In the math study groups we organize at home, we've moved past fractions and percentages into the wild and wonderful world of algebra. Translating a problem into an algebraic equations is somewhat familiar to J-, but the process of solving algebraic equations confuses all the kids. I have a feeling that we're either taking up the topic before the teachers have had a chance to adequately explain things, or the real-life situation ("Town") leaves the students little time to focus on other lessons. Well, it is what it is (this is becoming one of my mantras these days), so we just have to do our best.
The small-group format is still working well. We're going to try it with four kids to see if pairing them up to help each other will help the kids learn more effectively and build more confidence. W- has also checked out an armful of books from the library. I've been paging through "Real-World Algebra" and similar books to find some ideas for exercises the kids can relate to.
We try to liven things up with energy and amusing examples. They have to eventually become comfortable with abstract exercises such as 5n + 30 = 180, and it's difficult to make that more interesting. I don't want to just repeat the fake word problems of standard algebra textbooks, so I'm keeping an eye out for real-life situations in which I've used algebra myself. It can be hard to notice when you take math for granted, but math is everywhere, so I should be able to collect examples.
In the meantime, there are small things we can do to help them keep their attention on math or to remember the concepts more vividly. I tried this example for distribution:
2 * (number of lions + number of tigers + number of bears) = 2 * number of lions + 2 * number of tigers + 2 * number of bears.
I drew a lion, a tiger, and a bear instead of writing the corresponding phrases. =) Then J- said, "Oh my!" and everyone laughed.
The kids often forget that whatever they do to one side of the equation, they need to do to the other. As a result, J- once ended up with the interesting equation 2 = 4. Looks like we need to review how to use the equals sign. ;) We might try the see-saw metaphor. If you have a balanced see-saw, you can keep it balanced by adding or removing the same amount from both sides. You can keep it balanced by multiplying and dividing from both sides. If you add, subtract, multiply, or divide one side without doing the same to the other, you end up with an imbalanced seesaw. We'll see if that helps them remember.
Because we're discussing new material for them, we have to walk through the exercises together before they can try things on their own. When they try things out, progress can be slow and frustrating. We're seeing if we can take advantage of group dynamics by posing a question and encouraging the kids to talk out loud about the strategies they might use. They help each other out, too. The group format definitely pays off - seeing other kids struggle or succeed helps a great deal.
Do you have any favourite middle school group study resources or tips? =)