Scott Young has an outstanding article at Lifehack.org today on 10 tips to study smart and save time. These three tips from the list are related to each other and offer very good advice that most students, especially new college students, never hear:

**Leave No Islands**– When you read through a textbook, every piece of information should connect with something else you have learned. Fast learners do this automatically, but if you leave islands of information, you won’t be able to reach them during a test.**Test Your Mobility**– A good way to know you haven’t linked enough is that you can’t move between concepts. Open up a word document and start explaining the subject you are working with. If you can’t jump between sections, referencing one idea to help explain another, you won’t be able to think through the connections during a test.**Find Patterns**– Look for patterns in information. Information becomes easier to organize if you can identify broader patterns that are similar across different topics. The way a neuron fires has similarities to “if” statements in programming languages.

I implied in this post that being able to see the Big Picture of a subject — that is, to see how all the “islands” link together — is perhaps the best indicator that the subject has really been mastered. The connections between concepts in a course ought to be the first thing the instructor thinks about when designing the course, a lesson within the course, or an example within a lesson. Likewise, the student needs to master the minutiae (the formulas, terms, etc.) but the links back to the Big Picture are essential for the small stuff to really “get learned”. Students who are taught according to the “check stuff off the laundry list of topics” method of teaching see the importance of connectivity only by accident or serendipity. And that’s to the detriment of everybody.

Concept maps are a simple and effective way for students to study with topical connections in full view. I first blogged about concept maps here (and continued here, here, and here). I used concept maps pretty extensively in my upper-level math courses last semester and the students really connected (pun) with them, particularly the concept map of the Invertible Matrix Theorem (click the fourth link above). One of the review sessions for a test in Linear Algebra consisted of me creating a giant two-chalkboard-wide concept map of the material that was on the test, showing how it fit together. Very effective, like I said, and easy to implement.

One thing I would add to Scott’s list is that effective studying happens when you have a good idea of your capabilities and limitations in a particular moment and work in harmony with them. For example, I know that I personally don’t learn very well if I find myself getting tired or bored. On some days, I can go pretty long and study pretty intensely before that happens. On others (e.g. when one of the kids wakes once or twice in the night and wrecks my sleep) I start the day tired and never get better. In the latter case, I’ve found I have to have an almost 1:1 ratio of studying and breaks, usually about 15 minutes at a time for each. Or I look in my GTD next actions list and focus only on the items that require little brainpower and/or short amounts of time. It feels like I am not getting much done, but in fact I am getting as much done as is humanly possible for me at that time.

And another thing to add — since we can’t predict from one day to the next what our situation will be, you have to provide yourself lots and lots of lead time to study. If you assume that you’ll be perfectly undistracted and cogent the day before the test and plan only to study on that day, then you are begging for trouble — inevitably, it will be that day when you come down with a cold, something comes up that you must take care of, the kids don’t sleep well, etc. On the other hand, if you start early and build a daily habit of effective studying, then it won’t matter what the circumstances work out to be.

I’ll be handing Scott’s article out to my freshmen (well, to all my students) this fall.

Technorati Tags: Productivity, Profhack, Concept maps, Student culture

I just started making a concept map for my summer school geometry class that starts Monday. This map is for properties of special quadrilaterals.

You said your students “connected” with them. Do you think this helped in their understanding of the concepts? Did evidence of this show in results? Also, did you ever have them make their own map? If so, was it something you’d do again?

I’ve only incorporated concept maps deeply in two classes, calculus and linear algebra. I think the more conceptual the class or lesson, the more effective the concept map is. For example, many lessons in calculus are just down-and-dirty computational methods, and I found concept maps not to be such a great tool. Similarly for some linear algebra topics like how to compute a determinant. But when the theorems started flying, or there were big ideas in calculus that needed connecting (e.g. how a function and its first and second derivatives are related graphically) then they worked quite well.

In particular, the linear algebra students became almost addicted to the concept map for the Invertible Matrix Theorem — in the sense that whenever they got confused about something, they tended to pull out their IVT concept map for help first. And they didn’t like it when I didn’t let them use it on the final exam. 🙂 Linear algebra is hard because there are a lot of different major themes going on, usually simultaneously, and the challenge is seeing how they all relate via the various theorems. The concept maps helped a lot in making this less daunting.

I never had students make their own maps, although I wish I had done so in the linear algebra class. I am definitely thinking about doing so in the textbook-free Modern Algebra class this fall, which has the same sort of conceptual depth as linear (plus, no textbook).

Thanks for the detailed feedback (I wondered if you let them use them on an exam ;>)). Teaching with no textbook is interesting. I’ll be doing that next year for a pre-algebra class (not

quitethe same as modern!). It is definitely making me think about what I want them to know (and how).