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.
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
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
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
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
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
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
-- 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.