Personal Concerns and Next Steps

I wasn't sure if I should put this blog under this title, or under questions and answers. While reading the text, I completly agree that students need to be able to explore questions on their own, without the teacher giving them the answer. But where do we, as teachers draw the line? If the students aren't getting anywhere, their frustration level grows. Even mine, while working on formulas for irregular polygons, was eventually shot. And I'm a college student. Obviously they wouldn't be working on something quite so high of a level, but for them, multiplication will be as difficult as advanced algebra is to me. Hints and helpful, and very useful up to a point. But what if I have a student who just can't figure it out? Would it be better to try and have a peer explain it? Or would they feel worse because their peer understood it, but they didn't? There's a difference between giving them the answer, and explaining the process. Explaining the process is okay to do, isn't it? They still find the answer and their own. And just looking at the incredible time constraint teachers are under to help students understand math, I'm not sure that students could realistically explore too many processes on their own. I know I'm rambling a bit, but I'm trying to work it out in my own mind. Is giving an explaination as to why a formula works enough, or are the students supposed to figure out the formula themselves? I want to be a great math instructor for my students, and give them a good, solid foundation in math. Having them actually enjoy it is one of my main goals, since I never got that as an elementary student. I'm just not sure the best way to go about it. I need to balance the needs of my students against the needs that the administrators and state force me to adhere to. Thanks for any help you can give me!
Mary Fink