I recently read an article called, "Teaching Students to Think," from the Educational Leadership Journal that can be found on-line. After reading this article, I realized just how important the process is for teaching students new material. This article suggests that students sometimes can have problems thinking on their own to come up with solutions. Also, it highlights the issue that in can be hard to always teach lessons that inspire students to think on their own. For example, when the teacher was working on an algebra lesson, it became more important for the students to memorize the steps and not actually to understand why they were learning them this way. The teacher was concerned about their upcoming test and memorization and repetition are sometimes the best way to get students to learn in a short period of time.
However, this type of "rote" teaching can hinder students in the future. They talk about how some college students have difficulties once they enter into higher-level classes. Professors expect them to know how to come up with solutions on the own. Instead of teaching step-by-step through a problem and giving the students examples, they teach the theory as to why this works and expect the students to come up with the rest on their own.
Both of the methods of teaching present a problem to students and teachers. Teachers have a hard job with trying to balance motivating students to think on their own as well as creating useful memorizing techniques to help with difficult problems. Students on the other hand can struggle with transitioning from one teaching style to the other. A student that has always had things laid out for them will find it difficult to come up methods of solving problems on their own.
Personally, I have experienced this difficult transition when I went from my high school calculus class where my teacher was very helpful and did many examples to my freshman college calculus class where my professor stressed theorems, proofs, and theory. Not once during his class did he do an example for us to demonstrate how the theory actually works. Needless to say, his teaching style did not suit my needs as a student nor did it for the majority of the class. It's very frustrating to go in knowing you are a smart student and to be completely leveled by an over-the-top difficult test. I struggled so hard to get a passing grade in the class. In the end I did pass, but I would say about half of my class either dropped or failed by the end of the semester. I really viewed it as lose-lose situation. It had to be just as frustrating for him to see his students just give up.
I definitely think that there is a fine line that teachers need to find in challenging students to think on their own, but also to provide examples and help when things become confusing. To me, a teacher that can find this balance is a great teacher. They are able to understand when things get too hard for their students and instead of having them want to quit, they are inspired to push through and succeed.