You too can own a massive house if you sell enough calculus books.

There’s a new, five-story, 18000 square foot, $24 million house in Toronto that is built of curves and glass and boasts its own professional-quality concert hall. The owner? Not a billionaire financier, head of state, movie or sports star, or anything of the sort — it’s James Stewart, author of the Stewart Calculus franchise of books.

From the Wall Street Journal article:

As visitors descend into the house, the fins disappear and the views widen. On the first floor, push a button and a 24-foot wall of glass windows vanishes into the floor, opening the pool area to the outside. Curves are everywhere, down to the custom door handles and light fixtures. The architects are even working with Steinway to create a coordinating piano. [...]

An hour before five friends arrived for dinner, Mr. Stewart ambled around his kitchen, marinating some pork tenderloin chunks and tossing chopped leeks, red peppers and corn into a deep soup pot to simmer. He laid some ready-made sushi on a large red platter and then leaned back against a green-hued quartz countertop to relax.

Mr. Stewart say he isn’t overwhelmed by his home. “I just enjoy wandering around it,” he says. “Even now I’m still discovering details, and I’ve lived here for more than a year.”

Go to the article and look at the slideshow for more. It’s indeed a beautiful home (in a way it reminds me of St. Procopius Abbey near Chicago, which I visited last year).  I’m certainly not going to be down on Prof. Stewart for building his dream home, for which he apparently saved up money for 60 years. But it certainly destroys the old idea that professors never make money off of textbooks they write. And it also makes you wonder, if you recently spent $150 on a Stewart Calculus book, what part of that house you have a legitimate claim to. If you’re a Stewart Calculus book owner, I’d say you have a right to stop in at his place for sushi unannounced at any time.

A proposition for Prof. Stewart: Now that you’ve built your dream home and established your legacy, take all of your calculus books and make them available as free PDF downloads under a Creative Commons license, so students who are spending down to their last dime on textbooks can have a shot at saving for their dream houses, too.

So at the end of the comment thread on my iPod lust decision process about whether or not to buy a new iPod touch, I concluded somewhat glumly that I had probably better wait until the gap between what I’d saved up and what the 32 GB model costs is made up somehow. I am happy to announce the gap has been closed, and then some, thanks to the dude that comes around every now and then to buy back textbooks. He just happened to drop in this afternoon, and I freakin’ unloaded, to the tune of three dozen books sold back. (My shelves are happy too.)

In case you’re unfamiliar with this process, there are people who make a living off of coming by professors’ offices and purchasing unused books for cash (at a rate far less than their retail value)  and then selling them to the open market. Ever wonder where those used books in the college bookstore come from? Some of them come from students, but a lot of them come from the buy-back people.

But there’s an ethical dilemma. A lot of the books I am selling back are review copies which were sent to me, gratis, by the publisher. This practice of sending out free books all the time is a major contributor to skyrocketing textbook prices. I’m having some guilt pangs about taking the money I get from selling books, which I received for free but for which students have to pay exorbitant amounts, to buy an iPod. On the one hand, I feel like I am profiting from students’ misfortune. On the other hand, by selling books back to the book-buying dude, who will then sell them at a cut rate to campus bookstores, I am providing a robust supply of lower-cost pre-owned books to students who would otherwise have to pay a lot more for the new versions. And let’s face it, I really want that iPod.

Am I overthinking this?

The Fort Wayne Journal-Gazette has this article today by Karen Francisco which is an excellent, if troubling, survey of the problem of rising textbook costs and the things people are doing to offset those costs. I was interviewed by Ms. Francisco last week for this article, and I am happy to say that unlike in my previous newspaper interview experience, she got my comments exactly right (and asked if my name and position could appear in the interview). Here’s what I had to say, although you should read the whole thing:

Robert Talbert, an associate professor of mathematics and computing science at Indiana’s Franklin College, is one of several hundred U.S. college faculty members who have signed on to PIRG’s online pledge to help control textbook costs. He’s passionate about the issue.

“Many of my students are either first-generation college students, students from middle- to lower-income families, or both. They are struggling to afford college as it is – often having to work off campus, which then affects their class performance – and it really pains me to see textbook companies charge more and more for a less and less useful product,” he said in an e-mail.

Talbert said he’s bothered not just by the cost, but by the quality of the books, which he said are often “poorly written, chaotically organized and full of so many irrelevant graphical elements and sidebars” that the information students need is difficult to find. If he can avoid it, Talbert doesn’t require a textbook or directs his students to an inexpensive one.

“In my abstract algebra course last fall, I used no textbook but rather homemade course notes and a handful of helpful Web sites,” he wrote.

Of course this is all old news to Casting Out Nines readers!

Later, after discussing Rice University’s adoption of an open source textbook for their introductory statistics class, she went on to quote me about the potential for open source textbooks:

“Imagine having a calculus textbook, the contributors to which are some of the best calculus professors in practice today, and which includes not only text material but also links to Web sites, embedded video, interactive applets for visual/kinesthetic learners, and user-contributed problem sets – for free,” he wrote.

“There’s a stigma against such things now, just as there is a continuing stigma against Wikipedia in academia (because academicians have a hard time accepting the legitimacy of something that is not peer-reviewed), but I think once students start learning and getting engaged with material through these things, that stigma will go away quickly,” he wrote.

Actually I think the stigma isn’t so much against Wikipedia itself as it is the notion of putting Wikipedia on the same level of authority as, say, a peer-reviewed monograph or a published encyclopedia. But a lot of academic types let their stigma start there and pretty soon the entire concept of an open-source informational source is stigmatized. That’s just throwing the baby out with the bathwater.

Again, go read the whole article, especially for the stories from students about what they are made to buy at a high price that can be had elsewhere for next to nothing, comparatively. It’s shocking.

I was looking at the web sites of a few colleges the other day which use a “Great Books” curriculum. This is an approach to a core curriculum in which students work their way through a listing of the great books from the past, across a variety of disciplines. Here’s an example from Thomas Aquinas College, a highly-regarded Catholic liberal arts college in Santa Paula, California. St. John’s College is probably the best-known example; I remember getting a mailer from them when I was a senior in high school, and I was fascinated by the idea of attending a Great Books university at the time.  There are also a few public universities which offer a great books curriculum as an option within the larger curricular structure of the university, for example as part of an honors program. 

Apparently Mortimer Adler is credited with coining the concept of the Great Books, and he gives three criteria for a book to be a Great Book (taken from the Wikipedia article): 

• the book has contemporary significance; that is, it has relevance to the problems and issues of our times;
• the book is inexhaustible; it can be read again and again with benefit;
• the book is relevant to a large number of the great ideas and great issues that have occupied the minds of thinking individuals for the last 25 centuries.

Via Vlorbik, here’s a letter to the editor (PDF) of the AMS Notices by Seymour Lipschutz extolling the virtues of Schaum’s Outlines as course texts and giving some suggestions for those choosing textbooks.

I agree with Lipschutz’ feelings about Schaum’s Outlines, up to a point. I’m a big fan of Schaum’s Outlines; they cost less than $20 and are loaded with precise, succint summaries of course material and worked-out problems. I
survived college physics and advanced calculus largely because of my now-battered Schaum’s Outlines for those subjects. I ordered the latest edition of the differential equations Outlines as I was considering using it for my DE course next semester, and I liked what I saw very much; and the publisher sent me a gratis copy of the beginning calculus Outlines and it was very good as well. I will be suggesting these outlines strongly to the students in those courses.

But to use them as the textbook for a course? I’m a little skeptical.  They are, after all, outlines. I think that students in the lower-level courses like calculus, and to some extent mid-level courses like DE’s or linear algebra, would benefit from having a more fully-featured textbook.

On the other hand, a carefully-written set of course notes made up by the professor, augmented by Schaum’s Outlines and hand-picked resources from the web, make up a pretty good blueprint for a cheap, portable, and effective package of course materials that I think students would get a lot more out of than a single monolithic textbook that they can’t carry around easily and never read.

I got a nice surprise in the mail this morning — a review copy of the fourth edition of Marvin Greenberg’s classic text Euclidean and Non-Euclidean Geometries. It seems like this book has been in the third edition since time immemorial. I used the third edition in my first year of teaching after graduate school, 10 years ago, and loved the depth and clarity of the writing. That much seems not to have changed. There are some significant rearrangements and updates to the material, and overall the book just looks a lot nicer (And the color scheme matches my blog, to boot!) There don’t seem to be a lot of good intro-level geometry texts out there — and there are a lot of bad ones — so a new Greenberg is a nice early Christmas present. It’s the kind of book that makes you want to sit down and work through it just so you can learn geometry from back to front.

Freeman textbooks are on a roll these days, what with this new edition of Greenberg and with Rogawski’s excellent new calculus text. (Disclosure: I was a reviewer for Rogawski.)  I don’t advocate for textbook use often, but if you have to use one, use a good one!

I’m teaching differential equations next semester, and I’m changing the course in some fundamental ways since the last time I taught it — so much so that I needed a new book for the course. (I’ve ruled out the textbook-free option for this class for reasons I explained here.) After some searching, I ended up going with the Boyce/DiPrima text. But I gained a lot of respect, and found a lot of affection, for Tenenbaum and Pollard’s classic text on the subject from 1963.

First of all, the textbook is a giant brick of a book, loaded with great exposition, clear examples, and challenging problems. And being a Dover paperback, it’s only a measley $16.47 through Amazon. But the thing I love about it, which is something I love about all math and science books from this era, is its tone — clear, precise, tough-minded, and no-nonsense. And yet inviting and enjoyable at the same time. (Which precisely describes what I’d like the students in the course to be.)

A great example is the following quote that appears at the end of a solid review of functions and just before they start looking at differential equations proper. Note that there is no intervening review of calculus between these two sections. That’s because the authors expect students to actually know calculus upon entering the course. They say:

In the calculus course, you learned how to differentiate elementary functions and how to integrate the resulting derivatives. If you have forgotten how, it would be an excellent idea at this point to open your calculus book and review this material. [emph. added]

I actually cheered when I read that. Differential equations is an extension of calculus; calculus is a prerequisite; you had calculus once; so if you forgot how to do it, get off your duff and crack a freaking book. End of story.

It’s the exact opposite of most modern math textbooks that start by assuming that the reader is five years younger and 30 IQ points dumber than s/he really is, and scared witless of math and unable to read past a 5th-grade level on top of that, and which proceeds to hand-hold and touchy-feel its way through whatever subject it is supposedly about. But not so with this book, nor with any other post-Sputnik era math and science books I’ve seen. That softening up seems to have occurred sometime around 1980.

Ironically, this 1963 text is superbly written with great clarity, vivid illustrations to motivate the material, and plenty of useful examples. When books started softening up — supposedly in an attempt to help struggling students — the things that actually help those students such as clarity and completeness actually went away.

I ended up going with the more modern book because I needed more in the way of computer applications (not many of those were around in 1963). But I will be using this Tenenbaum and Pollard text quite a bit, for my own enjoyment if nothing else, and perhaps as a lesson in how to write mathematics clearly.

We’ve got just 4-5 weeks left in the semester and until the textbook-free Modern Algebra course will draw to a close. It’s been a very interesting semester doing the course this way, with no textbook and a primarily student-driven class structure. In many ways it’s been your basic Moore Method math course, but with some minor alterations and usage of technology that Prof. Moore probably never envisioned.

As I mentioned in this lengthy post on the design of the course, students are doing a lot of the work in our class meetings. We have course notes, and students work to complete “course note tasks” outside of class and then present them in class for dissection and discussion. The tasks are either answering questions posed in the notes (2 points), working out exercises which can be either short proofs or illustrative computations (4 points), or proving theorems (8 points). We have a system for choosing who presents what at the board — I won’t get into the details here, but I can do so if somebody asks for it in the comments.

So the class meetings consist almost entirely of students presenting work at the board, where their responsibility is to make their work clear, correct, complete, and coherent — and ruggedized against the questions that I inevitably throw at them.

I was thinking yesterday that this method of doing class has really done a lot of good for the students in the class, in several key ways.

• Students ultimately rely upon the soundness of their own work. The students can work with others or with print or electronic resources — although with no textbook, they have to learn how to find those resources and tell the good ones from the bad ones, which is a great skill by itself. But it boils down to presenting that work, on your own and with nobody there to bail you out, in front of your professor and peers. I think this is a good antidote to the occasional over-reliance on cooperative learning that we (in education as a whole, and in my department) have. Group work is all well and good, but to be a complete learner you have to be able to rely on your wits and your skills and not just prop yourself up on the strength of peers.
• Students prepare for class in advance, several days in advance, every night. To do reasonably well on course note tasks, students need to plan on successfully completing 15-20 course note tasks throughout the semester, which comes out to about 1-2 per week. Combine that with the fact there are 8 students in the class all trying to do this, and it’s easy to see that working ahead is really essential. You want to get so far out in front of the class that you have no competition for a particular range of problems. Very often in college, there is no sense that you have to get ready for class the next day — unless there’s an assignment due — and we profs reinforce this by running classes that do not penalize the lack of preparation. (It’s not enough to reward the presence of preparation.) The course design here, though, rewards the students who have read and practiced ahead and learned on their own.
• Students become skeptical and tough-minded about their own work. It’s quite common in traditional math courses for students completing an assignment to simply barf up something on a piece of paper, hand it in, and see how many points it gets. When you are presenting work before a class, that route leads only to embarrassment. When most of the class time is spent doing these presentations, students learn something I didn’t learn until graduate school — that if you are going to hand something in or present something with your name attached to it, you had better make very sure that it works. I’ve noticed the students anticipating not only the fact that I will be asking them penetrating questions about what they are presenting, but also what those questions are. At that point they are learning to think like mathematicians.
• Students pay (more) attention to detail, especially terminology and the sensibility of a proof. It’s easy to write a proof or a solution to a problem that has no coherence or sense to it at all — but that incoherence and senselessness vanishes the moment you do something as simple as reading the solution aloud. Which is what these folks are doing every day. Example: A colleague told me a story of a student who was asked whether or not two groups G and G’ were isomorphic. The student answered, “G is isomorphic, but G’ isn’t.”
• Students base their confidence on the math itself, not on an external authority. Students aren’t allowed to ask me “Is this right?” or “Am I on the right track?” To clarify, they can ask me those questions, but I will only greet them with more questions — mainly, “What justifies this step?” or “How do you know this?” It’s not about me or what I like or what makes me happy with regards to their work — it’s about whether each step of the proof follows logically from the one before it, and whether that logical connection is clearly validated. Students know pretty well now when they have got something right and when they don’t, and if they don’t have it right they have a better sense of what’s missing or incorrect and what they need to do to fix it.

A lot of these effects I’m describing are just embodiments of what it takes to be successful in math after calculus in the first place.

Editorial: This is article #8 in this weeklong series of reposts of “classic” articles here at CO9s. The article I’m posting below probably has the most references to it of any article I’ve written. It’s the culmination of a bunch of prior posts about the nature of college textbooks, and it kicked off a pretty major experiment of my own that is currently underway — the design and execution of an abstract algebra course that does not use a textbook. The story of the textbook-free algebra course is still unfolding, and there’s a lot of good coming out of my little experiment.

We hear a lot about “innovation” in education, almost as if it were an end in itself. But I like to think about and write about ways of doing college differently that actually make students’ college education better.

Escaping textbooks

Originally posted: March 28, 2007

Permalink

I’ve blogged before about my ambivalence towards textbooks, at least in mathematics (here, here, here, here, and here). But a couple of recent events have really motivated me to think seriously about not using textbooks at all in my courses. And this fall I will be taking the plunge, requiring no textbooks except for my precalculus class (which has to have a book because the course has to be somewhat standard across five different sections).

First of all, every year I teach, I become more frustrated with the way that even the best textbooks tend to stunt the intellectual growth of my students in the area of general intellectual process skills. What I mean is that at the college level — or at the very least in the sophomore-and-above level in college — students need to be learning not only content knowledge, but also process skills such as how to acquire, judge, synthesize, and apply content information from a variety of sources. In fact there are many instances where the process is a lot more important than the content. This is certainly what our alumni are constantly telling us, once they are out of college and into a career where the content is evolving rapidly and what’s needed is somebody who has the intellectual processing skills to keep up.

I have seen very few textbooks that ever attempt to focus on process skills at all, even in those little blurbs that you will often find sprinkled throughout the book. And of those that do, very few do it consistently well. How could they? The whole point of a textbook is to consolidate information into one place, and so by definition if you use only a textbook, you’re not exercising those information-processing skills. There’s something to be said about the processing skills a person has to develop in order to merely read the book in the first place, but this kind of skill could also be done in the absence of a book, especially when there is much out there that is free — either on the internet or which can be obtained by the college library.

The second event I mentioned revolves around a student I have this semester who showed great promise during the first couple of weeks, but then mysteriously stopped coming to class. I finally caught up with this student and asked what was going on. It turns out the student was from a relatively poor family and simply couldn’t afford the books needed for classes. The book for our class is close to $150, and it’s one of probably 5-8 books that this student needed to get. This student was actually on the road to dropping out of college altogether because of this. Fortunately the student and I worked out a plan to get her caught back up and the student does have a copy of the textbook now.

My student’s situation made me think — is the textbook really worth it? The book we use in the class is “OK” but not great. I find myself having to remix the information in it all the time, having to add examples and clarify existing examples, and having to make up additional exercises. It dawned on me that I really could simply remove the book altogether from the course, and not much would change. And if that’s the case, is it right to put poor students in a situation where they have to choose between going to college and spending money on a textbook that isn’t really even necessary?

I plan to take this fall to find out the answers to some of these questions. I am teaching four courses — two sections of precalculus, Methods of Problem Solving (a.k.a. MOPS), and Modern Algebra. Precalculus does have to use a book, as I said above. MOPS has been textbook-free since the second year I taught it, the only required text being George Polya’s classic How To Solve It ($12 new in paperback, $7 used, so I don’t feel bad about having students buy and read it). So the only real jump here is to have no textbook for Modern Algebra. I am a little loath to do this, since I’ve used Gallian’s Contemporary Abstract Algebra for the last couple of times I’ve taught the course, and I really liked it. But I am convinced I can teach just as effective of a course by a combination of the following:

• Handmade notes and Keynote presentations
• Class meetings run in a pseudo-Moore method style
• Homegrown problems and exercises culled from past course experience
• Useful web links for reference and practice

I’ll be blogging the process of designing and delivering this course throughout the summer and into the fall, and I’ve created a new category for keeping track. It may bomb, and I might find myself putting large chunks of Gallian on reserve in the library before week 3. But I think it may work out fine, and I believe it’s worth the risk if it can save students $114.48 and improve their thinking skills at the same time.

It’s been a while since I last said anything about the textbook-free Modern Algebra class experiment. This is mainly because the class itself is now underway, five weeks into the semester, and it’s only now that I’ve got enough perspective to give a reasonable first look at how it’s going. So, let me give an update. (Click to get the whole, somewhat lengthy article.)

After an initial idea that students would be doing a lot of library research to find and present basic course information, I decided to get away from any kind of lecture at all, whether it was given by students or by me. Instead, I ended up changing the whole structure of the course to be a sort of modified Moore method. I created (and am still in the process of writing) a large set of course notes that consist mainly of two kinds of things: information that I give the students, and stuff for the students to do. The information I give consists mainly of definitions, comments, and a few worked-out examples. The stuff for the students to do, which goes under the official name of “course tasks”, consists of three different kinds of things as well:

• Questions for students to answer;
• Exercises to work; and
• Theorems (and lemmas and corollaries, etc.).

To give a flavor of what this looks like, here’s a shot of a sample page from Chapter 3 of the notes, which is on basic properties of groups.

The questions are usually simple but designed to get students to develop the habit of asking penetrating questions when they encounter a theorem or a definition. The exercises are a little more computational in nature, having students do some things and then perhaps make an observation. Some exercises are also simple results that require a proof, or perhaps a proof of a special case of a theorem. Theorems are, well, theorems — basic and foundational results that are sometimes easy to prove and sometimes devilishly hard.

They are collectively called “course tasks” because it’s intended that the students will be supplying all the answers to the questions, all the solutions to the exercises, and all the proofs to the theorems. The notes just list them; the students work them out at the board, and that makes up most of the meetings. That’s what makes this Moore-method-like.

What makes the course a “modified” version of Moore is that students were not intended to be doing all this work from the outset. Instead, I created a graduated schedule for when students would be responsible for various tasks. During the first week and a half, I did everything for them; by doing so, they could see what sorts of methods were involved in doing tasks in abstract algebra and what kinds of thinking are involved. Then, in week 2, I declared them to be responsible for answering all the Questions in the notes, while I still held responsibility for the exercises and theorems. Then, after another week or so, I added all the exercises to their list of responsibilities while continuing to prove all the theorems. Finally, about a week ago, I handed over the responsibility for proving the theorems, so that now they do everything.

I like this way of doing Moore method, because if I were to do it again with a different class, I could accelerate or decelerate the schedule of handing over task responsibilities based on the strength of the students in the class. If I have a class with a particular weakness in proof-writing, I can wait longer to hand over the responsibility for the theorems. Conversely if I have a stronger class, I can give them that responsibility earlier. But eventually they will all be responsible for every task.

And my responsibility is now more of a traffic cop, coach, and irritating question-asker. Usually when somebody gives a response to a course task, there is some kind of discussion, and it’s my job to see that everybody gets their questions answered. And if there are no questions where there ought to be, my job is to initiate that discussion. But I do not lecture; the only time I work things out for the students is if there is an exercise or theorem that we must do right away before moving on, and nobody has it; or if they have a question that needs further work to get a sensible answer.

I am breaking one of the fundamental rules of the Moore method with the theorems in that I am allowing students, if they choose, to go find the proofs of the theorems in books or online and simply explicate what they find. This may seem like institutionalized plagiarism, but really it isn’t; I’ll allow students not to come up with original proofs, but their grade on the theorems is mainly based on the clarity of their exposition and how well they field follow-up questions from me and the rest of the audience. In other words, you can copy a proof out of a book and give it if you want; but you had better really understand it. This helps students get the really tricky proofs out there, such as the proof of the Division Algorithm; and it helps justify the one-size-fits-all point value of 8 points for every theorem, regardless of difficulty. And it encourages research, which was the whole point behind not having a textbook to begin with.

I am also incorporating technology into the course in the way I have students write things up. When a student completes a result, that student is responsible for writing it up and putting in our course wiki. Over the summer, Wikispaces started offering native LaTeX support so that you can type in the LaTeX code and it will compile when you save the page. We’ve used this to post results that were done in class with actual math formatting. Probably one of the future assessments will be “open-wiki”; I do not give points for posting results nor do I subtract or withhold points for not doing so, but it will be that much less information for students to use on an open-wiki assessment if they don’t do it.

As far as assessing all this goes, answers to Questions are worth 2 points; solutions to exercises are worth 4; proofs to theorems are worth 8. I will calculate a course task grade at the end of the semester by taking either 100 points or the highest point total earned in course tasks by a student, whichever is greater, and using that as a divisor to compute a percentage. So if a student earns 88 points in course tasks by the end of the semester but another student earned 120, the first students course task grade is a 73%. The 100-point minimum is, to make an analogy with eBay, the “reserve” that must be met. (Right now, in week 5, the high course task score is 38 points. That will climb a lot higher since they were only given the responsibility for proving the theorems, 8 points apiece, last week.)

Students will also do between 5-6 problem sets (the problems are sprinkled throughout the notes at appropriate places), take two in-class tests, and take both a midterm and a final exam. That gives five distinct types of assessed work. I am letting students assign their own weights to these five types. They can weight each type at 20% of their grade; or 40% on the course tasks, 30% on the problem sets, and 10% each for tests, midterm, and final; or whatever. The only parameters are (1) the weights have to add up to 100% and (2) no single item may be weighted less than 10% or more than 50%. This allows the students some flexibility to target the course at their strengths; all aspects of the course are pretty rigorous and so there’s no obvious easy way out here. However, everybody has weighted their course tasks about 35%. Fine by me — the higher you weight the course tasks, the greater incentive you have to be the student with the highest point total and (presumably) the harder you will work at those tasks.

So far, I would say that this course has been one of the most fun, satisfying, and academically rigorous courses I have ever taught. Students are working hard and, even when they make mistakes, the mistakes become lessons by which students learn and improve. And there are some surprises, such as the Religious Studies major with a math minor who is currently outperforming many of the experienced math majors, or the student who works 40+ hours a week and has not done so well in past math courses who has brought in some beautiful work on theorems and exercises and has really become a lead expert in the subject matter among the students. I’ve been contacted by one of the students in the class who said that not only was this the most interesting and engaging class he’s had in the math program, but could I please consider adopting this course structure for some more courses I teach in the future. (I’m thinking about it; I have Differential Equations coming up next semester and that seems like a good place to try this out.)

I credit the positive experiences in the class to the level of activity that is required of the students in each class meeting. Students cannot consistently be passive recipients of this material without failing the course. They have to get in and get their hands dirty to hammer out the concepts and tasks on their own, or they won’t make it. Students are working ahead every day in the notes because they realize that doing so puts them in position to do well.

And I credit the activity in the class not so much to the absence of a textbook — because my course notes are really “the book” — but rather to the sparsity of the notes. The notes give a bare minimum framework of information, rather than working out every conceivable angle for students like textbooks usually try to do. The bulk of the notes are questions and things to do; they can be used as a reference (hence the numbering of all theorems and other tasks) but primarily it’s a workbook, not a textbook.

To give credit where credit is due: I do have an underlying philosophy of my own as to what appears where in the notes, and maybe I will go into that in another post. But I am pulling a lot of my information and the structuring of that information from Joe Gallian’s textbook with help from Lindsay Childs’ book and Hungerford’s classic text which I used in graduate school. In the future, I may go back and decouple my notes from all these other sources to make them truly my own, and then put them out on the web for public consumption.

Coming up for us in the class is our midterm exam, which will be the most “expensive” assessment yet, and a formative assessment to boot — so we will see how well students are learning the material when they are put to a test like this. But I think that they will be OK.