Story: Gokusen is about a granddaughter of yakuza boss working as a math teacher in all-boy high school full of delinquents. The plot revolves around Yankumi (the heroine) getting her students out of trouble (kicking butts) and trying to keep her yakuza origin a secret, which is the source of all sort of gags. After all it is a comedy anime. Gokusen anime covers only a small part of the manga and even skips some of the stories from that small part. While anime is mostly faithful to the manga, it suffers from slow pacing. A single story in the manga can take one chapter and thats about 5 minutes of reading (because the dialogs are quirky and short). Now if you try to make a 20-25 minute episode out of that material it ends up being boringly slow. It's not visible in the first episode, because the first chapter of the manga is actually 3 times as long as most of the other ones. Another thing that lowers the story score slightly is the fact that they removed hints of Shin (one of the students) developing feelings for Yankumi. I kind of understand why they did that: it doesn't get far in the manga during the chapters adapted to anime. In other words they wanted to avoid leaving unfinished plot elements at the end of anime. Does it mean there won't be a sequel?
Animation: The art in the anime is improved in compare to the source material. They completely dropped the semi-chibi style, however the character designs are still very simple. Unfortunately they didn't include the ukiyo-e references in the anime, which is a shame. Also the animation is ok, but its certainly not top notch. The ED animation is worth mentioning, as it is very stylish.
Sound: Voice acting is good, OP and ED songs are very good, but there are only a few BGMs. Some of the BGMs are bad, but even the good ones get repetitive after a while. I didn't bother to check the dub, so I can't say much about it.
Characters: Yankumi is as likable as she is in the manga, but the fact that Shin's development got cut short lowers the characters score. The rest of characters are almost as fun to watch as they were in the manga, except for the dog. Yankumi does have a dog in the manga, but it has almost no role there and its just a normal dog (except for omakes). However in the anime they turned it\him into a secondary character, gave it a bigger role and turned it into a weird humanoid. The dog character is very annoying and lowers the this score even further.
Overall: Although the art is better in anime than it is in the manga, I recommend reading the manga version instead of watching this anime. But if you don't mind having an incomplete story and just want to watch something funny, then this anime might be for you. Just keep in mind it can get so slow at times that it gets boring.
P.S. I dropped watching the anime after episode 9, but I did check parts of the remaining episodes to see how faithful they follow the manga.