier to find and buy used copies, which would push prices down. Maybe you could rent them this way, instead of buying them – how many books from college do you still own after graduation? I have some math books, including a few from graduate school, and a couple of other random books, but it’s maybe ten percent of the total I bought over four years. I suspect some texts will still be delivered as plain old bound paper for years to come, but I see no reason why most of what is being bought now can’t be transformed into electronic format in the near future, if not already.

But I’m not

I just want it to be known that I solved the puzzle in today’s Foxtrot in about five minutes. I had to dust off some pretty long-dormant brain cells to do the integral, but I got it. The first comment at the link above has the answer, if you’re still scratching your head.