TITLE: Negative Splits in Learning AUTHOR: Eugene Wallingford DATE: August 22, 2005 7:55 PM DESC: Runners like to run negative splits. Learners should come to recognize them as an essential element of their learning, and teachers and leaders should use them to the best effect. ----- BODY: When I was a in school, I was a pretty good student. The first class I ever remember not "getting it" immediately was Assembler 2, at the beginning of my sophomore year in college. The feeling was a bit scary. Our first assembler course was the "traditional" assembler course, in which we learned basic computer organization and the magic of MOV, JNE, and LD commands. But this was the early 1980s, and my school required a second course in this area. In the second quarter, we did more assembly language programming, but we also learned JCL and how to control an IBM 360/370 at a fine level of granularity from the moment execution began. Our card decks and key punches and assembly language programming became a bit more complicated. For whatever reason, the different levels of abstraction in the 360/370, when combined with the massive gulf between the problems we were programming and assembly language, left my head spinning. I didn't get it. Good student that I was, I kept plugging away, doing what we were taught in class, getting mostly correct answers -- but not really understanding why. And when I did understand something, it did not feel natural. and scored well. But I was worried, because I didn't get it. I didn't feel like I was in control. Then one morning, everything changed. There was no great epiphany, no flash of light. I was simply standing in the shower when I realized, ever so naturally, that it all made sense. I walked to class, and all was again right with the world. Since that time, I have had this sort of experience a few more times. The learning process moves slowly for a while, with the effort exerted exceeding the gains in understanding. Then, there seems to be an acceleration in understanding, like compound interest on the effort exerted earlier in the process. Once I got used to the idea that this would happen, it wasn't so threatening to me, and I was able to proceed with relative confidence deep into new ideas that I wasn't getting -- yet. But there is always a nagging thought at the back of my mind that this is it -- I've finally reached a point I won't be able to get. Runners have an idea that bears some resemblance to this upside-down learning process, called negative splits. The simplest form of negative splits is when the first half of a run is slower than the second half, but the idea generalizes to any number of splits. For the mathematically inclined among you, think of a monotonically decreasing sequence of split times. In running, negative splits are generally considered a good thing. They are wise as a training strategy, as they ensure that you do not use up all of your energy too soon. Plus, they cause you to run faster at the end of the workout, which trains your body in the feeling of working hard when it is tired. They are often a wise racing strategy, too, for many of the same reasons. Many racing greats have set records running negative splits. As I have learned over time, there is a corresponding danger -- going too slow in the beginning. If I am trying to get better, I need to be careful not to create negative splits by virtue of not working hard enough early on. In a race, this can waste the opportunity to reach a goal. But for endurance training, it's hard to go too wrong with negative splits. The goal is to do the miles, and negative splits maximizes the chance of completing the miles successfully. Recently I wrote about my happiness with some long distance workouts. You will now notice that both my 20-miler and my 22-miler were characterized by negative splits. Much of my happiness comes not so much from running fast as from running faster as those long runs progressed -- in some cases, with eight or more miles increasingly faster than the previous. I've come to realize that negative splits in learning, of the sort I experienced in that second assembler course, are also often a good thing. Learning requires our minds to change, and that change often takes time. Changing habits, practices, and expectations is hard, because our minds are well-suited to remembering and employing patterns of thought as a strength. Some of us even have a harder time than others changing mental habits. I am one of those people. Runners use negative splits as an explicit strategy, but for the learner change often forces us to accept negative splits. They are simply cognitive and psychological reality. Coming to accept that, and treating negative splits as the way we sometimes must learn, can free us from a lot of fear and uncertainty. And surrendering that fear and uncertainty can help us learn even better. Students should keep this in mind. (And remember, we are all students.) Teachers should keep this in mind, too. We need to take negative splits into account for many or all of our students, especially with the most challenging or abstract material. This is one of the elements of teaching that calls for a little cheerleading, a little reassurance to students that they should hang in there with the tough stuff, with the promise of it all coming together sometime soon. Leaders of every sort -- even department heads -- need to keep this principle in mind, too. Introducing change to an organization has all the hallmarks of trying to learn new habits and practices. People feel fear and uncertainty. This is complicated by the fact that sometimes the change must come to personal interactions, which carry a lot of extra psychological baggage with them. Negative splits may be a wise strategy for the leader, introducing small, easier-to-master changes first and only accelerating when people gain confidence and realize their own strength. That old assembler course... I had one of my favorite CS professors ever in that course, one who taught me so much about systems, software, and professionalism. I still have the textbook on my bookshelf, too: System 360/370: Job Control Language and the Access Methods by Reino Hannula. Early in that semester, the name "Hannula" raised fear in students' hearts, was veritable poison to the ears. When we all got it, it became a beloved totem of our collective experience. And the greatest lesson we learned in the course probably wasn't IBM JCL -- as cool as it was -- but the idea of negative splits. -----