"There is no way my students could handle this."
"This is too hard for my students."
"Good luck teaching that. That's way above their heads."
If I complained that I didn't think that particular topics under discussion were that hard, I would get these answers:
"You don't have experience with (insert your favorite k-12 grade) students."
"You haven't been in our school."
These statements are correct. I do not have yet that much experience with K-12, but I am fairly positive that students respond to unstated expectations very well (and stated ones even better). What I mean by that is: if your students believe that you think they can not learn math or that the math is just too hard for them to grasp, then they do not have much incentive to prove you wrong. After all, you are the expert. However, if you set the bar high for them, their performance and in the process you let them know that YOU think they are able to become good in math, then they will try harder to prove you're right. I do think that the attitude teachers have influences greatly their students. The reason I am writing about this is the book I just started reading: The Teaching Gap by Stigler and Hiebert. I have a couple of quotes that I'd like to share:
One of the most striking impressions when watching the videotapes is that students in teh United States encounter a different kind of mathematics from that encountered by their peers in Germany and Japan. The content appears to be less advanced and is presented in a more piecemeal and prescriptive way.
As it turns out there were NO mathematical proofs in U.S. lessons. In contrast, there were proofs in 53 percent of Japanese lessons and 10 percent of German lessons.
Incidentally, German students did not perform significantly better on the achievement test then American students. The following figures also made quite an impression (I hope they will look decent):
Average percentage of topics in eight-grade mathematics lessons that contained topics that were DEVELOPED or STATED.
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