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Math E matics by Cathy Cashio
Spring 2003      


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Using nothing more than a laptop computer and a friend's company to host a web site, self-proclaimed math nerd Ted Mahavier ('95 Ph.D.) and his colleague Valerio De Angelis began responding to e-mail math questions from home in 1996.

Today, Mahavier, an associate professor of mathematics at Lamar University in Beaumont, and De Angelis, an assistant professor of mathematics at Xavier University of Louisiana, work with an international team of volunteers to answer more than 1,500 math questions each month through their web site,

However, the mathematicians, who donate their services free of charge, don't supply the final answers. Instead, they provide hints and references, teaching people to overcome their fears and solve their own math problems.

"It's no mystery that too many people have math phobia or math anxiety," says De Angelis. "It would be great if we could change that even in a small number of people."

Mahavier is well acquainted with the way people react to mathematics.

"Math is a serious subject that a lot of people — especially students — think is a four-letter word," he says. "We want to help people with math and show students it can be a very rewarding subject that can lead to a fantastic career."


Learning by doing

Mahavier's love of math was fostered at UNT. He was influenced here by an inquiry-based method of teaching, known as the Moore method, in which students are encouraged to discover much of the mathematical content of a course by following a carefully crafted sequence of problems.

  Ted Mahavier  
  Ted Mahavier  

Mahavier says by preparing students in this manner, the instructor assures that they possess a deeper understanding of the material. Students can "do" mathematics on their own as opposed to merely absorbing mathematical concepts that they were led through.

"Many of the faculty at UNT during my graduate-school years were, and still are, proponents of this method," Mahavier says.

He says the impact of UNT professors such as John Neuberger, John Ed Allen, Paul Lewis and Dan Mauldin and their philosophy was far-reaching. As he entered the teaching profession, Mahavier shared his enthusiasm for math and his commitment to the philosophy espoused by his teachers with his own students — in the classroom and on the web.

History of the nerds

In 1996 Mahavier and De Angelis worked together at Nicholls State University. At that time, they began managing a mathematics web site from their homes.

Additional mathematicians volunteered to help in 1998.

"From the moment we offered help on the web, we had more work than we could possibly do and we enlisted a few friends to help answer the questions," Mahavier says.

During the early development of the site, Mahavier and De Angelis realized that answering questions without concern for what students might do with the answers involved a certain risk.

"Imagine a student submitting an interesting problem they were working on related to their doctorate," says Mahavier. "While helping them, we found nice results and published this elsewhere. Would the student have a case against us?"

Because of legal concerns like this, the mathematicians felt the need to form a legal entity to protect their web site, so they created a limited liability corporation.

"Because we are nerds, and not business people, we took the path of least expense," says Mahavier.

With legal considerations settled, the group began to focus on funding and redesigning the site and recruiting more volunteers in 1999.

Mahavier received partial support from the Center for the Advancement of Teaching at Xavier University of Louisiana. The site is currently supported by funding from Lamar University. It now includes an archive of approximately 30,000 questions; a section of helpful exchanges between math experts and clients; a section devoted to discovery-based methods of solving math problems; and links to a host of other mathematical sites.

No spoon feeding

Nothing exemplifies the "math nerd" philosophy more than a quote by E.M. Forster found on the web site: "Spoon feeding, in the long run, teaches us nothing but the shape of the spoon."

"Our discovery-based approach enhances math education by guiding students through concepts so they can learn to find answers on their own," Mahavier says. "If students are really willing to work and use the material, they will be successful at this technique."

De Angelis agrees. "There's no learning without a degree of initiative on the part of the student," he says.

He should know. De Angelis and the other team members are established mathematicians or tenured professors at well-known universities. He says they offer their expertise as a way to share their enthusiasm about math.

Helpful hints clients choose a category, ranging from kindergarten level through graduate-level courses, then complete a form and submit a question.

A team member receives the question and can either answer it within 48 hours or move it to the general queue for others to answer.

The experts respond to questions differently. Allen Stenger, a longtime volunteer and retired computer programmer, says he responds to nearly everything he receives as well as questions from the general queue.

"After a lengthy exchange with a client, it's gratifying to see an understanding growing through their work with our hints," he says.

James Ochoa ('96 Ph.D.), an assistant professor of mathematics at Hardin Simmons University, began volunteering in May 2000.

"I try to figure out key parts to understanding the problem," he says. "Then I send the client a hint. A lot of people are appreciative for the help and say thanks for the hint, but a few grumble because I don't give them the answer."

Inquiring minds who want to learn how the process works can follow the "Best" link on the site, which includes selected problems and the hints given to solve them.

"These are the nicest and most interesting questions we've received over the years," De Angelis says.

For example, readers can discover how to find a false coin in a certain number of weighings or how to determine the shortest road required to connect a number of towns. And titles such as "The Case of the Missing Mangos" and "The Notorious Jumping Function of Continuum County" prove that math — or at least mathematicians — can be fun.

Satisfied clients

Before signing off the web site, many people comment about their visit in the "Guestbook" section.

"We currently have more than 55 pages of positive user feedback in our guestbook," says Mahavier. "People tell us they love the site. Others say it's helped them learn about logarithms and progressions."

One of Mahavier's favorite responses came from a client in India: "None of my teachers or friends is willing to help me (with math problems) unless and until they get some material gains out of that help, but you have been helping me throughout. Thanks a lot, sir."

Mahavier says he likes it when clients say, "Thanks. Now I understand."

De Angelis is gratified when clients overcome their fear of math.

Since the success of, Mahavier has set his sights on developing other web sites such as or

"You name it," he says, "there's a nerd for it."

>>> Excerpt from 'Rock Star Shuffle' problem

A concert starts in 17 minutes and four guys must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses (either one or two people) must have the flashlight with them. The flashlight must be walked back and forth. It cannot be thrown, etc. Each person walks at a different speed. A pair must walk together at the rate of the slower man's pace. Bono takes 1 minute to cross; Edge, 2 minutes; Adam, 5 minutes; and Larry, 10 minutes. For example, if Bono and Larry walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission. Note: There are two known answers to this problem.

  Valerio De Angelis  
  Valerio De Angelis  

Hint 1

This kind of problem is worked by trial and error, so the intellectual challenge is to think of ways to cut down the number of trials. Try this: Without worrying about who goes when, think about the number of trips that might be needed and what the time of each trip might be. For example, any trip including Larry is a 10-minute trip, so there is at least one 10-minute trip.

— Valerio De Angelis and Allen Stenger

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