I am a junior in an undergraduate math/secondary education program. I am trying to learn what teaching styles work the best to help students learn and understand the material being taught. I have gained some valuable input from current teachers through this discussion. However, I also have an opinion on this topic. I have experience working with students from lower level elementary through college level math. Some students really understand the concepts behind doing mathematical procedures. These are usually the same ones who have no trouble memorizing basic formulas, such as area formulas, pythagorean theorem, etc. However, there are many students who memorize formulas long enough to be tested on them and then forget them. This type of learning must be prevented if students are going to have any usable knowledge when they are done with school. For example, I tutored a junior in high school just last week for the SATs. Her parents were afraid that she would have trouble with the math part even through her grades in school are good. When I heard that she had a 97 average in Pre-Calculus, I assumed that her parents worrying was unwarranted. However, when I began to work with her, I realized what the problem was. She had crammed for every math test for some time and really knew very little about the basic concepts. In fact on one problem on which she became stuck, I questioned her about what was wrong and she replied that she didn't have her calculator and needed to know what twelve minus five was. I tried not to act shocked, but you can imagine what was going through my head. The point is that she will study her review book and probably do okay on SATs, but will anything she "learns" really help her in the long run. The other thing that I found interesting was that she told me that the reason that she is bad at math and that she hates math is that she has had boring teachers every year for quite some time. I really don't think that this is just an excuse. While I know that putting variety into teaching math is often quite difficult, I firmly believe that the students level of understanding after such teaching is well worth the effort.