Many main characters in children's shows (and in adult's shows featuring children) are explicitly shown as doing very badly in school, despite showing themselves to be of at least average intelligence in most other areas of life. This isn't inconsistency on the part of the writers, though. The kid is just Book Dumb.
Making your child character Book Dumb is seen as a great way to appeal to the masses (especially when creating a This Loser Is You) without having to show them being outsmarted by other characters on a regular basis. A Book Dumb character will usually show excellent "street smarts" and is often very good at problem solving most of the time, but he (and it is usually a boy) does not function well within a regimented learning system. Maybe he's just not good at that type of learning. Maybe he's clever, but can't resist an opportunity for mischief. In extreme cases, he may even be a genius or inventor at home, but devolves into a functionally illiterate bad boy as soon as he enters through the school gates. Maybe he's just Too Dumb to Fool.
On the other hand, some writers will try the opposite rationale and use it as a criticism of the school system, either claiming that schools are staffed by incompetent idiots who don't know intelligence when they see it, or that schools are deliberately designed to stifle innovation and free will in order to turn kids into mindless future wage slaves.
Some characters are book dumb due to having been denied a formal education for various reasons. They might not be in any way stupid or lazy but a lack of opportunity has simply restricted their progression.
His own attitude to his schooling varies considerably, often within the same series. One episode may call for him to seem to care about his problem, and try very hard to get the work done, whereas another episode may show him really not caring about schoolwork at all. This doesn't matter; as long as the writer gets across that this character isn't some kind of fancy intellectual at whom the audience should sneer, then the Book Dumb has done its job.
In shows with high school characters, Book Dumb overlaps with Troubled, but Cute.
This is also common among adults, who will be portrayed as not having done very well at school, even though today they may be a famous novelist, celebrated artist, top sportsman, or nuclear safety inspector. If the character is doing a non-creative job, he will usually be just as ineffective in his job as he was at school (though always managing to avoid George Jetson Job Security), while displaying considerable intelligence in other areas of their life.
More or less the polar opposite of the stereotypical Nerd, who does excellently in school but is shown as being almost completely incompetent in all other areas of life. Both can be very intelligent people, but only in certain circumstances. The different attitudes of most people to each type of character betray our society's mistrust of intellect. Both, however, can be Geeks.
Book Dumb female characters are quite common in Anime and Manga but in Western media this trope tends to skew heavily male, possibly because Girls Need Role Models. The popularity of the Uptown Girl trope might also be a factor.
This trope has quite a bit of Truth in Television. As any teacher can tell you, there is something about the school system that does alienate a certain portion of otherwise intelligent children, although the pervasiveness of this trope frustrates some students that are held to Teen Genius standards by their parents, wondering why nobody that actually does well in school is ever the main character. Most troublingly, this trope is popular among anti-intellectuals, who argue that academic smarts are entirely worthless. Of course, being anti-intellectuals, their arguments lack...a certain something. Luckily some school systems are trying to do things to solve this problem, as it often makes learning easier for everybody anyway, and several systems have been in use since just after the Turn of the Millennium, although wide-spread adoption has yet to occur anywhere.
Contrast TV Genius, who only seems intelligent in the classroom, and Ditzy Genius, who is a genius in academics but inept in everyday life. Compare Brilliant, but Lazy, which underlies this most of the time, and Everybody Hates Mathematics, the roughly mathematical equivalent.
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Anime and Manga
Ermengarde in Shokojo Sera, like her original incarnation, is portrayed as scatterbrained and scholastically backward; in a flashback, we also see that this may be related to neglect by her father, a university professor. However, she is also portrayed as good-hearted and generous, loyal to Sara even after she loses both father and fortune, and nurses Sara when she falls seriously ill. She also is the only person, apart from Sara, whom Lottie can relate to, at least to some extent.
Tomo, Osaka and Kagura from Azumanga Daioh play this one to some degree. The three of them are pretty much as intelligent as any high school girl, yet their scores are so low, they once added them and got 104, or in American, an A++ (if Chiyo, Sakaki and Yomi did that, it would be roughly a 270 / AAA++++++). This is mostly justified, though, because Tomo is a Genki Girl with the attention span of a squirrel, Osaka is a Cloudcuckoolander with the attention span of a squirrel, and Kagura is a Jockwith the attention span of a squirrel.
It's actually played with until the end of the series, where Tomo, Osaka, and Kagura all pass their entrance exams to college before the pseudo-Geek Yomi (complete with a Lampshade Hanging from the teacher on how weird that is).
Yue Ayase from Mahou Sensei Negima! is one of the smartest girls in the class, not counting the Mad Scientist or the Time Traveller. She adores reading, especially philosophy. It's just that reality is so incredibly pointless that she doesn't care to try at all, which places her in the lowest grade percentile of the class. (The so-called "Baka Rangers.")
When she starts studying magic, however...
Also, arguably fellow Baka Ranger Kaede Nagase, who actually seems to be a very wise girl for her age. Perhaps the Ninja training just gets in the way of her studies.
Both Asuna and Ku Fei (also of the Baka Rangers) have both shown impressive tactical skills and Asuna is very good at judging the emotions of others. Admittedly Ku Fei has to work with the handicap of a less than perfect grasp of Japanese (you try learning to speak language A taught in language B when C is your native tongue), and it is widely speculated that what ever spell keeps Asuna from remembering her past also interferes with her general memorization skills. In fact of the five only Ensemble Dark Horse Makie is arguably just plain dumb.
Inversion: Despite being an apparent Delinquent and shonen lead, Ichigo Kurosaki of Bleach has one of the highest grade point averages in the school, to the chagrin of his normal friends who are upset that he betrays his stereotype. He replies that he gets enough flak from the teachers for getting into fights and his strange hair colour, so he studies hard to make sure that at least they can't complain about his grades. However, in battle he tends to charge in without a plan, and ignore his allies plans.
It's the same with Chad (who gets a higher score than Ichigo), except he's not so much of a delinquent anymore.
Then there's Orihime, who, despite her space-case tendencies, manages to get at least 3rd in their entire grade.
Keigo, however, is a straight example. He takes great pride in having low grades and being an idiot. However, when push comes to shove, he's the Genre SavvyAction Survivor who was the only one in his group to think to run while Aizen and Gin were talking. Not to mention, his immediately attempting to attack Aizen with a stolen zanpaku-tou, remembering something he had seen nearly a hundred chapters ago. Sure, he was interrupted before he could actually go through with it, but it's the thought that counts.
Naruto routinely comes up with winning strategies for his squad, yet placed dead last in the exams (the databooks give his intelligence score pre-Time Skip as 1.5 out of 5) and one scene implied that he is barely literate. It seems he can only think properly under life threatening danger, but has apparently grown out of this after the Time Skip (said score has gone up to 3).
Sakura's something of an inversion in Part I, as she aces every test in the academy, but rarely puts her intelligence to practical use in the field (for example, she doesn't see through either of the fake Narutos in the Forest of Death before Sasuke, who has 1.5 fewer intelligence points in the databook, pointed them out).
Justified with Shikamaru. His Academy grades are not much better than Naruto's (mainly because he's so lazy that applying pencil on paper tends to be a drag for him and he sleeps through the exams), but he has an IQ of over 200 (which if he lived in the real world would make him quite possibly the smartest person who ever lived) and demonstrates his intelligence through his brilliant strategies. Even his intelligence has been admired by people like Kakashi and the Third Hokage. Sakura once said that Shikamaru is the smartest ninja in the Land of Fire.
Jonah, in Jormungand may be one of the best and most badass member of the group but even though he can take down a whole camp by himself he still can't do basic multiplication. (The fact that he's still a 10-12 year old kid who spent his entire life as a child solider doesn't help.)
Despite being in a school practically designed to take advantage of his abilities, Judai Yuki from Yu-Gi-Oh! GX is perpetually stuck in the lowest dorm of Duel Academy due to his low scores...at least, with any of the written or studying parts; during the actual field exams, where he actually gets to duel, he excels greatly. This does appear to be partly by choice, as he's turned down promotion at least once on screen. Perhaps the writers just think he'd look horrible in Yellow or Blue...
He gets those low scores because he's too lazy to bother with actually doing the work. In addition, he did turn down one promotion because he likes the seaside view that the Osiris Red dorm offers, that the higher dorms lack.
This actually becomes a plot point in Season 3. Because he's widely regarded as one of the best duelists at the school, many younger students start emulating him - meaning they skip or sleep in class and don't study. According to Professor Satou, those students lack Judai's natural ability at Duel Monsters. Satou ends up forcing Judai into a duel with another student's life hanging in the balance - and somehow still pulls off being a sympathetic character. The whole ordeal functions as part of Judai's Deconstruction .
Sho was also like this for a while, being a fairly competent duelist and student whose fear of failure always sabotaged his efforts in season 1. By season 3, he is temporarily promoted to Blue, but goes back to Yellow because he doesn't believe himself worthy yet. In season 4, though, he accepts the promotion.
Jotaro Kujo from JoJo's Bizarre Adventure is an outright delinquent who skips school regularly—although this may be because all of the girls at his high school can't stop fawning over him, and he can't stand most of the others—but despite his self-imposed lack of formal education, he has incredible intuition and deductive reasoning skills (which, in a rather odd Shout Out, he attributes to his obsessive watching of Columbo as a child). Jotaro actually ends up being a marine biologist (of all things) later on, which goes to show he isn't as dumb as one might think.
Kyon from Suzumiya Haruhi is clearly intelligent and knows a lot for his age, as displayed by his continual references to widely varied aspects of culture, history, mythology and advanced scientific concepts, many of which a high schooler would have no reason to know, but is far below average as a student, possibly due to his cynical and apathetic personality. In the novels, he ends up needing Haruhi's help on at least one assignment.
Lampshaded by Kyon himself: "Why is it that I can be so smart when it comes to reading Nagato's facial expressions or Koizumi's hidden clues, but fail to answer every single test question?"
In addition to knowing a lot, he has a damn sharp mind, as evidenced by his deduction of what really happened on their summer trip at the end of book 3.
Tsukasa from Lucky Star is a hopeless lazy ass capable of sleeping from 10:00 PM to 2:00 PM, while Konata is so otaku she actually forgets to do her homework. In fact, Konata admits in one particular episode that's she perfectly capable of achieving high marks, but her obsessive and procrastination habits just fill in more than academics. The minor character Misao is similar to Konata, but she'd more inclined towards outdoor activities.
Konata got into this locally prestigious high school by the lure of a PS2and a PC.
In one episode she demonstrates her ability to cram for a test with a single all-nighter; she manages to get the same good score as Kagami, despite of that the latter studied for the same test well over a week.
YuYu Hakusho features Yusuke, who is incrediblyBook Dumb. He once got a twelve (yes, twelve out of 100) on a test. However, on the battlefield, he's a fairly competent strategist, and in one episode, he correctly applies the principle of light reflection to defeat Hiei. There's also Kuwabara, who starts out Book Dumb (he got a seven on that same test; Yusuke was bragging that he was smarter), and, as part of Character Development, studies hard and gets into a prestigious high school.
Fruits Basket both subverts and plays this straight. Kyo is a subversion, he has the personality of a delinquent, is obsessed with fighting, sort of, and is, oddly, a good student. Played questionably straight with Tohru, who tends to struggle (though not due to lack of effort). And then there's Saki, who's smart, but simply doesn't give a damn (except when faced with the threat of summer school in non-air conditioned rooms, when she makes sure to avoid failing grades).
Tohru is The Ditz in pretty every area of ability except social skills, where she's an absolute genius.
A Slam Dunk episode features four members of the Shohoku Five-Man Band failing their exams with ridiculous results. They had to stay up stufying in Captain Akagi's house all night long. Hilarity Ensues there.
Luffy in One Piece is a textbook example. He's a complete idiot most of the time, yet he's extremely good at coming up with the best ways to use his Devil Fruit powers to their fullest in various situations. One that particularly sticks out is when he out-smarts Eneru's Mantra mind-reading ability... by out-dumbing him. He intentionally thinks of nothing (The name of said technique translated as "Gum-Gum Space-Out"). That trick actually fails, since Luffy realizes too late that he can't attack without thinking, but he then immediately starts bouncing punches off a wall. He has no idea of what the redirected punches will hit, making it impossible for Eneru to dodge them by reading his mind.
One of the rare female examples is Maya Kitajima from Glass Mask, who is able to memorize full scripts and acknowledges lots of acting techniques, but is barely average at school. She lampshades this by thinking she's just not interested in academic prowess.
Hajime of The Kindaichi Case Files is a great detective and has the IQ of 200, yet he has no interest in schoolwork and his chance of getting into a college is precarious, to say at best.
Keiichi of Higurashi has an interesting case of this, it's revealed that whilst his grades are standard to mediocre, he has a rather good to great understanding of the real life implementations of whatever is being done.
However, in Tsumihoroboshi-hen, it is revealed that Keiichi has scored into genius level on iq tests, and is quite smarter than he initially seems, yet has a pathological block that requires him to be interested in the subject to do well. He is also shown to help Mion and Rena with their studies, and Mion is a year older than him...
Kagome Higurashi from InuYasha is a female example - at least when it comes to Math, a subject that she's always shown to be struggling with. Apparently not a complete BD as she manages to graduate from high school at the end of the manga. However, it doesn't seem like she has the usual over-the-top excellent battle skills that most BDs have; her heroicness seems more emotionally based, even after she doestake a badass level.
Interestingly enough, Kagome's friends remark that she used to be in the top 30 in Tokyo, meaning that she is very competent in studying...it's just that ever since her adventures started, school work inevitably took a backseat.
Sawada Tsuna from Katekyo Hitman Reborn!. To an extreme. In the beginning, he's pretty much the school's Butt Monkey that gets the worst grades. And for the longest time, it really did look like he was all-around useless. However, after the series got more serious, he's shown to not actually be stupid - when he's determined and tries, he's very smart about fighting and utilizing his abilities in combat. He still has bad grades, but it's shown that if people actually bother to help him, he actually can sufficiently well in class (e.g. the time when G disguised himself as Gokudera and tutored Tsuna, and he manages to solve a problem in class).
Yamamoto, though not as bad as Tsuna, is definitely smarter outside the classroom than in it. Interestingly, Troubled, but Cute Gokudera pretty much has perfect grades despite his Delinquent appearance and attitude towards everyone but Tsuna.
As episode shows that Sousuke's problem is he is just unable to think outside of military terms and situations. He reads classic poetry and somehow comes to the conclusion that it's talking about a WW 2 Naval battle.
Ends up subverted at the end of the TV anime series, when its revealed that Miaka passed the entrance exam to Jonan while Yui, who's more traditionally smart, did not. They both end up going to a different high school together.
Ash from Pokémon inevitably ends up like this any time he's placed in a traditional school setting. A recent episode of DP has him failing miserably during a Pokémon quiz, leading another character to question how a trainer with such poor academic knowledge of Pokémon could have earned 6 badges. The episode eventually leads to an Aesop about how learning theory in school doesn't necessarily make one good at actually doing something in real life.
The character who mocked Ash's low score gets curbstomped in a real battle against the Team Rocket trio, without any dirty tricks, because he had no actual experience and had no idea what to do other than list off attack names.
A particularly interesting case is OdamakiSapphire - the girl is almost illiterate to the point she had to ask an assistant how certain words sounded during the intellectual portion of Roxanne's qualification exam, but due to certain aspects of her upbringing she's much smarter than she appears. Roxanne lectured her on learning how to read after the test was finished... only for her brain to crack when she realized the girl scored the highest of everyone in the room! The look on Roxy's face was priceless.
Fuyuki Hinata from Keroro Gunsou is an average student at school, but is an outright expert on occult matters, and even an Amateur Sleuth in the anime.
Baka To Test To Shoukanjuu: Yuuji's scores are consistantly low, but actually shows ability to strategize battle plans very well. And when he actually studies, he can get quite high. Also, Minami since she is bad at reading Kanji.
Sekirei has the protagonist Minato himself who cannot do well under pressure. But give him time to think and he aces through tests and is actually quite competent in making up plans.
Ichika from Infinite Stratos is very bad when it comes to theoretics, much to his, his sister's, and his haremettes' annoyance.
Yuuri from Kyo Kara Maoh, is shown as having very average grades (and baseball abilities), but evidently has enough street smarts (well most of the time, anyway) to make it as king.
Nobita in Doraemon is an extreme and somewhat exaggerated version of this trope. He literally keeps getting zeroes in his tests. Even the resident Dumb Muscle Giant gets some questions rights, Nobita just zeroes everything. On the other hand, he can be intelligent at times and quite cunning, usually when trying to get his hands on Doraemon's gadget.
Joey/Jounouchi from Yu-Gi-Oh!. Besides being a slacker in school, he's often confused by cards everyone else knows about, doesn't understand how the game's chain mechanic works, and often has to count on his fingers to do math.
Goku from Dragon Ball is an extremely simple-minded person who never went to school, but shows brilliance when it comes to training and fighting.
Nozomi of Yes! Precure 5. When she finally gets her teammates together and they find out how poorly she does, Karen suggests getting together and studying. However, her implied Attention Deficit... Ooh, Shiny! makes it hard for her to get her head into the game and she ends up bailing in frustration. Coco's able to convince her to keep going and try again and she does better... but not that much.
In Maoyuu Maou Yuusha, The Hero is the resident World's Strongest Man, but lacked a formal education. In the first episode, he didn't even know what pollution is. He sadly lampshades this in that he is only suited for fighting and is not equipped to help in problems concerning economics and politics. He is quite clever and practical, just ignorant, and he learns quickly.
In the sixth episode of Kotoura-san, it was revealed Hiyori failed most of the subjects, despite looking smarter than the local Idiot Hero Manabe, who barely passed.
Chase Stein from Runaways, despite being the child of genius inventors, has no scholastic aptitude whatsoever and is easily the dumbest member of the group (including the 11-year-old):
Yet when on his own, he was clever enough to come up with a simple plan to deal with the Gibborim; find and threaten those smart enough to help. His "anonymous white van" idea also shows some he has some degree of cleverness.
Worth mentioning that in recent books, Chase shows a skill with fixing and using tech devices close to his parents, and is as skilled with the Staff of One as Nico, the resident spellcaster herself.
Batgirl III (Cassandra Cain) is one of the top martial artists in the DC Universe, but barely able to speak and illiterate. She has one of the better excuses for this, as she was raised without access to books or speech.
She was learning to read and was able to write down phone messages by the end of the series.
A lot of Marvel and DC characters on both sides get this not because they are stupid, but because they hang out with too many super-geniuses. Depending on the Writer, they will be shown as either dumb, just a bit outclassed, or even having Common Sense as compared to the overcomplicated plans of their teammates/nemesis.
The Thing compared to Mr. Fantastic and Doctor Doom, who all went to college together. People tend to forget that Ben Grimm has multiple engineering degrees and was a military test pilot and NASA astronaut. In large part because he doesn't talk like the highly educated man that he is, along with being overshadowed by his super-genius former classmates.
With Superman it really is the writers' faults. Clark Kent is a world renowned investigative journalist and a prize winning novelist. Superman helps maintain the advanced Kryptonian equipment in his Fortress. And on at least one occasion he has said to Batman's face that he was just as smart as Batman, which Batman openly agreed with. If anything Superman is an inversion; he's book smart but does not have a talent for combat and tactics, so people (both in and out of universe) assume he is less intelligent based on how he fights.
When asked by the professors on his final theology exam how many parts (and what kind) a good sermon should have, Hieronymus (from a story illustrated by Wilhelm Busch) answers (sorry for not rhyming): "Two parts: One part that no one can understand, and one part that's understandable."
Zipi y Zape: The twins. They can build a time machine out of a barrel and a broken grandfather's clock, but then they'll struggle to do their assignment: calculate 5*13.
Hobbes: You know, if you actually studied, you'd get a few things done school-wise.
In The Blind Side Michael Oher is presumed to be worthless and unteachable, until a teacher administers a test verbally and he actually receives a passing score. The problem lies not in his inherent intelligence, but rather in his borderline literacy and the methodology of the test itself. Throughout the remainder of the film, Oher is depicted as being highly competent so long as a task can be adapted to a metaphor he understands.
Bill and Ted in Bill and Ted's Excellent Adventure will apparently mature into musical geniuses, display a high degree of creativity, and have a surprisingly sophisticated vocabulary. However, they are failing history and clearly have not paid much attention in school. They also get a quick grasp on manipulation of events via time travel.
Jean-Baptiste Grenouille of Perfume displays a high level of intelligence in addition to his brilliance in perfume making. However, he was raised as a simple tanner's apprentice in 18th century France, so he has no education at all. Even in adulthood, he must ask simple questions like, "What's a legend?"
Malik from Un prophète is almost illiterate (though he does get some education while in prison) - but he's very, very clever.
Subverted in The Waterboy. Bobby Boucher seems to be mentally retarded, but that's really due to years of excessive sheltering by his mother, who taught him everything "is the Devil!", as he has practical knowledge about water filtration, and later does well with every college class, even having a near-perfect score on his high school-equivalency exam.
Huckleberry Finn from The Adventures of Huckleberry Finn is the EPITOME of this trope. He's able to come up with elaborate plans on-the-spot to turn the tables around in a bad situation but he can't even spell his own alias correctly.
Arguably, Jim too. As a slave, he's uneducated (and it shows), but he can be pretty philosophical about what he does know.
D'Artagnan from Alexandre Dumas' The Three Musketeers is very perceptive and good at Indy Ploys, but "had never been able to cram the first rudiments of [Latin] into his head, and [...] had by his ignorance driven his master to despair".
Fanny Price in Mansfield Park is from a poor family and hasn't had access as a child to the governesses her rich cousins had; as a result, when she first meets them they laugh at her for not knowing basic facts about geography and history. However, she's got more common sense and a better sense of morality than they do, and does a better job of making up for lost time in academic knowledge than they do in developing character.
In William King's Warhammer 40000: Space Wolf novel Grey Hunters, Sven's marked lack of interest in history and the archives makes a Foil for the more studious hero, Ragnar. At one point he drags Ragnar away from the hologlobe for beer.
Julia from 1984 is barely literate, yet able to guess the Party's innermost goals almost intuitively, and evade capture by a fascist regime for ten years.
It's entirely possible, however, that she's actually an agent of that regime used to lure people like Winston into a false sense of security before the Thought Police come after them.
In Maskerade, Granny Weatherwax is described as "grudgingly literate but keenly numerate".
Though in an early book, she initially couldn't comprehend the un-reality of a local play.
Of course, given the plasticity of reality and the effectiveness of a really convincing narrative on Discworld, I wouldn't trust a play to stay unreal...
Cohen the Barbarian is illiterate, though he loves books (they make for good lavatory paper), but he's got so much cunning and guile it doesn't matter.
It is a trait he respects in others, though. He had a Geography teacher as part of his retinue and trusted adviser in Interesting Times.
Leonard of Quirm, despite being possibly the most well-read and brilliant man on the Disc when it comes to what we Roundworlders would call "actual" science, seems to think that an excess of education or training can be a bad thing, leading to a flaw he calls "learning the limits of the possible"—i.e., a failure of imagination. He failed the Alchemists' Guild exam due to doodling complex devices in the margins and absent-mindedly correcting the questions. Is also rather bad at coming up with names for his inventions for some reason.
Perhaps the finest example of this in Discworld, however, is Harry King, who like Cohen tends to use certain kinds of paper for lavatory use (his wife likes newspaper when it's recycled, but King himself prefers to "cut out the middleman"). He was born a poor street kid and eventually came to be the waste management consultant in Ankh-Morpork. William de Worde, by no means stupid and possibly the most well-read person in Ankh-Morpork outside of the Patrician, had the "uncomfortable moment when an educated man realizes the illiterate person sizing him up could probably out-think him three times over"
His Grace the Duke of Ankh, Commander Sir Samuel Vimes is also a key example. He doesn't know much in terms of education (he grew up as a street kid, with all that entails in old Ankh-Morpork), and struggles manfully with his paperwork and other more intellectual duties, but he knows people better than almost anyone else in the setting. Smart People Play Chess, he questions why the pawns don't overthrow the nobles and set up a republic.
The world of Temeraire features several people like this, though it certainly wouldn't be uncommon as public schooling was all but unthought of during the Napoleonic wars. Laurence forced himself to cram the necessary mathematics to be a sailor into his head when he was a boy, but was not much skilled beyond that, and had little love for books. Laurence, though, is not a slow man by any means. However, it's subverted when Temeraire's love of books and joy in reading and knowledge infects Laurence. Laurence also insists that his adolescent ensigns and cadets do their schoolwork, when he's not so busy he forgets, and though they perform their duties ably and, as children and youth are wont to do, pick up languages faster than the adults in the crew, they show great resistance and dislike of it. Similarly, uneducated dragons, even from breeds not particularly renowned for thinking, prove quite capable of debating advanced mathematics with Temeraire. The trope is also inverted in a minor character, a lieutenant who, "If ships could be sailed by figures could sail around the world without fear" but when called to order others around habitually gives the wrong order.
Claudia Kishi from the Babysitters Club series is this trope. Basically her entire personality, and many of her plotlines, revolve around the fact that she does poorly in school despite being talented at art and having generally good judgment and social skills. In the early books she's just uninterested in school, but she seems to get dumber as the series goes on, even going so far as to be sent back to a grade she had already completed.
Percy Jackson and the Olympians also has several examples of this—most of the demigods are ADHD and dyslexic, which results in their doing rather poorly in school, despite their hyperintelligence in other areas.
In the Harry Potter series, both Harry Potter and Ron Weasley have rather mild interest in academics and usually rely on their uber-nerd friend to succeed in them.
If you thought Harry and Ron were bad academically, Ron's prankster twin brothers, Fred and George, are even worse. Case in point: Mrs. Weasley commented once of Ron achieving seven "Exceeds Expectations" grades in his O.W.L. exams as more than Fred's and George's added together. On the other hand, they managed to found a highly successful joke item shop that sells their magical inventions that impress even Hermione. However, they were not always Book Dumb; In the first book, Ron mentioned that they make high grades, despite being goofs. Thus, although they were always Brilliant, but Lazy, it took sometime for them to become Book Dumb.
Their grades declined because later years of school got to the point where they could no longer breeze through exams without even trying. And given their career plans didn't require getting into the advanced classes, it wasn't worth the effort to them to study harder.
Jakub Wedrowycz, a genius and master exorcist Badass Grandpa, only went to elementary school for three years back in 1910's, so his knowledge of anything not related to the supernatural is... sketchy (he can barely read and write the Latin alphabet). He personally despises any higher education and considers it a disgrace when his grandson turns out a Teen Genius who reads books all day.
Peyssou from Malevil is a skilled farmer and mason but is otherwise uneducated. He often asks Emmanuel or Thomas to define some of the less-common "smart" words they use.
Vin from Mistborn has this to an extent; she's actually pretty good at reading and writing but hates doing them. Also, she once encounters an obscure mathmatical puzzle and doesn't even realize it is one.
P. G. Wodehouse's Psmith series owes its setup to this trope. Mike Jackson is pulled out of his school on account of his failing grades and sent to a private school, where he meets Psmith, exiled from Eton for a similar reason. Despite their academic deficiencies, Mike is a near-infallible cricket player and Psmith is an underhanded genius hiding beneath the guise of a stereotypical Cloudcuckoolander.
Skylar in Gives Light is witty and perceptive, but says he doesn't perform well in school. It's not clear whether he's legitimately Book Dumb or just plain lazy, as he also claims to hate reading books and never finishes them.
Galaxy of Fear covers its bases. Zak Arranda is reasonably intelligent but hates to study. His big sister Tash is a bookworm who likes study and cites her sources when she writes essays - admirable, for a thirteen-year-old.
Scarlett O'Hara from Gone with the Wind is mentioned to have barely scraped by at the Fayetteville Female Academy, and never willingly opened a book since her graduation. However, this is purposefully cultivated because intellectual women found it harder to catch husbands in the antebellum South. However, she is highly skilled in wrapping men around her little finger. Melanie, on the other hand, is not afraid to discuss literature and philosophy with her fiance.
In It Cant Happen Here, much of the American populace is book-dumb after the Windrip regime's educational "reforms", book burnings, and censorship campaigns. Institutions of higher learning have been evicerated, and the remaining schools only teach practical or useless classes, meaning that much of the populace is ignorant of history, literature, and civics. When citizens revolt against the Corpos, this works against them as well as the Corpos.
So, after the first gay eruptions of rioting, the revolt slowed up. Neither the Corpos nor many of their opponents knew enough to formulate a clear, sure theory of self-government, or irresistibly resolve to engage in the sore labor of fitting themselves for freedom ... Even yet, after Windrip, most of the easy-going descendants of the wisecracking Benjamin Franklin had not learned that Patrick Henry's "Give me liberty or give me death" meant anything more than a high-school yell or a cigarette slogan.
Aximili from Animorphs is an Andalite military cadet, a member of a super-advanced alien species, with all the complete-education and training that implies, and all the vastly-superior-to-human-science knowledge that comes with it - and his actions throughout the series show that he's quite intelligent and quick-thinking as well. He also conveniently knows very little about a great many plot points and other miscellaneous details that he should reasonably be expected to know by the standards of his people, because while he has completed his education, he spent most of that education staring at the attractive female Andalites in adjacent learning cubicles. Some things, it would seem, are universal
Live Action TV
Family Ties: Mallory is frequently portrayed as a space cadet and average (at best) student who posits that there may be "special verbs for dead people" since they don't "do" anything. However, she is clearly a very talented fashion designer who nearly beats Alex in the PBS scholarship contest of her own accord.
Arrested Development: High-school age Maeby Fünke is able not only to con her way into a job as a film executive, but to actually execute it competently, despite only getting a crocodile in spelling and a daisy in arithmetic.
Although it appears that most of the films she makes are terrible. How much of this is her fault is unclear.
Buffy herself comes off this way, largely because her slaying cuts into her studying. Those of her teachers who aren't jerkasses recognize that she is actually very bright, and she gets a great Verbal SAT score.
Charles Gunn from the Buffy spinoff Angel is far from well-read due to growing up on the streets but has a first-rate intellect, though he gets self-deprecating about being the "dumb muscle" in the group in later seasons. In Season Five, this is subverted when he becomes the group's legal expert after getting a mental download of a comprehensive knowledge of the law, along with some Required Secondary Powers like golf, foreign languages and Gilbert and Sullivan.
The Doctor in Doctor Who is portrayed as an incredibly brilliant scientist, one of the most intelligent people in all of time and space. Nevertheless, in "The Ribos Operation" it is revealed that he barely passed his graduation exam (at the Time Lord academy on Gallifrey) on the second attempt.
At the start of the 2007 episode "The Shakespeare Code", in the TARDIS Martha remarks "Blimey! Do you have to pass a test to fly this thing?" and the Doctor replies "Yes and I failed it!"
Barely passing at a Time Lord academy is probably what most humans would consider Book Genius.
Noble Savage Leela may not be the most educated or intellectual of the Doctor's companions, but she is highly observant and intuitive. This makes her an excellent complement to the Genius Ditz Doctor.
EUReKA's protagonist, Sheriff Jack Carter, has an average IQ in a town full of supergeniuses. This makes him the local Book Dumb, but his street smarts, not shared by the majority of brainiacs in town, end up saving the day and his job security at least once an episode.
Cappie, the president of Van Wilderesque fraternity Kappa Tau on Greek is shown to be extremely smart, to the point of being able to converse freely in Latin and figuring out what the point of a psychological experiment was that the research assistant didn't realize, but he's also shown to completely not care about school, such as showing up to a class for the first time two months after it started.
Matt Parkman on Heroes, although he's no genius, is streetwise enough to have been a cop and cunning enough to have literally thought his way through some nasty situations. He's also dyslexic, hence Book Dumb through no fault of his own.
Scott from Teen Wolf. He's failing several subjects in school, but he can cook up an Indy Ploy in a tight spot.
To be fair, he's largely failing due to werewolf drama and it's implied that normally his grades are good. When he gets a paper with a failing grade, there's a comment that says, "Not like you," Stiles says he just needs to study, and Coach Finstock seems confident that Scott can get his grades back up so he can be on the lacrosse team next season.
David Lister in Red Dwarf, at least in later seasons, is Book Dumb but can be a reasonably intelligent guy. In "The Inquisitor", where he is put on trial to justify his existence (before himself as Judge), he fails because he could have been a better person than he was, whereas both The Cat and Rimmer (who are easily just as, if not more, a waste of DNA) get off by their own low standards.
Not to mention the plan he uses to defeat the Inquisitor.
And his plan to outrank Rimmer by passing the ship's chef exam, chef being just high enough in rank to surpass Rimmer but not so high as to actually imply any additional responsibility or work on Lister's part.
The way he defeats Cassandra in Series 8 is complete genius.
The Cat is shown to be good at piloting Starbug and having a good sense of smell and perception of nearby danger. This is despite the fact he's not intelligent in other areas.
Rimmer's idiocy is only countered by his ability to get out of things. For instance he writes his exam notes on his hand, and presses his hand down on the page, only for them to smudged handprint. He then pretends to faint and escapes the exam this way. He gets out of sex with women by saying he's had enough. He runs away from every monster they have come across. He escapes death by kicking the grim reaper in the balls.
Ace Rimmer (what a guy!) knows he's this...he was terrible at school (having to repeat a year) and his whole character is based on not letting that hold him back, inadvertently becoming the opposite of the Rimmer well known to us.
Darlene Connor from Roseanne is a D student more interested in sports than useless studying. However, she's quick-witted and a talented writer, and becomes the first person in her family to go to college, presumably doing well when she's studying something that matters to her.
Turk from Scrubs was a C student in high school, but managed to get into medical school and eventually makes head surgeon. This is to some extent true to life; it is often far easier to focus on academics when one has a clear direction, goal, and interest. He notes himself that his college marks picked up soon after he decided where he wanted to go with his studies.
Dean Winchester, the elder brother in Supernaturalis this trope. He almost never reads unless he has to while researching a case, and he chose not to go to college (mostly to please his dad, but still). However, he is a great mechanic, managing to keep his beloved 1967 Chevy Impala in great shape and even rebuilding it by himself after he semi crushes it in the first season finale. He also made an electromagnetic frequency (EMF) meter out of a busted Walkman. And his knowledge of pop culture (mostly horror movies) has come in handy a couple of times. Not mention he's a great liar and fairly smooth talker.
The concept of Dean being this might not be entirely accurate, however, as he apparently does not share his reading habits with Sam or with anyone, really. In Season 4, it's revealed that he's pretty much read all of Kurt Vonnegut's works. We can surmise from this that it's entirely possible Dean is also familiar with other similar literature.
And in Season 5:
Dean: I have a GED, and a Give-'Em-Hell attitude.
Wizards of Waverly Place: Alex Russo regularly fails exams, but is the craftiest and most competent character in the series. This is lampshaded by her best friend, Harper, when is looking for a substitute teammate in an academic contest after one of her original teammates dropped out:
Harper: I wish you were smart. Then you could fill in. Alex: I am smart! I'm street smart. Harper: But not book smart. Alex: I am too book smart! Sure, I don't read books, but I hollow them out and hide things in them.
iCarly: Sam Puckett takes this trope so far that a realistic question can be asked of how she hasn't been expelled or held back. Again. She got held back already in the 3rd grade. She's also a bully. Yet outside the school, she can scheme and plan.
Jeremy Clarkson and Richard Hammond on Top Gear — not stupid by any definition but completely uninterested in the kind of engineering, mathematical, or mechanical trivia that fascinates their colleague, James May.
An episode of The Twilight Zone dealt with a girl who was mute and presumably illiterate, but with incredible mental powers (like Cassandra Cain minus the whole assassin thing). When her teacher showed her a picture of a boat and asked what it was, the girl had a vision of the boat rocking at sea, and she felt very sad that she couldn't share this with the teacher. The story ends with the girl's caretaker finding her, but she's been DePowered to a normal child.
Romeo is this on The Steve Harvey Show. Although he's been in High School for nearly seven years, he actually does well on his SAT's and by the series end, he gains admittance into a four-year university.
The titular character of Life With Derek obviously isn't stupid. He just has other priorities.
Chief Engineer Trip Tucker is an engineering genius, head of the engineering department on Earth's first Warp 5 starship, and consistently throughout the series is shown managing tricks on Enterprise no one else in Starfleet could have pulled off. He also appears to have the same instinctual knowledge of the engines as his successor (predecessor?) Montgomery Scott - and struggles with basic algebra.
In the TV version of Sweet Valley High Jessica is a complete airhead in the classroom, assuming amongst other things that makeup tests are about the use of cosmetics and that Paris is in Italy. Otherwise, while definitely shallow and impulsive, she can be plenty cunning and manipulative.
Kim Parker from The Parkers is a dimwit in academics which is a running gag of her having bad grades, but she does have a big heart and dreams to reach success. At the show's end, she never graduates from Santa Monica College, but she went on to become a successful fashion designer.
Gentarou Kisaragi, the main hero of Kamen Rider Fourze is this. So much that he considers getting a 50 his greatest accomplishment! Plus, that 50 was originally an 18! Due to helping out the detention teacher's son, he bumped it up to the 50 to pass!
The other half of this trope is shown in Gentaro's social skills (he's incredibly good with people and can befriend just about anyone, plus is a very good judge of character and when someone is hiding something), his deductive reasoning (figuring out who the Monster of the Week was based on a character tic), and his ability to learn, adapt, and improvise during battle.
Penny from the Big Bang Theory is this having dropped out of community college and having trouble learning scholastic topics. This contrasts with the rest of the characters who all work in different scientific fields.
Several of the street dealers from The Wire, while having received partial high school education at most, are nonetheless able to demonstrate a respectable amount of intelligence, particularly Bodie, who gets out of getting charged when Hamsterdam is shut down by correctly identifying his situation as entrapment (or "contrapment", to use his exact phrasing).
Abba's "Thank You For The Music" is about someone who people see as this until she sing.
Calvin of Calvin And Hobbes is shown to be very far behind his classmates academically, but is a loquacious philosopher in his spare time, showing a vocabulary and critical thinking skills far in advance of what you could expect from a normal 6-year-old. In this case, it's an explicit criticism of the school system.
Bill Watterson has also said that he enjoyed having Calvin use big words to describe stupid ideas.
It's also implied Calvin, while intelligent, is simply not motivated to apply himself. In one strip, for example, his father sits him down and asks him why he doesn't do better in school, noting that he's obviously smart because he managed to devour every dinosaur book he ever got his hands on. Calvin simply replies that they never study dinosaurs in school. He has shown considerable aptitude in school-grade subjects like math and reading comprehension in situations where the subjects, such as dinosaurs or time travel, were interesting to him. Calvin is a classic case of a gifted child in an education system that isn't engaging him properly. In addition, Calvin is also just very mischievous, more interested in causing trouble and messing with the teacher's head than actually learning. He regularly gives bizarre answers on his tests ("What is the significance of the Erie Canal?" "In the cosmic sense, probably nil,") which seems to be as much for his own amusement as an attempt to cheat the system.
Dennis the Menace (UK) is an example of this being taken to a ridiculous degree. In the comics these days, Dennis even has a futuristic car that he designed himself, with protective armour and water cannons, and yet is shown to be completely (and cheerfully) lost at school.
In For Better or for Worse, one word: Gordon. While Gordon graduates high school with average grades, he is a gifted mechanic who turns out to have a decent head for business. He goes to work for a local outfit, and within ten years all but owns the place, it being sold to him when the owner retired; he then takes the store from a local landmark ("Oh, right, that place") to a thriving business which, the last time it was seen before the strip's conclusion, may well have been on the verge of becoming a franchise.
Peppermint Patty in Peanuts. She would rather be playing sports than sitting in a classroom, compounded by not getting much sleep weeknights because she waits for her father to get home from work at night. On the other hand, any girl her age who could be capable of mistaking a dog obedience school for a human school to the point of enrolling in it, "studying" with the dogs, graduating and being so sure that she doesn't have to go to regular human school because of that "diploma" is on her own level of stupidity.
That's nothing. She already thinks Snoopy is a 'little kid with a big nose' and treats him accordingly.
Remember, with Patty, we're quite far into Jock territory, too. As if she didn't have enough downward pressure on her grades.
Caulfield, from Frazz. He dislikes school and frequently derails lessons, but reads books far above his age's reading level and has intelligent discussions with the titular janitor.
Shark 2: "Sure... but they're worthless, taste like cardboard."
Shark 1: "I didn't want to eat them."
Shark 2: "What then?"
Shark 1: "I wanted to know how to switch them on."
Lan (or Netto for you purists) in Mega Man Battle Network has defeated evil organization after evil organization with Mega Man countless times, which obviously requires a lot of problem solving. However, he receives poor grades in school. Somehow he becomes a scientist, just like his pop 25 years after the games
Note that, in a filler episode, he created a wireless battlechip port. It's more likely that he is simply bored by the classes.
They also only show Lan/Netto being below average because of distraction. If he fails homework it's because he didn't do it, not because he didn't understand it. He fails in class because he fell asleep or was daydreaming, not because he didn't understand the subject. He also is shown to listen to information given as if he was intrested, possibly meaning that he just doesn't like the average subjects, but with new or different subjects he is interested.
Kyo Kusanagi of The King Of Fighters may be an excellent fighter (having won the titular tournament at least 7 times), but because of this, he's been kept out of school for so long that he's at least 25 and has yet to graduate (not counting the time he was kidnapped and missing for at least a year). The problem being that, despite the successive year appellations, he hasn't aged?nor, for that matter, has the rest of the cast. No wonder they changed the sequel labeling style.
It's more of a case of Kyo being The Slacker. He's not an idiot; he just gets bored very easily and decided to drop out from school by the time the NESTS saga rolled around. BTW, he's only won KOF from '94 to '97.
Then you find out it might be more justified than it previously appears, since he's actually only seven years old. And been cooped up in his own house the entire time to boot.
Tales Of Symphonia's Lloyd Irving is like this, also. Starts off seeming like he'sbeing completely clueless, but by the time Martel shows up you get the feeling that Lloyd has figured out exactly how to plow through the Gambit Pileup. Dawn of the New World pretty much confirms this, because even when you consider that most of the evil deeds that Lloyd was blamed for were actually Decus in disguise, the real Lloyd is still pretty much running his own plan, as evidenced by his demanding the cores and then running away when he realizes he's outnumbered by his former friends, rather than just joining up with them. Yet, despite now being nearly twenty, academics-wise, he's still only managed to get around to memorizing his multiplication tables, as revealed in a skit with Raine.
Tales Of Vesperia has it's own protagonist, Yuri Lowell. Though he is the one that keeps the party steps ahead of the other groups throughout the game, he states outright that he has little patience for reading. While most of the others in the party tend to be experts in their (book) researched fields, they each end up relying on Yuri for his street smarts.
While not strictly educationally relevant because of the world it takes place in, Phantasy Star IV has Chaz. Whenever he's presented with anything technically complex, it's mostly lost on him, and he's easily impressed and surprised by technology (a particularly dumb moment is when he's impressed that Demi— who is an android— is adept at handling machines). He even lampshades this, pointing out that Rune has basically had to explain everything to him since he joined the party. However, his understanding of people is top-notch, and he's usually aware of other characters' feelings and thoughts before they express them; this also leads him to his Crowning Moment of Awesome when he recognizes the hypocrisy inherent in his destiny and chooses to Refuse The Call.
Rosie of Valkyria Chronicles finished her education (and therefore military training) at middle-school level. Nevertheless, she starts off as one of Welkin's squad leaders and is more experienced in combat than most of Squad 7's recruits.
Most of the Investigation Team in Persona 4. With the exception of Yukiko and the Protagonist (whose aptitude depends on the player), neither of them are seen to do well on their exams. In spite of this, none of them are actually stupid. Rise has only just restarted school after suspending her career as a teen idol, Teddie has never been to school but picks up ideas fast, and Naoto is by far the most intelligent and educated member of the group, albeit without any visible academic record to prove this. Both Yosuke and Chie don't really stand out in regards to intelligence but help move the investigation along regardless. Even Kanji - who is clearly the least intelligent of all - makes up for his lack of intellect with a rather specialized interest.
Dekar from Lufia II: Rise of the Sinistrals is pretty consistently portrayed as an idiot, but he's also resourceful and very philosophical. Also, he was the only one to see through Idura's trap at the Tower of Sacrifice. (Of course, Idura DID manage to trick him into the trap after a few minutes - but it didn't matter, as Dekar simply tore the thing apart.)
According to an NPC in his neighborhood and his friend's comment in the anime adaption, Endou Mamoru from Inazuma Eleven is this. However, in a soccer game, he's a Bad Ass and Hot Blooded captain who is a huge source of Heroic Spirit.
In Touhou, Mystia Lorelei canonically cannot read kanji ("fine print" in translation), yet runs a successful con act using her power to inflict Temporary Blindness to sell grilled lampreys as a folk cure for blindness, making her one of the most successful youkai in Gensokyo despite being functionally illiterate and on the business end of the Superpower Lottery (and a lot of poultry jokes).
Played for Drama in Little Busters with Kud, who is a very eager and hard-working learner, but because she isn't used to the Japanese examination system and isn't very good at multiple-choice tests while under pressures tends to consistently do pretty badly in tests.
In The Inexplicable Adventures of Bob!, since Bob starts out as officially the world's most average man, he's not really dumb, but since the rest of main cast (Jean's a scientist, Molly's a prodigy, and Voluptua's a 300-year old alien) are much brighter and more well-educated than average, he tends to come off looking Book Dumb by comparison.
Rak from Tower of God, who has no idea of the basics of the Tower or weapons, but has an intuition and empathic intelligence that is incredibly accurate.
Orville from Hodges Pond does not know what a vegetarian is and can't spell the word "scholar".
Solange of the Whateley Universe is cunning, smart enough to see how to apply her father's business practices to ruling her high school, but Book Dumb because she's already a billionaire heiress who is never going to have to work for a living. There's nothing any teacher has to tell her that she sees any value in learning. Too much work.
Egoraptor in Game Grumps can discuss game design, theoretical economics, and quantum physics at length, but is a high school dropout that can't tell you the difference between a century and a millennium.
In The Fairly Oddparents, Timmy Turner is incredibly resourceful and able to outsmart adults, fairies, pixies, snarky genies, aliens and all sorts of other beings many times his age, but the series goes out of its way to ridiculously illustrate how bad he is with anything that involves language arts and math.
Though given the asshole teacher he has to "Work" with, it's no surprise.
Danny Fenton in Danny Phantom, while similarly portrayed to be resourceful and clever in intense situations, is the standard C-student male teenage protagonist commonly seen in shows with High School settings. Of course, this is at least partially attributed to the notion that fighting ghosts constantly interferes with his studies. Nevertheless, his attitude towards his studies was subject to much varying.
However, it's been subverted once or twice, explaning why he didn't just do the obvious thing in a given situation (IE: Wishing a ghost who's playing genie into her containment) and instead spends the episode doing as he is wont to do.
With his exaggeratedly short attention span and prodigy for playing mindless video games, Yang of Yin Yang Yo is almost a blue anthropomorphic rabbit version of Timmy, complete with Jerkass tendencies. This is especially apparent when compared to his naturally more studious and level headed twin sister. The three shows share writers and directors, so it's not much of a surprise.
While the title character of Kim Possible is shown to be anything but Book Dumb and able to maintain A-average grade (but not at Teen Genius levels mind you), Ron is yet another example of the typical C-student male protagonist. Yet Ron regularly assists in saving the world, and while evil was the best villain in the series, invented several doomsday devices. Also built one when kidnapped by Drakken using stuff lying around, and gave Senior Senior Senior the ideas to build traps.
Subverted in the last episode of Fillmore!, where the main suspect in the poisoning of a class tarantula seems to be a Book Dumb kid who was often kept behind after class to look after it. The character's Big Secret is that, against his image, he's an A student, and was looking after the tarantula because he wanted to.
Will from W.I.T.C.H. is a rare female example. She appears at least as smart as anyone else the rest of the time, but her grades are so bad she tries to hide them from her mother.
Irma Lair also counts, saying she "lives in the now" and doesn't worry about her grades. Both are very good examples that Book Dumb doesn't mean incompetent as they display intelligence and creativity at their Guardian positions; one notable example is Will using Teletransportation to save herself and a group of her allies, a feat that requires ten years of training to do safely. And this was her first time attempting it. Of course she did freak out when it seemed she teleported them into a wall. Naturally, waking up, going to school and saving the world causes grade loss on its own.
Pete, from Goof Troop. They make it clear a few times that he didn't even finish High School, yet he runs a successful used car lot, is a successful Manipulative Bastard and would probably be considered upper-middle class in economic standards. His son PJ as well but in different ways. He doesn't do very well in school most of the time it's mentioned, but he's consistently the Only Sane Man.
Jade Chan from Jackie Chan Adventures is generally Book Dumb on the basis that at times it could be argued if she even cares about school, for she would rather be on Jackie's adventures, see Adventure Rebuff. It doesn't help that at school she is often talking about said adventures instead of learning. Outside of school however Jade possess a smart and cunning mind and seems to be a very good problem solver, not the mention the ability to break into underground military installations. She is definitely street smart to the point that it scares Jackie how clever she is, at times it seems like he would have to be cunning himself to outsmart Jade. The leader of the super-spy organization Section 13 gave her a standing offer to join when she gets old enough. He was laughing at the time, but it is uncertain if he was joking (though later states this seriously when she managed to get into their most secured vault with no trouble). Her future version was actually competent enough to become leader of that organization, until being demoted for a mistake.
Matt Stone and Trey Parker have admitted that Eric Cartman is a genius: the smartest character in South Park. However, he refuses to care about anything that does not immediately help him, especially school. He never pays attention in school and remains ignorant. Despite this problem, he forms very detailed plans, considers complex issues and is a brilliant manipulator. Despite this, he demonstrates frequent belief in totally ungrounded assumptions (which, given the nature of the South Park 'verse, are sometimes proven true.)
Baloo and Wildcat on Disney's series Tale Spin are good examples of Book Dumb characters.
Wildcat seems pretty unintelligent, but give him any mechanical task to work on and he shows his true genius. Give him a broken telephone and he can fix it in ten seconds flat.
Baloo is revealed in one episode to be poor at spelling, and in a later one that he never even finished primary school. He is, however, a top-notch pilot and is capable of coming up with some cunning strategies when dealing with the various villains in the series.
Not terribly uncommon in the 1930s when the show takes place. Back then getting a HS diploma would be like getting a BA now, and getting a BA was very uncommon of outside of the brilliant or rich until the GI Bill.
Todd Daring from The Replacements is shown to be brilliant schemer, but seems to have an aversion to anything to do with schoolwork. At his most extreme, he replaces his German teacher with someone who only speaks German so his father cannot find out how badly he his doing.
Brendan Small from Home Movies is a parody: Everyone claims that he is very intelligent but in reality, he is egotistical, incompetent and a failure at everything.
An episode of Ozzy and Drix (the spinoff show of the movie Osmosis Jones) emphasized the importance of book learning in a painfully Anvilicious way. After Book Dumb Osmosis spends the entire episode berating Drix for not having any street smarts to offset his prodigious book smarts, it is ultimately Drix's book smarts that save the day. Ozzy, realizing for the last thirty seconds of the episode that book learning can sometimes go a long way, asks Drix to educate him. Drix obliges by quoting well known sciency things ("Well, for example, E=MC2") without offering anything resembling context, to which Ozzy reacts with obnoxiously exaggerated excitement.
TJ from Recess is perhaps the perfect embodiment of this trope. While his grades are notoriously average/below average, once on the playground he can pull off elaborate schemes from (quite literally) under his hat.
Luanne Platter from King of the Hill did terribly in school but she is a gifted mechanic, a good example of this was in an episode where Hank's truck is taken apart for evidence when a delinquent broke into it and Luanne puts it back together in less than two days. Not to mention how he let her touch his truck, something he never let his own friends do greatly suggested her level of skill. However this side of her is rarely shown in the later episodes mainly due to flanderization.
Most of the male characters in The Simpsons fit either the child or adult versions of this trope to some extent, including Bart, Homer, Barney, Nelson, etc.
Bart Simpson is clearly an excellent example of this — at school, he is falling behind everybody else, barely managing to stay in his own grade, whereas in his spare time he thwarts criminals and solves mysteries, often displaying intuitive thinking skills on a par with his sister Lisa.
Further proven in the few situations where he does apply himself academically, and manages to do quite well for himself.
Although it must be noted that even when he applies himself, he manages to fail tests, even though he retains knowledge.
He has also proven himself to be an excellent linguist, becoming fluent French in two months, and Spanish and Japanese in a matter of hours.
Even Ralph Wiggum, despite having a reputation for rather dim, could fit this. Although he's as Book Dumb as one could possibly get, numerous scenes have been dropped throughout various Simpsoncentric media from the comic, to the series itself that he's possibly creatively gifted. When his head's on somewhat straight(er than usual) anyway.
Hank Venture from The Venture Brothers. Earlier in the series he would have probably fallen under the category of an ordinary dumbass, but as of late he has acquired a rather typical teenage mindset. Even so, Hank still is as uneducated as a doorstop.
Jefferson Twilight: Hank, aren't you just a little ashamed of your ignorance?
The Alchemist: Like, just a little?
Hank: Yeah. Constantly.
One episode had the two of them graduating "high school" and looking into colleges, with Hank instead deciding to join S.P.H.I.N.X. so he could work with Brock. To basically everyone's surprise, Hank manages to pass every single test they put him through to keep him from joining the organization, and he shows a freakish level of competance in handling dangerous situations. This can be attributed to being raised by resident-badass Brock Samson, and having picked up tricks from his life as a boy adventurer. But that same episode brought up that both Hank and his brother Dean have so little experience living in the real world, they have barely any actual life skills and wouldn't last a week outside the compound.
In the Ben 10 franchise, Kevin Levin is a justified example in Ben 10 Alien Force and Ben 10 Ultimate Alien; he's 17 years old, has spent most of his life on the streets, and hasn't gone to school since the age of 11. He's an utter genius at practical things like energy weaponry and mechanics (from cars to starships), as well as math due to managing his own finances and history from keeping track of who hates who and why, but is understandably lacking in most academic areas.
Bugs Bunny, arguably. He's a genius, but he seems to have trouble reading: "diabolical sabotage" becomes "dy-a-bo-likkle...sab-o-tay-gee".
On Static Shock, protagonist Virgil Hawkins was a below average student. He was formerly a good student, but being a super hero has interfered with his study time. Similarly, his best friend Richie (before gaining superpowers of his own) was shown to be a very poor student who excelled in engineering, making high-tech devices for Static to use constantly, but never passing a math test.
Phillip J. Fry from Futurama is frequently portrayed as a lazy, childishslacker who is impulsive to the nth degree*
(has a soda addiction that nearly cost him his (best) (girl)friend's life (It Makes Sense In Context) and caused him to suffer near-lethal radiation poisoning, and on a trivia show blurted out the answer before any others were listed)
Finn from Adventure Time. He doesn't have a school to do bad in, but he's terrible at math and doesn't understand Princess Bubblegum's science experiments. He's also quite impulsive and sometimes gullible. That being said, there are numerous episodes where he gets by through cleverness or subterfuge rather than just running at monsters with a sword. (Not that he doesn't do that too.)
Comedian Russell Brand did terrible in school. His book even has notes from his teachers who suspected he was Obfuscating Stupidity. Listening to his stand up and reading his book he comes off as extremely intelligent even culturally well versed.
George Carlin didn't do too well in school and has said that either the work would be too difficult or too easy and he'd be bored. Carlin also goofed off in class quite a bit as well. Knowing his stand up Carlin is possibly one of the smartest comedians in recent memory and some even call him a philosopher.
Frank Zappa hated mainstream education and was a self-taught performer and composer. He even took his children out of school at age 15 and refused to pay for their college. Mind you, he has been diagnosed as having an IQ of 172, so he's not short on the intellectual side.
This video (removed) shows an amazing, real example of this trope. A poorly educated Chinese man with no electrical training builds complex robots out of stuff from junkyards. His creations are amazing. He is clearly ingenious and clever.
A classic real-life example is Dave Thomas, the founder of the Wendy's restaurant chain: ridiculously successful restaurateur, philanthropist, advertising icon and high-school dropout. He finally got his GED in 1993 (at sixty-one, mind) because he thought his success might encourage others to take the wrong lesson and drop out like he did.
Bill Lear - if his name sounds familiar it's because he invented the personal jet that bears his name - and he never even had an opportunity to drop out of high school as he never went beyond the 8th grade. The Wright brothers themselves were simple bicycle mechanics who possessed what amounted to only a basic education for that era (which wasn't much).
Sammy Davis, Jr., worked in show business his entire life and never attended school.
From a study that was quoted on The Colbert Report: out of all the billionaires in America, 5% come from Harvard while 35% come from "the college of No College Education".
Also keep in mind the percentage of Americans who graduated from from Harvard, it's got to be less than six million people.
As quoted above, Albert Einstein supposedly wasn't successful at school, and thus ended up as a clerk in patent office. Fortunately, this gave him plenty of time to daydream, and while Einstein wasn't a particularly fast thinker, he was a very deep one, which in turn led to his discovery of the theory of relativity. This is, in fact, a 100% thoroughly debunked myth (except about the speed/depth of his thoughts—depending on his knowledge of trivia, he might have done very well on Who Wants to Be a Millionaire? but poorly on Jeopardy!). Einstein did extremely well in school. Einstein was actually a child mathematics prodigy who was doing both differential and integral calculus by age 12. It is true, however, that he didn't like the then-very-militaristic German schools. The myth may have arisen because the grade rankings in Switzerland (where he was born and went to school) are opposite to the ones in Germany (where he lived later). In Germany, 1 is the best grade, 6 the worst. In Switzerland, 6 is the best and 1 the worst. It could be assumed some Germans heard that Einstein "only" got 6s and came to the wrong conclusion. Also, when he first tried to apply the ETH Zürich (a science and technology university) he did not pass the entrance exam, because it was written in French. He still got exceptional marks in mathematics and physics. The other source of this myth may be the opinion of his teachers who claimed that young Einstein was often prone to daydreaming and had trouble in focusing. Which is not surprising given that Einstein already mastered large part of his curriculum and was simply bored as hell. And one more thing: Einstein was not 'just a clerk in patent office'. He was technical expert tasked with approving patent claims, a job that usually required a doctorate just to apply.
Thomas Edison did poorly in school, yet became one of the most successful inventors the US has ever known. It just so happened that his mother started homeschooling him when he was around ten-ish.
Whether Edison was exceptionally clever or exceptionally sneaky is a matter of debate. While no doubt some of his inventions were original, he wasn't above straight-up stealing ideas from others or using underhanded tactics to discredit other inventors who had beaten him to the punch. In one infamous case, he used alternating current to publicly electrocute an elephant in order to "prove" that his rival, Nikola Tesla, had invented a dangerous means of transmitting electricity. Edison, of course, was promoting his own invention, direct current.
Edison's maxim Ingenuity is 1% inspiration and 99% perspiration must be one of the world's most misinterpreted maxims. He didn't state it so because he was a diligent, hard worker. He did state it because he had absolutely no theoretical knowledge on why things worked that way. He simply built a prototype one after another until he got a working one. In informatics, this is known as "brute force approach". It is not considered a good approach unless you have much computing capacity.
Especially talented and intelligent children may often receive poor grades for a variety of reasons. Studies have shown that intelligence can manifest in many different ways. For example, a kid with good tactile intelligence might perform poorly in mathematics even if he has an intrinsic understanding of mechanics. Teaching styles often only address certain kinds of intelligence, putting certain children at a disadvantage. Intelligent children with learning disabilities such as dyslexia can fall behind if their needs are not properly addressed.
Adolf Hitler is an example. He was a notoriously bad student, yet rose to seize control of a country and made some considerable headway towards conquering the entire world. As time went on, however, poor decisions and generally degrading sanity caught up with him.
Marshall Mathers is an interesting case of this, he hated school and did poorly in it, repeating ninth grade multiple times, but he loved books and read the dictionary front to back multiple times, which he saysgave him his incredible skill at rhyming.
Craig Ferguson dropped out of high school at age 16 and since then has had no formal education. He considers himself an autodidact, having read for pleasure pretty much everything the rest of us are forced to read in school. He is thus incredibly well-read and extremely literate and articulate. He now has his own show, a Peabody Award, and two well-received books to his credit. Keep in mind that in the British educational system, leaving school at 16 is equivalent to graduating high school in the U.S. Only those students seeking to move onto university (U.S.: "college") go to school beyond the age of 16, as they study up for their A-levels (exams intended to be used for entry into university).
In fact, this trope would partially apply to a majority of people in some countries. For example, studies show that, in France, people who have been reported to have a higher IQ than average (above one standard deviation from the average, meaning approximately superior to 130) are also globally low achiever at school. They have lower ratios of success at the "Baccalauréat" (High School graduating exam), and a higher proportion of them drop school before actually taking the "Baccalauréat". This might or might not be true in other countries as well (since this troper lacks data to analyse the phenomenon on a broader scale). This is frequently believed to at least partly stems from the rather rigid and conformity-oriented French education system and the lack of formation of teachers relatively to this matter (although significant changes have been made thanks to governemental initiatives).
The late stand-up comedian Mitch Hedberg. During an interview, he revealed that he lost interest in being book smart around 10th grade and barely graduated with a high school diploma. He also lampshaded it a bit with this great one-liner:
I never went to college, but if I did, I would've taken all my tests in a restaurant because the customer is always right.
Quentin Tarantino never finished high school but has been tested with having a genius-level IQ and has an encyclopedic knowledge of film. He also admitted in an interview that he loved his history classes.
Christopher Titus brings up that he barely finished high school and that he still had a substandard education at "California public schools." While not academically intelligent, his stand-up routine brings up a great deal of fantastic insights into human interaction and the importance of self-awareness. In his podcast he also points out that his close friend (and fellow podcast member) Tommy Primo was actually put into special ed only because he was too hyperactive to pay attention and was a troublemaker, one time even jumping from the second story of the school to escape some teachers. Tommy eventually became a stuntman (among others, doing work on Titus) and was asked back to the school for a career fair.
Ringo Starr was notoriously uneducated due to years spent in the hospital as a child, but he was far from unintelligent. Besides being an excellent drummer, he had a very quick wit even for a Beatle.