Prof. Burger designs virtual textbook

Williams College Associate Professor of Mathematics Edward Burger recently “authored” the first ever web-based virtual textbook. He is currently using his virtual text here at Williams in two sections of Math 101.

An internet program of interactive lectures, explanations, examples and personal quizzes, Burger’s virtual textbooks for pre-calculus and calculus offer everything normal textbooks include.

The course material is presented as a sequence of vignettes. Each presentation consists of a video lecture (10-15 minutes in length) and numerous visual and interactive components to emphasize the ideas at hand. The style of presentation is lively and attempts to keep the user focused and also entertained.

For example, in one lecture, Burger gives a Casey Kasem-esque countdown of the “Top 10 Classic Mistakes” complete with original songs (sung by professional musicians) illustrating the errors – something difficult to find in the typical pre-calculus textbook.

“I believe we should constantly be rethinking how we teach,” Burger explained. “We should not expect a paradigm of teaching that originated hundreds of years ago to resonate with today’s students. We need to be sensitive to who our audience is and be responsive to what leads them to real understanding.”

Burger’s texts are published by, a company that designs virtual textbooks for high school and college students to use as a text, supplement or tutorial resource. The company launched the two textbooks during the first week of September in order to coincide with their use in Burger’s classes.

Currently, offers calculus, college algebra and micro-economics web books, in addition to high school AP Calculus and Algebra II (also by Burger). A biology text will be offered soon. Students in Math 101 pay around $90 for use of the program.

Burger is taking this new environment for learning a step further in his Math 101 classes by inverting the roles of homework and class work: his students watch his online lectures from their virtual textbooks as part of their homework and then are active in class.

Students in his class present material, solve problems at the blackboard, ask questions, answer questions, make mistakes and learn by doing. Traditionally, Burger explained, students in mathematics classes passively listen and write.

Now he hopes to get his students to teach and learn from each other. “We must actively digest and internalize anything we truly wish to understand. That is the only way to make ideas our own and to discover new ones,” Burger said.

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