A lesson she might have learned: It's a big world out there, and some of it, e.g., the view of women in that store, is not good, and sometimes, too often, in life we have to be selective.
It's been a while since my brother and I were in grade school and he was collecting comic books. So, only vaguely do I remember Donald Duck and Batman, and those comic books weren't right up against the line, the other side of which was porn.
Instead, say, take your seven year old daughter to a music store, not one for pop music but one where seven year old girls have a nice violins and are learning the "Preludio" to the Bach E major Partita for unaccompanied violin,
https://www.youtube.com/watch?v=2KYRdRnnBYw
with Hillary Hahn, the Chaconne of Vitali,
http://www.youtube.com/watch?v=i4B1ifcWa9o
with David Oistrakh, the Bach "Chaconne"
http://www.youtube.com/watch?v=Tezau3hlRxs
with Alina Ibragimova, or the Bach Busoni piano version
https://www.youtube.com/watch?v=sOFflFiLlT8
with Valentina Lisitsa, a store where the seven year old violin students are looking forward to playing the violin part to the Wagner "Prelude to Act I" of Lohengrin
http://www.youtube.com/watch?v=7prUFflX0_E
with Otto Klemperer, also from the same opera In fernem land
https://www.youtube.com/watch?v=hHHCeEO_0-4
with Peter Anders and, of course, especially since she is a seven year old girl, starting at about 3:00, the bridal chorus
https://www.youtube.com/watch?v=ebx9KhcnyLM
with Andris Nelsons. Of course, also tell her the story of Lohengrin.
More? Sure: Camille Saint Saens "Mon coeur s'ouvre à ta voix" from Samson et Dalila
http://www.youtube.com/watch?v=X79OkSayPSw
with Elina Garancas.
More generally expose her to places and media content where girls and women are actually doing things, good things. E.g., currently there is the Nova program on he LHC and the Higgs boson at
http://www.pbs.org/wgbh/nova/physics/big-bang-machine.html
Two detectors there found the same basic result, and one of the detector groups was led by a woman. That program has more examples of women doing things.
Yes, there's a lot out there where the women are all interested in nose jobs, breast implants, micro skirts, and thong panties, but there's also a lot out there for women being productive, building a home and family with love, victory over loneliness, being productive, and with pride in accomplishments and emotional and financial security.
Get her a copy of the classic E. Fromm, The Art of Loving which is about getting emotional security, exchanging knowledge, caring, respect, and responsiveness, and a role for religion -- best thing I ever read to understand people and personality.
Maybe take her to some Saturday classes in cooking school where she can learn to make, say, some really good cookies she could make and share with her friends, e.g., at school. If I were 7-9 and a girl 7 gave me 2-3 really good cookies she had baked herself, then she would have a good friend for years, prom dates, etc. If she could play classical music on piano or violin or sing opera, even better.
How to get her interested in working hard on, say, piano or violin? One way: Let her hear some of the music that is easy to like. Then let her see some people working hard on learning piano or violin and liking it. Example: A sister in law tried to get her daughter interested in piano. No luck. At the farm at Christmas, I was upstairs working on the Bach "Chaconne", and a niece, about 7, came up to watch. I put my violin under her left chin, showed her how to hold the violin and the bow, and to draw the bow across the strings. The next day her father asked me: "How much is a violin going to cost me?". It works.
More? Sure: Get her the DVD of the Australian Ballet performance of Coppelia -- it's a total sweetheart story, nearly all about young women, and where nearly everyone on stage is a young woman. And the actual young women on the stage, the real performers and not the characters they play in the story, are examples of astoundingly hard work, productivity, and, in particular, are just fantastic as actresses, artists, and athletes, especially aerobic athletes.
Of course, at Christmas, get her all dressed up in some sort of a princess outfit -- when I was that age the style was dresses with red or black velvet with lots of satin ribbons and bows -- and take her to a good performance of The Nutcracker. Also get her a Nutcracker doll. It could be one of the happiest times of her life, make her feel more secure as a girl, and be a memory she will have and value forever.
Also get her DVDs of some of the movies from American Girl. They may also have some retail stores it would be better for her to visit than that fake comic book store.
For books, maybe Nancy Drew? Or something similar but more recent?
Since she's seven, a girl, and bright, it may be that she could get good at French with blinding speed -- try to find a way. Talk to some people who know about how a girl of seven could learn French. Maybe have her join a group, e.g., where also she could meet other girls learning French. Maybe try a local Alliance Française. Maybe try some Internet learning materials.
Connection with her being a girl? At that age, typically girls have much better verbal aptitude than the boys and are just fantastic at learning a language.
Be sure to have her learn touch typing -- one of the best skills to have in life now. Talk to some people who know how a girl of seven could learn touch typing, get her some materials, and pay attention her efforts, encourage and praise them, and help her learn.
Then encourage and praise her in writing: Have her start writing on nearly anything -- letters to grandma, how to train a kitten or puppy, how to bake terrific cookies, how to tie a bow tie, how to wash out stains, how to iron a dress, how to sew on a button, how to use a text editor, how to use Facebook, blog posts (anonymous), etc. Then get her started on English grammar -- sentences, subjects, verbs, prepositions and prepositional phrases, adjectives and adverbs. Then make friends with a high school English teacher (nearly all women, right?) and have that teacher help your daughter improve her writing. Then have your daughter write some longer pieces with sections, subsections, table of contents, figures, references, etc. on anything: If your family moves, then have her write on moving to a new house. On getting a puppy or kitten. Whatever. Get her going on writing, then reading, the more in writing, then more in reading.
For being better in talking to her, and to others, too, get, read, study, think about, and use
Thomas Gordon, Parent Effectiveness Training: The Tested New Way to Raise Responsible Children.
also called reflective listening.
For more, get her several, used will be fine, high school texts in plane geometry, pick a favorite, use the others for alternative sources, and work through plane geometry with her, that is, get the fun of doing the proofs. Emphasize orthogonality and the Pythagorean theorem: Orthogonality is one of the most important ideas in all of pure and applied mathematics, mathematical physics, engineering, multi-variate statistic, and best approximation, e.g., in computing, right up to how to do ad targeting on the Internet, Fourier theory, the fast Fourier transform, digital filtering, etc. Sure: Quite generally every closed convex set has a unique element of minimum norm, and quickly get to a supporting hyperplane with orthogonality. Sure, one of the biggest results in college math is the polar decomposition in linear algebra and, right, about orthogonal eigen vectors. Can get going on orthogonality right there in high school plane geometry, and she likely has all the prerequisites. If not, in a few places take out a few minutes and get her caught up.
Give her a little on electrons, protons, neutrons, atoms, energy and energy levels, and chemical bonds. Then, right, presto, bingo, guide her to the Internet videos of the Eric Lander lectures on biology at MIT, say,
http://ocw.mit.edu/courses/biology/7-01sc-fundamentals-of-bi...
Also, don't have her miss (get her a bowl of popcorn for the occasion)
http://www.princeton.edu/WebMedia/flash/lectures/20100419_pu...
with
April 19, 2010,
Eric Lander: "Secrets of the Human Genome"
Sure, have her watch some Brian Greene videos.
Get her a freshman college chemistry book and help her work through it, learn about NaCl, CaCO3, C-H bonds and methane, gasoline, and converting O and C-H bonded hydrocarbons to CO2 and H2O -- e.g., as in heating the house, powering the car, flying an airplane, etc.
Look at the GED materials and get her through all of them by the time she is 8-9. A bright girl of seven should be able to get through all of that in one not very busy summer.
The GED materials are minimal -- in particular in addition she will need to get through algebra I and II and trigonometry and high school physics.
Then, to heck with high school -- then get some good advice and guide her in home schooling through, say, at least the first two years of college. So, for calculus, just get her some good college calculus books (my view of AP calculus is that it is to be avoided, skipped, ignored because the authors didn't understand calculus very well -- similarly for Khan Academy -- repeat, just get some good college calculus books, period), and, sure, make friends with a college math prof to help her not get stuck and to stay on track. Then, sure, have her do college freshman physics -- that's heavily just what calculus is for.
Then when she goes to college she will be nicely ahead.
"Youth is such a wonderful time of life. Too bad it's wasted on young people."
Don't have her waste hers.