
Terezi's mother, "Eggy" Pyrope got pregnant as a teen--her family didn't approve, her boyfriend was already married, she wanted to keep the child anyway, long story. All Terezi ever really knew was that she lived in a small town with her mother but most of their family was elsewhere and that they never visited each other.
Eggy was very laid back and easygoing. She taught Terezi (by example, mostly) to be tolerant of others, even if their behavior seemed strange. She also let Terezi do pretty much whatever she wanted. She also was actually kind of scatterbrained and neglectful. Her family may have had a point about her not being the best suited for the single mother lifestyle.
Terezi grew up very self-sufficient. She had always had to take care of herself for the most part, because her mother was just not much of a caregiver--but she rarely actually felt neglected. Her mother provided plenty of emotional support and attention, and they had food most of the time. And when they didn't? Well, Terezi knew the way to the store, and where her mother kept her money. And if her mother was simply out of money? Terezi knew how to talk various neighbors into inviting the Pyropes over for meals.
Terezi's invitation to Hogwarts came as a complete surprise to Eggy, who frankly had never noticed the odd little things that happened around her daughter, but it explained a few things to Terezi, who had begun to suspect that she was more different from the other kids in Yarm than anyone else realized.
Once at Hogwarts, she was reasonably good at most of her classes... except for potions. For some reason, she just didn't have the knack. She decided that she wasn't happy with that state of affairs. She was getting fairly good marks in all her other classes! So she got some out of class tutoring.
From herself, because that's how she rolled.
Basically she was experimenting on her own with potentially dangerous ingredients she'd nicked from class. The extra practice did in fact help her with the procedures, even if she still didn't always get the amounts correct. Then in second year, one of her homebrew potions exploded in her face.
The nurse determined that she'd managed to blind herself, probably permanently.
Disturbingly, this also made her improve slightly at potions. (Since she now paid more attention to scent and feel, instead of relying on vision.)
Her proficiency in all her classes (save for history of magic) took a hit when she went blind, but she is working steadily to get back to her old levels. She remains pretty good at the theory part of her courses--it's the practical work. As previously stated, however, she is improving as she grows used to working with her blindness.
Terezi, Year 3
She continues to climb back up to previous levels of proficiency in her core subjects. Shinra, her friend in Ravenclaw, helps her with Transfiguration practical work, and she explains the legal system to him.
Additionally, she takes Divination, which she turns out to have a talent for, and Care of Magical Creatures. She hopes to interact with a dragon someday--this is a higher goal than before, where she merely wanted to see one. Sight is no longer an option, so the stakes are raised!
She particularly enjoys the "hatch a pretend dragon egg" assignment given this year.