I have experience tutoring algebra and trigonometry one-on-one at the college level as well as experience in a commercial tutoring center working with young children on introductory concepts as simple as telling time and addition. (I have also served as an assistant teacher for first grade students in an art class.) The actual process--helping the student think about the problem and what it means and understand why the answer is what it is--is really pretty similar. Nearly all math can be viewed as counting (subtraction is counting backwards, multiplication is counting by groups, exponents are just a fast way to write a specific type of multiplication) and mathematicians have just found shortcuts to make it go faster.
The hardest problems for students at all skill levels are always the story problem, because even students who have mastered the algorithms of working out a problem often don't understand what any of it really means. When asked in written word form to solve a problem, the student often is stumped at how to even begin. Language is fluid, carrying multiple meanings, and it's sometimes tricky to understand what is really being asked. Once a story problem can be re-written as a simple (possibly lengthy, but still simple) math problem, you're almost done. The most important lesson in math, the one you will use (or fail to use to your frustration) throughout your life, is learning how to interpret a real-world problem using math concepts. The fancy calculator will do you no good if you don't know what to type into it. My goal with students is to help them understand more than just the assignment in front of them.
I prefer to meet with students in college study areas where we can sit at a table without distractions. The McCormick Tribune Campus Center (IIT near the Green Line) works well for me, but I'm willing to take suggestions for other similar areas accessible by public transportation.
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