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How Come You Never Got an "E" in School?

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With most schools in the US about to let out for the summer, reader Sarah in California had report cards on her mind. She wrote to ask how letter grades originated, and why no one ever gets an "E."

Making the Grade

Credit for the idea of grading students' work quantitatively generally goes to William Farish, a tutor at the University of Cambridge in the late 18th century. The Industrial Revolution was in full swing in Britain, and piecework payment systems—payment based on the number of pieces produced rather than hours worked—were becoming popular even outside of manufacturing. Some schools were paying teachers per student instead of per hour.

Under this payment system, Farish saw that any limit on the number of students he could take on would limit the amount of money he could make. So he followed the lead of the industrialists and devised a teaching tool that would allow him to streamline his work and process more students: grades. The time and effort it took to evaluate students' work and ideas were reduced considerably by Farish's grading system (exactly how that system worked is unknown). The system could be scaled up or down easily, too, and worked just as well with 100 kids in the classroom as with 10. Farish could take all the students he could get and rake in the dough.

Update, 10-2010: Dr. Paul Worfel, an Associate Professor of Education at Huntington University in Indiana, has commented below to point out that I did not check my sources carefully enough, and to clear things up a little. Information I was able to find on William Farish on a few websites echo statements made by radio talk show host Thom Hartmann. Worfel, who’s done a bit of research on Farish, has pointed out here and on other sites, that these statements are largely fabrication on Hartmann’s part.

Worfel says below: “Except for the reasonable evidence that Farish started using a numerical grading system in Cambridge in 1792, the rest of the article from a historical basis is fabrication by Hartmann to try and assert his point of view regarding grades… The reason Farish instituted the use of numerical grades was to provide better equity to an oral examination system that was filled with favoritism and bias… Farish would not have improved his financial picture a bit by instituting numerical grades since students were not graded in relationship to lectures. There was only one exam at the end of a three-year study at the university. And that exam was not open to all students, only those determined by the university heads to be possible honors students… [Farish was also] instrumental in promoting a petition for the abolition of slavery [in the] 1780s, instrumental in working with students to organize the Cambridge Auxiliary Bible Society, instrumental in the development Cambridge Missionary Society… In Cambridge he was vicar of the third largest church, but also the poorest, which lead to his involvement in starting schools for the poor children in his parish. I've just touched on a few of his accomplishments.

He also points out in the comments on this post from Beyond School: “…Farish used a quantitative system for grading the single exam given Cambridge undergrads. Notice I said single exam. This was the only exam used to score a select few undergrads in what was called the Senate House exam during what we in the US would call the senior year. There were no other exams or papers prior to this point. The grading system was not, as Hartmann claims, used to increase the number of attendees at lectures. In fact attending lectures was quite voluntary. …Farish along with many other fellows recognize there was a good deal of favoritism in the examination process. Farish introduced (this is based on a good deal of circumstantial evidence) numerical grading as a means of providing a more equitable means of differentiating students’ response. Farish didn’t need grading to attract students to his lectures because they were not used in the context of any of his lectures or teaching during Farish’s lifetime.”

My apologies for providing bad info to the readers here, and a big thanks to Dr. Worfel for calling out my blunder and setting things straight.

Grading in the USA

Universities and colleges in America spent the 19th century experimenting with different ways of grading their students with various numerical systems or descriptive adjectives.

Yale got the ball rolling in 1785, when it handed out the first grades in America to a group of 58 students taking an exam. Twenty earned an "Optimi," sixteen got a "Second Optimi," twelve got an "Inferiore," and ten got a "Pejores."

A few other highlights from the early years include Harvard's first numerical system, which was a scale of 1-200, except for mathematics and philosophy classes, which switched to a 1-100 scale. Yale, meanwhile, started using a four-point scale starting in 1813, switched to a nine-point scale at some point, then went back to four in 1832. Harvard later ditched the numbers and, in 1883, gave out the first reported letter grade in the United States (a "B," for what its worth). Harvard changed gears again three years later and graded students as Class I, II, III, IV (IV was not quite as good as the first three, but not failing) and V (fail).

In 1897, Mount Holyoke College instituted a letter grade system similar to what is used today (with the exception of an "E" grade), but by the turn of the century, percentage grading on a 100-point scale became the norm and stayed so until the 1940s, when letters again made a resurgence. Recent surveys show that letter grades are the most common grades used in elementary and secondary schools and two- and four-year colleges and universities.

Understanding the System

The ways that percentages correspond to letter grades and GPA point values varies from school to school, but the following grading scale is pretty common.

Grade Percentage GPA value
A (highest grade, excellent)
90-100 3.5-4.0
B (above average) 80-89 2.5-3.49
C (average) 70-79 1.5-2.49
D (minimum passing grade, below average)
60-69 1.0-1.49
F (fail)
0-59 0.0

Some schools tack a plus or minus onto a letter grade and, if they use a 100-point scale, will usually assign the regular letter grade a value at the middle of a decile, the + grade a value in the top part of the decile and the − grade a value in the bottom part. In other words, getting an 80 to 83 in a class would earn you a B−, an 83.01 to 87 would be a B and 87.01 to 89.99 would get you a B+.

In most schools, an A corresponds to a 4.00 GPA, the highest one can achieve, which makes the A+ a strange beast. Some schools will award A+'s as marks of distinction, but still cap the GPA at 4.00. Others extend the GPA scale beyond an even four and assign an A+ a value of 4.33.

Where's the E?

Simply put, there's no E grade because there doesn't need to be. The only alphabetical intent in the letter grading system is in the four passing grades: A, B, C, and D.

The F comes next not because of a missing E and alphabetical order, but because it stands for "Fail." Even if F were the last letter in the alphabet, it'd probably be used the same way on report cards and mean the same thing.

The E is actually used in some grading systems, though. Since WWII, some schools, mostly Midwestern, have used E instead of F to denote a failing grade. A few schools even use U ("unsatisfactory") or N ("no credit") instead of F.

Grading the Grades?

Since their inception, grades have been the subject of simmering controversy. Critics claim that they're unreliable and encourage students to take only courses they know they'll do well in, while proponents say that they're necessary for the evaluation of student performance. We no doubt have both students and educators out there reading the blog (my girlfriend and I both majored in secondary education for a little while in college), so tell us: does the grading system at your school get an A, or are we better off with a different system—or no grades at all?

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iStock // Ekaterina Minaeva
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Man Buys Two Metric Tons of LEGO Bricks; Sorts Them Via Machine Learning
May 21, 2017
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iStock // Ekaterina Minaeva

Jacques Mattheij made a small, but awesome, mistake. He went on eBay one evening and bid on a bunch of bulk LEGO brick auctions, then went to sleep. Upon waking, he discovered that he was the high bidder on many, and was now the proud owner of two tons of LEGO bricks. (This is about 4400 pounds.) He wrote, "[L]esson 1: if you win almost all bids you are bidding too high."

Mattheij had noticed that bulk, unsorted bricks sell for something like €10/kilogram, whereas sets are roughly €40/kg and rare parts go for up to €100/kg. Much of the value of the bricks is in their sorting. If he could reduce the entropy of these bins of unsorted bricks, he could make a tidy profit. While many people do this work by hand, the problem is enormous—just the kind of challenge for a computer. Mattheij writes:

There are 38000+ shapes and there are 100+ possible shades of color (you can roughly tell how old someone is by asking them what lego colors they remember from their youth).

In the following months, Mattheij built a proof-of-concept sorting system using, of course, LEGO. He broke the problem down into a series of sub-problems (including "feeding LEGO reliably from a hopper is surprisingly hard," one of those facts of nature that will stymie even the best system design). After tinkering with the prototype at length, he expanded the system to a surprisingly complex system of conveyer belts (powered by a home treadmill), various pieces of cabinetry, and "copious quantities of crazy glue."

Here's a video showing the current system running at low speed:

The key part of the system was running the bricks past a camera paired with a computer running a neural net-based image classifier. That allows the computer (when sufficiently trained on brick images) to recognize bricks and thus categorize them by color, shape, or other parameters. Remember that as bricks pass by, they can be in any orientation, can be dirty, can even be stuck to other pieces. So having a flexible software system is key to recognizing—in a fraction of a second—what a given brick is, in order to sort it out. When a match is found, a jet of compressed air pops the piece off the conveyer belt and into a waiting bin.

After much experimentation, Mattheij rewrote the software (several times in fact) to accomplish a variety of basic tasks. At its core, the system takes images from a webcam and feeds them to a neural network to do the classification. Of course, the neural net needs to be "trained" by showing it lots of images, and telling it what those images represent. Mattheij's breakthrough was allowing the machine to effectively train itself, with guidance: Running pieces through allows the system to take its own photos, make a guess, and build on that guess. As long as Mattheij corrects the incorrect guesses, he ends up with a decent (and self-reinforcing) corpus of training data. As the machine continues running, it can rack up more training, allowing it to recognize a broad variety of pieces on the fly.

Here's another video, focusing on how the pieces move on conveyer belts (running at slow speed so puny humans can follow). You can also see the air jets in action:

In an email interview, Mattheij told Mental Floss that the system currently sorts LEGO bricks into more than 50 categories. It can also be run in a color-sorting mode to bin the parts across 12 color groups. (Thus at present you'd likely do a two-pass sort on the bricks: once for shape, then a separate pass for color.) He continues to refine the system, with a focus on making its recognition abilities faster. At some point down the line, he plans to make the software portion open source. You're on your own as far as building conveyer belts, bins, and so forth.

Check out Mattheij's writeup in two parts for more information. It starts with an overview of the story, followed up with a deep dive on the software. He's also tweeting about the project (among other things). And if you look around a bit, you'll find bulk LEGO brick auctions online—it's definitely a thing!

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