I believe that my job as a math teacher is not to make things as easy as possible for my students. I do not give them the shortest explanation with the most straightforward formula and ask them to solve different versions of the same exercise for homework and tests. I do not tell kids how to do problems from the next section in the textbook so that their 1-29 odd homework will be as painless as possible. I will not become impatient and compromise a deep conceptual understanding and let kids get away with just knowing the procedure.
Or at least I try really hard not to do these things.
I always let kids explore an idea and try to build an understanding themselves before I tell them anything. I will give homework problems that are unlike any problem we've talked about in class. I do think "play with it...look for patterns...make observations" is a legitimate homework assignment. I do ask students to work on messy problems, problems that I don't know the answer to, and open problems. I have let kids leave the classroom with a misconception that I know about and did not address.
Or at least I try really hard to do these things.
I see the need to teach math as a verb. I teach the activity of doing math as much as I teach the subject of math. This means teaching kids to enjoy, embrace, and feel confident working with hard problems that they won't solve in thirty seconds, five minutes, one sitting, one week, or maybe ever. This means caring about beliefs, perceptions, and attitudes as much as I care about fractions. I want kids to enjoy the process of thinking, playing, trying, failing, and lots of other -ing words.
But this post isn't my call for you to see the wisdom of my ways and throw out your lesson plan for tomorrow. No, it is a plea for help. Tonight I don't need help with fractions. I need help with teaching the activity.
This student has been on my radar after an email from the father about frustration at home and "disliking math for the first time." A conversation was had, but I now know that the attitude equivalent of a deep conceptual understanding has not been made. The one positive note is that the student is talking to me about this instead of repressing these feelings that will develop into yet another adult who hates math.
Via email: " I just want you to know that even though you said [all] the [homework] problems aren't mean't [sic] to be finished sometimes when you hand in unfinished work it can make you feel stupid and like you failed. I thought that that was something you should know."
So any ideas on how to teach "the activity of not finishing problems in five minutes" to a super smart sixth grader who still participates actively in class but is clearly not enjoying math on the home/homework end? If it helps, here and here are the homework assignments that sparked this frustration.
It also might be helpful to know that my policy is that students should spend no more than 30 minutes on homework. If they spend any more than 30 minutes it should be because they'd rather be doing this than playing, reading, running around outside, talking with friends, or whatever else they're allowed to do. For these two assignments, the first 2 problems gave me all the information I needed to know about their understanding of the content at hand. Aside from the students who tried to compute 2 to the 57th power, everyone made it past #2 but only a handful finished the sheet(s).