A Textbook Education


Jonathan Ernst/World Bank
Digital textbooks in the math class have transformative potential, says the author. For instance, it “should soon be possible for the instructor of a course to get a detailed, cumulative report on the work of the entire class,” then cater the next lesson to emerging weaknesses.

The landscape of postsecondary textbook publishing is undergoing a significant makeover with the introduction of high-quality digital textbooks. As with the introduction of most technology, there is resistance, not the least arising from nostalgia for a product that has been around, in its essential form, for centuries. Nonetheless, the advantages of digital textbooks in cost, accessibility, and, especially, pedagogy are overwhelming. Here, we only address mathematics textbooks, but similar arguments can be made for other disciplines as well.

Digital textbooks, at least in mathematics, are as old as the Internet. In the early years, these were mostly noncommercial products: instructors, unhappy with traditional textbooks for reasons of both cost and pedagogy, wrote up their course notes as books in HTML or perhaps some computational algebra engine, such as Mathematica, Maple, or an open-source version like SAGE. Initially intended for their own students, they often posted these for anyone interested in learning the subject. The production values were low (recall those early web pages) and adoptions few. Sometime in the 2000s, the large publishing companies began to offer PDF versions of their print textbooks as a means of bringing down the cost to students. These had limited features, such as search capabilities and built-in mark-up tools. Savings were usually in the order of 30 percent to 50 percent but, other than the convenience of having the book on a laptop, there was little pedagogical advantage to these versions.

More recently, there have been some start-ups, perhaps most notably Inkling.com, which partners with some of the traditional publishers to transform their best-selling textbooks into genuine digital products with video, interactive quizzes, and more. Because the production is so labor-intensive, these textbooks cost nearly as much as the print versions from which they are derived. The list is still relatively short, but does include selections from across the undergraduate, graduate, and professional school curriculum, including economics, chemistry, music, art, and others. These books are available for tablets and smartphones as well as laptops.

The benefits of digital textbooks are many. First, let’s address cost. Typically, new textbooks for a mathematics course cost well over $100 a piece, a significant fraction of which is the actual cost of materials and production. Prices are also driven up by the frequent introduction of new editions, which are only cosmetically different from earlier versions. By contrast, the cost to produce a copy of a digital textbook is virtually zero, which makes it possible to price them at a fraction of the cost of a physical textbook. That difference can be translated into both substantial savings for the student and greater compensation to the author.

Second, there is the unwieldy size of modern textbooks. The typical mathematics textbook is quite heavy and perhaps twice the size of the textbook for the same course given in the 1960s (when I took calculus). Printing textbooks requires cutting down lots of trees (the principal sink for atmospheric carbon) and, ultimately, they enter the waste stream. With digital textbooks, a student can carry around her personal library under her arm. Moreover, the environmental cost of a digital textbook is limited to the energy necessary to power the platform (laptop, tablet) on which it is mounted.

Third, and most important, are the pedagogical benefits of digital textbooks. As large as textbooks have become there are obvious limits to what can be included. In particular, good education practice calls for spiraling through the content—periodically returning to essential and fundamental previous concepts that are necessary for understanding new definitions and results—but to do so in a print textbook would increase its size by a factor of two or more.

In my experience over more than 40 years of teaching mathematics at universities, a major contributor to student underachievement has been the failure to adequately understand fundamental concepts. In a typical college mathematics course, there are likely to be 100 or more definitions introduced that students need to master. Many students try to get by with “kind of understanding.” As a quarter or semester progresses, this incomplete comprehension becomes increasingly problematic, and eventually students reach a point where the instructor may as well be speaking a foreign language.

With a physical textbook, it is difficult to regularly review definitions: the student encountering a term that is unfamiliar will need to mark her space, go to the index to find where the concept is defined, and then go to that place. Then she may discover that the definition involves one or more further concepts of which she has, at most, a partial grasp. This is discouraging.

Furthermore, most lower-division mathematics courses require students to master a large number of algorithms (also referred to as methods, procedures, or recipes) for finding solutions to assigned exercises that will make up a substantial portion of the students’ evaluations in the course. Generally, limits of space mean that these will not be included in the textbook.

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EdTech Stanford University School of Medicine
The advantages of digital textbooks—their ease of use, the accessibility of information—open potential well beyond the math classroom. Pictured here is a surgery guide for medical residents.

On the other hand, an e-textbook can be customized to meet the needs of each individual instructor who can select the content included in the book he or she assigns. There can be regular and frequent spiraling, so that all important definitions and methods are reviewed as needed for the introduction of new concepts, theories, and algorithms. Each instance of a fundamental term can be linked to its definition in order to facilitate understanding. Each exercise in the book can be linked to a description of the algorithm needed to solve it. Citations to theorems can be linked to their original statement and proof. And historical references can be linked to exterior websites.

Because there are no limitations of size, the book can have numerous and dynamic examples for every algorithm. By dynamic, I mean that each time an example is accessed it has different parameters.

There can also be frequent opportunities for students to test their understanding of concepts and results as well as their mastery of the algorithms. These self-assessments can include concept quizzes and interactive, dynamic exercise quizzes with immediate feedback. (That is, the quizzes involve an algorithm which creates new problems each time the quizzes are accessed, and students can submit their solutions and be given appropriate feedback.)

In addition to routine exercises, the book can have a rich source of challenging exercises that require reasoning and demonstration of familiarity with concepts and theory.

All of the above are currently possible with existing technology. On a more speculative note, it should soon be possible for the instructor of a course to get a detailed, cumulative report on the work of the entire class, consisting of data on which definitions, algorithms, theorems, and examples the students accessed from the readings and how often they accessed them, as well as information on how the class did on the quiz questions. This can then inform the preparation of the instructor’s next lecture, beginning with a review of the material that, the evidence suggests, students found confusing.

As of yet, digital textbooks only occupy a small percentage of the marketplace and the reasons for this are varied. A good source of shortcomings can be found at the blog “Ten Reasons Students Aren’t Using eTextbooks” (edudemic.com/2012/06/10-reasons-students-arent-actually-using-etextbooks). Among the most significant are: promised savings have not been delivered, digital textbooks use up lots of computer or tablet memory, the books can’t be lent to other students or resold, and digital textbooks are not available for every course or are only available in certain formats or for certain platforms. The other reasons are mostly subjective and have to do with the student experience. For example, students may find it strange to mark up a digital textbook or feel reluctant to give up the physical textbook they are accustomed to.

Some of these criticisms are contradictory. For example, a student intent on reselling a text should not mark it up since this destroys most of the potential resale value. In any case, I have not observed student reluctance to mark up a digital text: in a course in Mathematical Problem Solving that I recently taught, I observed several students using the iPad app Notability to mark up a PDF version of the text.

On the other hand, whether digital textbooks deliver on the promise of significant savings will depend on whether the future marketplace is truly competitive or continues to be dominated by a small number of large publishers wedded to old technology and marketing models. I have been using e-textbooks in my classes for about six years, books that I have written myself and sold at about one-tenth the cost of a traditional book through Lulu.com (www.lulu.com). More recently, my e-textbooks have been published by the Worldwide Center for Mathematics (www.centerofmath.org) where the cost runs from $10–20. They have since been adopted and used in some community- and four-year-college classrooms, and the instructors have reported to me mostly positive experiences. As for taking up lots of computer memory, one of my textbooks would be nearly 1,000 pages if printed, but in digital form, it is only six megabytes. A 16 gigabyte iPad could hold 1,000 books and still have plenty of space for videos as well as thousands of songs in its music library. When bells and whistles are added (for example, explanatory video), more space will be used, but there are easy fixes. For example, the book can be stored in the cloud or on a university server and accessed as needed.

To be sure, there is something special about holding a physical book that cannot be replaced with a digital version. However, we should not over-romanticize the qualities of the print book and let this stand in the way of significant advantages, not the least of which is much better pedagogy.