I often have students who will get stuck on a math problem or will not even know where to start. My students accuse me of giving them problems that are "too hard" or that I "never taught them about." I confess, I am guilty of giving challenging problems and pushing students to their limits. My reply to their claims of "too hard" is, "It's not too hard, you just gave up too soon!" To their assertions that I "never taught them" a certain concept, I reply, "I know. I want your brain to get a good workout today." At this point, I encourage my students to at least try to do the problem. I tell them to write something. "If you think the answer is 3, write down 3" I say, or "if you think the answer is elephant, write down elephant" (so far the answer has not been 'elephant' but I did have a student write it down once).
I noticed something interesting about my students as they struggled. There seemed to be a distinction between those who had no idea how to get the right answer but tried anyway, and those who had no idea and gave up without trying. Those who tried were usually the ones who were fairly successful in school (as indicated by their overall grades and dispositions). Those who gave up without trying were those who were not performing particularly well in most or all of their classes. Now, I do not bring this up to pick on any student or group of students, and I know there are a few factors that I am not considering. I only want to point out that there is a value in struggling, in trying, in working something out even when we do not know what the end result is supposed to be. I believe the willingness to try is a key to success in math (and in life). I believe that anyone can be successful at math if he/she will put in the effort. From my observations, I would even submit that the most important factor in a student's success in math is work ethic. If a student has the determination to solve the problem--however may tries it takes, and however much time it takes, and however many erasers it takes--that student will succeed!
Those are good thoughts. There is value in the struggle. "It is better to have tried and failed than never to have tried at all" because of what it does to you inside, and because, eventually, you will win some, which will boost your confidence. Possibly the ones who don't try lack confidence that they CAN win or get the right answer. I think trying and struggling boost confidence.
ReplyDeleteAaron,
ReplyDeleteThis is a great post. It made me think of the students I teach. It is interesting that those students who will get after the work and attempt to get it done on their own, are generally more successful. Those I need to prod a bit more are, of course those that still need to learn self motivation. This last year I tried to make sure all my students finished their math with 100% everyday. A lot of times this required a lot of handing the papers back. Most days I was able to get most students to that level, but it seemed that there was always one or two that no matter what I did, it didn't seem to happen. I suppose that is the point where teacher has done all they can!
It is true that a student who has a good work ethic is most likely going to be successful. I also spend a good deal of time trying to convince students that self motivation is the best motivation. I also tell them "I'd rather be a loser than a quitter." I don't know if that helps very much, but I am trying to help them develop the understanding that quitting is one of the worst things they can do for themselves.
Thanks for the great post. It is good to see I am not alone in trying to teach students motivation.
Jeff Corry
I tell my maths students that they must get stuck. It is inevitable and happens to me and everyone I know. New Scientist a couple of years ago had a great article arguing convincingly that Insight only ever follows Impasse. Dan Meyer has it right with 'patient problem solving.' But before dy/dan, there was this:-
ReplyDelete"Do not worry about your difficulties in mathematics; I can assure you that mine are still greater." - Albert Einstein