Inventiveness

I don't think that inventiveness and creativity are rewarded much in schools.  For the most part, students are instructed to complete worksheets that ask questions taken directly out of the textbook and tested on said worksheets.  They do projects created by the teacher with little to no autonomy involved in the process.  Conformity, not creativity, is rewarded in schools. 

I think this lack of creativity in schools is sad, because creativity is an incredibly important skill in the 21st century.  Employers are looking for employees who can come up with new ideas and solutions to problems, not employees who look up the answer in a textbook.  It is amazing to me that the American education system knows what employers are looking for, and yet does nothing to drastically change curriculum as it needs to be changed.

I think the best way to "teach" creativity is to incorporate autonomy in classwork.  Let students choose their own method of completing assignments or let them create their own project.  Teachers could also ask questions in class that force students to think out of the box--things that don't come out of a textbook.  If students are given more freedom, I think they will flourish creatively and become more productive (and interesting) adults.

Reflectiveness

I think that many teachers and students find it difficult to reflect on things because that kind of thinking isn't what we've been taught in schools.  We have been taught to fill in blanks on worksheets and to use "process of elimination" on standardized tests.  To just think about things and what they mean is a foreign concept to most people.  This is sad, because reflection is a vital part of the learning process.  Filling in blanks or bubbles with a #2 pencil won't necessarily help you remember things.  Thinking and reflecting on a topic will actually teach students.

Personally, I reflect on things all the time.  I don't really talk very much in class because it makes me a bit nervous, but I'm always actively listening and thinking about what we are talking about.  That's why I think that "class participation" is a little bit overrated by most teachers and professers.  Some students think and some students talk, and a few do both.  I don't think that any one of these catagories is better than the others.  But alas, I digress.  I think that effective reflection can only happen when a student has really been stimulated  by a lesson.  If they aren't interested, they won't want to put very much thought into it.