First of all, make SURE that you are reading material with her that is on an appropriate level (or just a little above). If you are unsure where her reading level lies, try a couple of the online tests found here: http://homeschooling.gomilpitas.com/articles/060899.htm. I especially recommend the San Diego Quick and the Reading Level Estimator. Don't focus too much on the test results, none of these tests are perfect and students scores often vary from day to day, but this should at least give you a basic idea of her comprehension level.
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It can be tough to find books that are simple enough to tackle with low level readers but still interesting to them as young adults. Below are some that I have found that my students (about the same age as your niece) especially like:
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Bluford High series, by various authors (Eye of the Tiger, etc.)
Hoops, by Walter Dean Myers
Monster, by Walter Dean Myers (or, really, pretty much anything by this author)
Goosebumps series, by R.L. Stein
Tears of a Tiger, by Sharon Draper
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Once you have a good book to read together (your local library or her school library should hopefully have at least some of these if you are cash strapped) take turns reading out loud. You read a little, let her read a little, etc. Generally I have found that my kids with lower level reading skills really like to be read to, even though they won't always admit it. As you read, try to stop every so often and model for her what is going on in your head as you read a story. Reading comprehension is a way of thinking and of processing material. Showing her how you read will (hopefully) help her learn to go through the same process in her own head. Some of the things I focus on when reading with my students are:
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* Good readers make predictions. Stop reading every so often and ask her what she thinks will happen next. Will the main character get into a fight? What will Sara's mom say when she gets home? How will he ever get out of this situation!?
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* Good readers visualize. Depending on what type of artist she is you can either stop every so often and ask her to draw something (small) or just ask her what her mental picture is of the scene just described by the author. Do you think it is loud in that room? What color do you think his bedroom is? Ooh, I bet it is cold out! What kind of jacket is she wearing?
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*Good readers make connections. When you come to a point in the story, a word, character, phrase, image that reminds you of something let her know. You know what, this is like that time Jessica went to the park and fell off the slide! Remember how scared we were that she had broken her arm? Yuck, I bet it smells really gross in that house! Remember that time I left the pizza in the refrigerator for so long it started to smell? I bet that is what it smells like. Wow! I would be scared if I were there. I bet I would run away. Etc.
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The key here is to get her mind to process text, and not just let it slide by her eyes. A dictionary (for difficult words I presume) is a great tool for those school textbooks and assignments she has to read but doesn't understand, but a dictionary alone will not ever help her reading level increase. I suggest at least half an hour of reading something fun, both of you reading together whenever you have a chance. The more you model good reading strategies (out loud!) hopefully the more she will internalize. As she is reading, don't jump in right away with the words she stumbles over, let her puzzle through them. When she gets stuck, help her, but try giving her syllables instead of the whole word. If she is stuck on "challenged", for example, say, "It starts with 'chal-'" instead of giving her the whole word.
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I really admire you for what you are trying to do. Too often, these kids are given up on and then the problems simply pass on to the next generation. The suggestions I have given may seem simplistic, but if it is truly reading comprehension that is the problem, they should help her analyze a text.
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Please feel free to PM me if you would ever like some materials, book suggestions, or anything else. Good luck to you!