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…

I’ve been enjoying Quintessence of Dust, the blog of Calvin College biologist Stephen Matheson, quite a lot lately. It’s a high-level but clearly-written excursion through all sorts of issues in biology — including evolution, though not from the stance you might be used to coming from a Christian.

Anyway, two cool things from this blog today:

This incredible optical illusion, attached to a neuroscience-related article explaining how it works and how it relates to the brain’s processes of interpreting visual information. I agree with Matheson’s remark: “If you have built your worldview around the perfection of your sensory input, you might want to skip this one.”

This online biology textbook from an Arzona community college. I don’t have a print copy of a biology textbook to compare it with, and can scarcely remember enough biology from college to know how even to make such a…

Here’s a promotional video for a new math curriculum from Pearson called enVisionMATH. (It must be a sign of the times that grade school math curricula have promotional videos.) Watch carefully.

Four questions about this:

Should it be a requirement of parenthood that you must remember enough 5th grade math to teach it halfway decently to your kids?

Does the smartboard come included with the textbooks?

Did anybody else have the overwhelming urge to yell “Bingo!” after about 2 minutes in?

When will textbook companies stop drawing the conclusion that because kids today like to play video games, talk on cell phones, and listen to MP3 players, that they are therefore learning in a fundamentally different way than anybody else in history?

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….

A. If math were a color, it would be –, because –.

B. If it were a food, it would be –, because –.

C. If it were weather, it would be –, because –.

I’m not sure exactly what the point of an exercise like this is — perhaps the curriculum is just trying very studiously not to get too deep into mathematics itself, thereby teaching math without the social stigma of being very enthusiastic about it. Or maybe the idea is to get kids to see math from a different point of view, as a sort of oblique path through math anxiety.

Either way, it’s the wrong approach. The only way to come to terms with math, conquer math anxiety, and appreciate (and learn) the subject is… to get good at …

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.

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…

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.

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.) (more…)

I am a mathematician and educator with interests in cryptology, computer science, and STEM education. I am affiliated with the Mathematics Department at Grand Valley State University in Allendale, Michigan. The views here are my own and are not necessarily shared by GVSU.

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