Web Native Textbook — Cousino Math

Preamble

For a while now, I had this idea of a “web native” textbook. It’s still just an idea, and far from being realized. But I think that it is time to share the idea with the public. I’m quite certain that the technology exists today to realize this idea. However, the work yet to be done so is significant, and will take at least the better part of a year to complete.

Clarifying the Meaning of Web Native

Perhaps an easy way to describe a web native textbook is to explain what it is not. A web native textbook is not a PDF posted on the internet. It’s much more than that. An online, PDF can have both internal links—links to other parts of the document—and external links—links to resources outside the document. Furthermore, a PDF textbook can easily have a table of contents, index, glossary, and other characteristics of dead tree textbooks. Also, search engines like Google can add such a PDF to their index, and thus bring it to the public.

What a web native textbook can do, that a PDF cannot, is have complex dynamic behavior and complex memory—a state to use the computer science nomenclature. My idea of what consitutes a web textbook elaborates on the features that memory and dynamic behavior can provide. Note having memory requires some sort of login to the textbook. Login could be done through a learning management system or passed off to a third party like Google or Facebook. Therefore, our textbook memory would not need to add another username and password to each students’ library of logins. The dynamic behavior of the textbook need not require any memory and does not require any login. But whenever a dynamic feature of demands the use of memory, such a feature will also demand that users log into the textbook.

Features of a Web Native Textbook

Examples Unbounded

Sometimes, students need more examples than the textbook provides. A web native textbook can have as many examples as the student wants. At the bottom of each randomly generated example, we can simply add a button labeled “Generate Another Example&rdquo which performs this very task. For those who worry that randomness will not be appropriate for every kind of example imagine the following example of factoring a quadratic polynomial. Most quadratics don’t factor nicely. So a truly random quadratic would serve as a poor example for factoring. However, we could randomly generate integer or rational roots for the example quadratic as well as generate its leading coefficient. From these parameters, we can calculate the coefficients of the quadratic in it’s general form, and present this form of the quadratic for factoring in such an example.

We can constrain the random examples to have prescribed characteristics, like being nicely factorable, by choosing the correct parameters to generate randomly. This allows us to provide students with an unbounded number of appropriate examples.

Interactive Visuals

We can embed dynamic graphs thanks to Desmos and Geogebra. But there are also Javascript libraries like JSXGraph and D3.js. The advantage of all of these interactive components is that the teacher no longer needs to switch from dead tree textbook to computer, or from the tab of the PDF textbook, to the tab of Desmos/Geogebra. More lessons can be taught from fewer resources.

Merit Badges for Personalized Learning

This is the first feature that necessitates memory, and therefore user login. It is also one of the most complicated features. If you’ve every been in Boy Scouts, Girl Scouts, or Venture Scouts, then this idea of merit badges will be familiar. This idea can also be fairly described as “gamifying” education, at least to a limited extent.

Imagine a course where each student could explore the aspects of the particular discipline which interest them, while having students master the core ideas and techniques. A web textbook could support such a class. Differential equations is a subject quite naturally suited to this feature, and so will be the subject of the motivating example. Let’s say that instead of trying to pass differential equations, students are trying to increase their rank in differential equations, from “Not knowing” to “Knowing differential equations”. In this course, there are some required tasks that every student who wants to rank up in differential equations must complete. Upon successfully completing a task, award the student with a merit badge. Further, there are optional tasks, of which each student must complete no fewer than some fixed number. Let’s say that completing an optional tasks earns the corresponding optional merit badge, and that completing a required task earns the associated required merit badge. While all students must earn each required merit badge, it is up to each student which optional merit badges they earn.

In our example here, we may suppose that all students must demonstrate proficiency in solving first order differential equations, second order linear differential equations, first order linear systems of differential equations, power series solutions, and solving differential equations using the Laplacian. Whether or not this is a good and/or complete textbook for differential equations is besides the point, the point is that a web native textbook can be one where some of its topics are required of all students, and the other topics are not required of all. Suppose in this example that each student must earn at least four optional merit badges. Some of these optional merit badges could be topics like the following: existence and uniqueness proofs for particular kinds of differential equations, spring mass systems, algorithms for numerical approximating solutions, solving by the method variation of parameters, Van der Pol oscillators, parametric oscillators, predator-prey systems, etc.

This idea is far too hazy and too radical for me. A “choose your own adventure” style course is so foreign to the introductory college math courses that I teach. For instance, I am still a bit unclear as to what a student has to do to earn a merit badge. For the required merit badges, it might be doing well on an exam. For the optional merit badges, acquisition might be achieved by passing the exercise in the textbook on the topic or giving a presentation to the class. But let this be a foundation for further ideas about a true web based textbook. These ideas are worth pursing because such a textbook would then put the student in a more active role in their own learning.

Student Annotations and Modifications

Remembering each users’ interactions with the textbook, allows us to save modifications and annotations that each user makes to the textbook. These two topics, annotation and modification to the textbook, are different enough to require separate descriptions. When thinking of annotations to web native textbooks, think about margin notes and highlighting in dead tree textbooks. And within the web textbook, each student’s annotations can be stored and displayed only to the individual student. But instructors could create annotations which are displayed on all their students textbooks. Or instructors could highlight a particularly good annotation by a student by publishing them to everyone’s textbook.

With modifications, students could rewrite their own textbook. The ability to revert their changes back to the original would be necessary. But in principle, students could delete, add, and rewrite content to suit their own pedagogical needs. Again, an instructor could push modifications to all of their students’ textbooks. Otherwise, one student’s modifications will remain local to their copy of the textbook. Needless to say, modifications are much harder to implement than annotations. But one advantage is that students can write their own textbooks, which is another instance of more active learning for students.

Tracking Student Interaction

This feature may worry some because of its similarity to tracking done by companies like Facebook and Google and by governments like United States of America. But this is just an example of what such a web native textbook could do and not what such a textbook must do. And I will also ask the reader to remember that the morality of tracking depends, partly, upon the reason for tracking users. And tracking can be done after stripping away all personally identifiable information, thereby anonymizing the data.

As to what tracking can do for a textbook, it can determine which paragraphs get the most annotations, which examples get randomly regenerated the most, which interactive elements get used the most, etc. In other words, it helps you determine which parts of your textbook are working best and which parts need to be revised. Also, it will be important to note what tracking won’t be able to do. Tracking won’t be able to tell at which parts of the textbook your students are looking. It will not be able to accurately tell you how much time your students are spending reading/interacting with the textbook. This is because a student could be looking at another tab in their browser or another app on their computer. For that matter, a student could leave the textbook open on their computer while watching television, going out to do errands, or any other activity off their device.

In short, tracking the textbook can give the instructor a decent idea of how the textbook is being used by students in general and by each individual student.

Offline Too

Thanks to modern web development, an online textbook doesn’t have to be dependent on a constant internet connection. The whole textbook can be a web app, a website that can be downloaded as an app to desktops, laptops, tablets, phones, and any other capable device. This textbook app can do just about everything offline that it can do online. It could do everything that I've described in this post offline. All an internet connection provides the textbook app is the ability to interact with others in real time and save a copy of its memory to a server.

Conclusions

The features that I have listed here are just some of what a truly web enabled textbook could do. If you have any additions, criticisms, and/or comments, please leave them in the comments below. My hope is that someday soon, web textbooks will go far beyond their PDF ancestors.