Frequently Asked Questions

We get a lot of questions from faculty interested in adopting the Discovering the Art of Mathematics (DAoM) approach into their Mathematics for Liberal Arts (MLA) and other general education classes. If your question is not answered below, please contact us. We're happy to hear from faculty and will do our best to answer your questions.

Yes, the eleven books and all of the associated materials are free for educational use. You can copy them for your students or simply have them downolad the .pdf files.

How do you think your MLA students feel? They have the opposite worry. The connections are build into the materials. You can learn more about the connections to their field in parallel as they learn the mathematics. Please read also our math for liberals arts audience blog .

All? MLA students are typically not going into another mathematics course, so there is not really a set curriculum that needs to be covered. In a given course it is important to have goals and to have students work hard, but is there any urgency for a a specific curricular point of arrival for this audience?

Certainly. There are significant limitations, just as there are with any other pedagogical approach. MLA are typically single semester, terminal courses. As a teacher you have one shot, one semester/quarter to do something significant. Other courses are part of a continuum where specific curricula, skills and abilities are expected to be reached in specific courses. This needs may be at odds with the structured, guided discovery approach used here. For MLA courses, this approach is remarkably effective for its particular audience.

It is a pragmatic, practical version of constructivism tailored to the specific needs, interests, and abilities of MLA students.

These are quite important areas. They should be regular parts of the K-16 curriculum. However, if, as part of a general education college-level course, you are doing straight remediation, if you are reviewing for the umpteenth time, doing financial mathematics that these students have been exposed to many times previously, we urge you to ask yourself a few questions: Do you really think the students will learn this time? Is there that much value that they might get out of the experience, or could something more beneficial be done?

Two answers in the words of others are below. We also refer those interested to read the short, wonderful, provocative book A Mathematician's Lament by Paul Lockhart.

College students study the best paintings, the most glorious music, the most influential philosophy, and the greatest literature of all time. Mathematics departments can compete on that elevated playing field by offering and making accessible to all students intriguing and powerful mathematical ideas… Indeed, these courses [general education and introductory mathematics courses] should be developed and offered with the philosophy that the mathematical component of every student’s education will contain some of the most profound and useful ideas that the student learns in college. (Committee on the Uundergraduate Program in Mathematics, 2004, p. 28)

Almost everyone knows that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of philosophical thought, has destroyed and rebuilt religious doctrine, has supplied substance to economics and political theories, has fashioned major painting, musical, architectural, and literary styles, has fathered our logic, and has furnished the best answers we have to fundamental questions about the nature of man and his universe... Finally, as an incomparably fine human achievement mathematics offers satisfactions and aesthetic values at least equal to those offered by any other branch of our culture. Despite these by no means modest contributions to our life and thought, educated people almost universally reject mathematics as an intellectual interest. (Morris Kline, from Mathematics in Western Culture, 1953)

In explorations with our students over that past decade we have found inspiration in these eleven areas. So we have sought to share materials with others so they can explore with their students.

A typical MLA text has about 10 chapters, and rarely are more than a few covered. So DAoM is not so different. Practically, this gives you the option to change things up from semester to semester. You have choices.

Yes, because it is not A curriculum. It is a wealth of vehicles to help bring inquiry-based learning and fundamental mathematical connections to the libearl arts and humanities into classrooms. We call the collection of books a library because we hope that they are used by others AND because we hope they will enable others to put together additional materials that involve MLA in the mathematical experience in positive ways.

Jump right in. Seriously. Each of the four DAoM authors just dove in one semester, committing themselves to using this approach.
If this is too scary, try a single chapter or section of a chapter. You can use this as a replacement unit for a topic that you typically teach.
You can find some helpful ideas about choosing a topic and the first day of classes on our getting started page .

They can look all sorts of ways. We have many videos online that show you some IBL classrooms in action.
Check out our IBL blog which contains a video clip of one of our "typical classes".
Our colleague John Judge says "My job as teacher is to make myself irrelevant." If you can walk out of your classroom and students continue to work effectively, you are doing something right - your students are actively inquiring.
The mathematician John Kemeny said, " is the greatest achievement of a teacher to enable his students to surpass him. "
And the great playright George Bernard Shaw said something similar: I am not a teacher: only a fellow-traveller of whom you asked the way. I pointed ahead -- ahead of myself as well as you."

The mathematician Hugo Rossi once gave a talk entitled “The Goal of Teaching is Learning, Not Teaching.” Look around, if your students are actively problem solving, thinking, arguing, reading, drawing, computing, building, making conjectures, compiling data, trying to create proofs and communicating, then they are working as mathematicians do. You help by setting a tone, being supportive, asking questions, reassuring, clarifying,… They need you for this. But if you take over more, they will retreat into being less active. We find that most days our students are entirely unaware that it is time for class to end. We have to tell them it is time to pack up. This is symbolic of a good level of teacher intervention.
There are many ways in which the teacher/facilitator is active during an inquiry-based class, but the tools are entirely different from the tools you use during a great lecture. Check out the conversation tools and our assessment page to get an idea what your new "control knobs" might looks like.

Absolutely. While the volumes in our library have been developed to serve as coherent, connected treks through a particular area of mathematics, they are largely made up of chapters/modules that can be considered outside of the context of the book. In fact, several of the DAoM authors do exactly that when we teach. For particular information on the modularity (e.g. prerequisites, logical dependencies, etc.) see the mixing it up blog and the individual teacher manuals for each volume.

This isn’t a surprise, is it? They have been bombarded with information that they are expected to regurgitate on high-stakes tests their entire mathematical career. They are used to being told what to do. They are used to mathematics being little more than exercises that they learn to mimic and forget. Challenging and changing this is a major goal of the use of inquiry-based learning. Have patience.
There are activities that help set a positive tone and create a supportive learning environment, some are included in our audience blog and out first class blog .

It takes a while for students to get used to their new roles, being the center of the learning experience. However, after a bit they find the experience liberating. For once they are in control of making sense of mathematics.
We will continue to add to the teacher resources ideas for motivating students.

Certainly not. The investigations are not meant to be worksheets. They should not seem like an endless march of the students will get "IBL fatigue." The investigations are supposed to guide discoveries. In our classes we mix things up often - in terms of both mathematical content and pedagogy. Mathematical asides can be short modules from a different book, some breaking news from the world of mathematics, "cool things," a video, etc. In terms of pedagogy, there are some mini-lectures, larger project based tasks , poster sessions, etc.

Absolutely! That would be great. We hope our materials serve as a vehicle for helping faculty nurture the mathematical experiences of their students. This is why we call it is library.

All we ask is that you acknowledge in your materials that they have borrowed from ours.

No. You must simply follow the copyright/fair use guidelines. It would be very helpful for us to know that you are using our materials. You can officially register by creating a DAoM account or you can simply contact our team at .

Absolutely! We use some of our chapters or sections from elementary school through math major classes, depending on where the topics are motivating or appropriate. Certainly our pedagogy ideas apply as well. It is amazing to see that you can basically use the same teaching tools in a 3rd grade class, a calculus course and a workshop for professors. :) More blogs about this will appear soon...