Sunday, October 02, 2011

A true story of grit in education and life: The complex analysis class of 1999

Summary: Grit is the character trait of persisting in the face of hardship. My high school class faced an unintentional test of grit. Life outcomes differ starkly between the 4 who passed and the 12 who didn't.

The grit scale

Duckworth's grit scale is a short self-assessment quiz for persistence, with questions like "I finish whatever I begin" or "I often set a goal but later choose to pursue a different one." It has been tested to work immensely well in the military:

Duckworth and her collaborators gave their grit test to more than 1,200 freshman cadets as they entered West Point and embarked on the grueling summer training course known as Beast Barracks. The military has developed its own complex evaluation, called the Whole Candidate Score, to judge incoming cadets and predict which of them will survive the demands of West Point; it includes academic grades, a gauge of physical fitness and a Leadership Potential Score. But at the end of Beast Barracks, the more accurate predictor of which cadets persisted and which ones dropped out turned out to be Duckworth’s 12-item grit questionnaire.

(HT: Steven Hsu, Aretae)

The complex analysis class of 1999

Päivölä is a math-oriented high school. Before entry, candidates are screened for mathematical aptitude. The special sauce of the school were university-level math courses. Initially all 16 of us attended unimath. The school was still in formation: We were just the second boarding year-class there. Teaching was a bit shaky and there were few exercise sessions. Consequently students kept dropping out of unimath. The school was designed to teach the top as much as they could handle, so little was done to address those who dropped out. It was an unintentional test of grit: persisting despite woefully inadequate background and few exercise sessions.

In the last spring, there were 5 people in unimath: me, Vesa, Tuomas, Mikko and Jussi. The final course taught complex analysis. I was the last one who dropped out of unimath. At that point, 1/3 of the course had passed and I was completely dropping out of cart at lectures, not understanding much anything.

It was preceeded by 6-month limbo of linear algebra and calculus. During the limbo, lack of preliminary knowledge and mathematical maturity meant increasingly severe dropping-outs (not understanding anything about the taught topic). The first lecture where I completerly dropped from cart was about QR decomposition and numerically more stable way to solve linear equations, so complex analysis dropping-out was anything but surprise or whim.

This divided the class into 4 who passed the grit test, and 12 who didn't. It was not just about talent, because everyone had been screened at entrance.

The wall of abstraction

CS lore describes programming students "hitting the wall" during teaching. Some understand the subject swimmingly, while others struggle even after explanations. Some consider this "IQ in action": Either you have innate ability to get it, or you don't, in which case you need a lot more exercise to learn it.

Little research has been done about this. Dehnadi and Bornat assumed that setting a variable is one such wall. They measure one's grasp of variable assignment with questions like below.

The students had not yet been taught programming, so it was enough to use any consistent mental model. For example, the mental model "assignment moves the values from left to right" produces answer "a=10, b=10". The consistently wrong need to learn just one thing to get all correct.

44% answered the test consistently, and the test predicted well if the students would pass or fail their first programming course(*):

(*) Some attempts to replicate failed to find correlation, and a meta-analysis with improved test protocol found clear but weaker correlation.

Hitting the wall

The first time I hit it was at a physics lecture. A visiting Russian lectured about mechanics. Unlike in earlier lecutres, there were no numbers involved: the masses of the objects were m and M. I had all the required background (high school mechanics; math problems without numbers) but still couldn't answer a single exercise. Afterwards, I heard others commenting happily that at last someone was lecturing things properly. Before that, I had always been on the other side of The Wall, delighted to skip slack.

Life outcomes

Out of the 4 gritty and talented ones, 75% are now in managerial roles. Vesa is a vice president at Pohjola Insurance. Mikko has worked for 6 years in various managerial roles in Nokia. Tuomas is an assistant professor and has 30 publications. The only remaining professional is Jussi, but he is quite short (under 160cm). Jussi still has a PhD degree, so he is not a total loser even by the yardstick of this group, unlike me.

Only 25% of the remaining 12 ones have done well in career. Jani already had industrial-strength programming skill when he entered the high school at age 15, so he was right to ignore the class. Tarmo and Tommidefy the complex analysis cutoff limit.


Tiedemies said...

I was never in Päivölä, so I cannot compare, but I never blacked out anywhere, and I am still a total loser. The only standards that I don't fail is, I am tall and good looking.

Simo said...

> but I never blacked out anywhere,

Congratulations, you are smarter than me.