math creativity

So I tutor kids at Murrah High School in geometry but mainly algebra 1. I was working with one boy on factoring and the quadratic formula. He got to a problem where he needed to do the formula but did it in a weird way. There is a plus/minus sign in between the number and the radical and he just didn't put it in there until the very end when he got his answer. I asked him why he did it that way and he told me that throwing it in there while having to work the problem confused him. He always got the correct asnwer so I let him keep doing it his own way. It reminded me of what we were talking about in class today... about school and creativity and the teacher knwoing when to let the student do their own thing and explore ways to get the answers. It was really cool to see it happen first hand. I want to be a teacher and I think experiences like this one will help me to know when to let a student do things there own way. I hate it when teachers are so strict about a procedure especially when there are multiple processes that will get you to the right answer. Teachers need to want to teach and be very open minded to new things. Teachers also need to allow time to actually explain a method rather than just throw random examples on the board. What good is it to keep building and building on the material you're teaching if no one understands the basic building blocks? Teachers do have pressure when it comes to standardized tests. I went to a public school where we were number one for a very long time and had the highest public school test scores. I was force fed so much material to ensure that I did well on the test. and I did do very well but that doesn't mean I actually understood what I was doing. Thankfully I had many excellent teachers years after that explained and made up for my lack of comprehension as to why something was the right answer.