A Calculating Web Site Could Ignite a New Campus 'Math War'

June 12, 2009

The long-running debate over whether students should be allowed to wield calculators during mathematics examinations may soon seem quaint.

The latest dilemma facing professors is whether to let students turn to a Web site called WolframAlpha, which not only solves complex math problems, but also can spell out the steps leading to those solutions. In other words, it can instantly do most of the homework and test questions found in many calculus textbooks.

The new tool will be a bane to teaching, some professors say—but others see a blessing.

WolframAlpha was created by Stephen Wolfram, an entrepreneur who invented Mathematica, one of the first computer math engines. His new site debuted last month to much media fanfare and, like Google, provides answers to questions typed into a simple search box. It is free and already boasts millions of searches.

But unlike Google, WolframAlpha features a supercharged math engine based on the Mathematica software used by many researchers. It makes a graphing calculator look like a slide rule.

Such math engines—they’re called “computer algebra systems,” or CAS's—are not new. But they usually cost hundreds of dollars and involve a steep learning curve. The goal of WolframAlpha is to bring high-level mathematics to the masses, by letting users type in problems in plain English and delivering instant results.

As a result, some professors say the service poses tough questions for their classroom policies.

A Pandora's Box in Math Education

“I think this is going to reignite a math war,” said Maria H. Andersen, a mathematics instructor at Muskegon Community College, referring to past debates over the role of graphing calculators in math education. “We are still in the process of adopting graphing calculators,” she said. “It’s kind of like the Pandora’s box that’s open now.”

Ms. Andersen predicts that students will rush to WolframAlpha because it is free and easy to use, but that some professors will ban it.

In a posting on her blog, Teaching College Math, she wrote:

“Given that there are still pockets of instructors and departments in the U.S. where graphing calculators are still not allowed, some instructors will likely react with resistance (i.e. we still don’t change anything) or possibly even with the charge that using WA is cheating.”

Ms. Andersen will not be one of them, however. In fact, she thinks WolframAlpha will be a powerful teaching tool. Ms. Andersen had avoided computer algebra systems in her courses because she did not want to require students to purchase the software or travel to a campus computer laboratory to do their homework. But she is excited to incorporate WolframAlpha into her curriculum for the fall—though she admits she is not exactly sure how she will do that. She says the issue will be especially tricky in the online calculus course she teaches.

“I still think that anyone who is not a little scared by the changes that WolframAlpha brings hasn’t thought about it enough yet,” she wrote on her blog.

Adapting Tests and Assignments

Derek Bruff, a senior lecturer in mathematics at Vanderbilt University and assistant director of its Center for Teaching, shares Ms. Andersen’s mix of excitement and caution. He recently started an online discussion forum for professors to discuss the implications of WolframAlpha for their instruction, arguing that the service “has the potential to make a bigger impact on mathematics instruction than graphing calculators or commercial CAS’s did.”

His concern is that professors may need to adapt their assignments or test questions.

“Next fall and maybe in the spring, we’ll have students coming into our classes saying, ‘Why can’t we use WolframAlpha?’” he said in an interview. “We’re trying to get as much conversation going this summer as we can so that folks aren’t blindsided by this issue in the fall.”

Both professors argue that the service will affect more than just mathematics classrooms, since it can be used in economics, physics, chemistry, statistics, and other disciplines.

Using Tools to Get Ahead

Mr. Wolfram said in an interview that he was proud that his new service could easily do calculus homework. “This is the nature of progress,” he said. “One of the things that advances is that technology lets you do more and more stuff automatically.”

He said that Mathematica raised similar debates when it was released, but he argues that computer algebra systems improve education because they allow students to explore complex problems on their own, and to intuitively determine how functions work rather than simply learn rote processes. “This shortcut is going to be there for these students when they grow up,” he said. “It’s better to let them stand on that platform and go further.”

And he noted that plenty of professors and teachers are likely to embrace the service. The week WolframAlpha opened, one of its first heavy users was a class of middle-school students in Canada. The students submitted so many requests that the service blocked the school’s Internet address, mistakenly thinking that the students were spammers trying to disrupt the site, said Mr. Wolfram. The block has been removed.

Mr. Wolfram, a former child prodigy who earned his Ph.D. from the California Institute of Technology at age 20, said that using computers helped him get ahead of his colleagues when he was a young scholar.

“I’m a person who believes that at any given time, one should use the best tools available,” he said.

When he published some papers on particle physics decades ago, before computer algebra systems were common, he said, a colleague from another institution asked him how he had derived some of the complex equations he used. “The answer was I used a computer,” he said. “I suppose I have a personal experience that if you use more tools, you can get more done.”

“A lot of it boils down to, Can you use these tools to get intuition rather than just mechanical skills?” said Mr. Wolfram. “After kids see Mathematica, or now WolframAlpha, some fraction of them become curious and wonder, How does that actually do that?”

Calculating or Cheating?

Dan Petrak, associate professor of mathematics at Des Moines Area Community College, agrees with that philosophy and has already tried using WolframAlpha in a course he helped teach this summer.

But Mr. Petrak also demonstrated for The Chronicle how easy it would be for students to cheat on their homework with the service. He opened WolframAlpha and entered a homework problem from his calculus course. The problem involved limits and square roots, and the service solved it easily. By clicking the link titled “show steps,” Mr. Petrak illustrated how students could write down those steps and pretend they understood the process when they had simply copied it.

Still, he said, the service also opens the door to teaching more advanced concepts. It shows graphical representations of the equation and introduces concepts he would not usually get to in an introductory course. “It puts the complex solutions in the same pane” as the simple answer, he said. “It’s really cool because you can actually start talking about it with students, and I usually wouldn’t have mentioned it.”

Now he just has to decide whether to allow WolframAlpha on exams, and if so, how to stop students from just having the computer do all the work for them, he said.

For Some, Less Than a Revolution

Roger A. Freedman, a physics lecturer at the University of California at Santa Barbara, said he had experimented with the new service “a bit” and thought it would lead to changes in teaching in his discipline as well.

“It may have the same kind of impact as calculators did when they became prevalent in the 1970s and 1980s,” he said in an e-mail interview. “It will make it possible for students to do different things than they did before, and it may require instructors to ask questions differently than they might have done in the past.”

Not everyone thinks that WolframAlpha will cause a stir on campuses, either in a positive or a negative way. David Bressoud, president of the Mathematical Association of America and a professor at Macalester College, said most professors had already been forced to change their teaching as a result of previous computer algebra systems.

WolframAlpha "packages features so that they’re a little bit more accessible, but I don’t see it as revolutionary,” Mr. Bressoud said. “Most math instructors now realize that the end-all and be-all of math instruction is not to give students algorithmic facility, but it really is to understand the mathematical ideas and understand how to use them.”

As Mr. Freedman, the physics instructor, put it: “The greatest challenges that science and math students face are conceptual, not computational, and neither calculators nor WolframAlpha can do much about that.”