To Show Or Not To Show (Work)
For many years, I've insisted to see math problems solved with work shown. Because of the complexity of math in the future, it's important that students take time to organize and detail their work. That's not something that fifth graders can possibly understand--there's no sense of future in their minds. So...
"Rather than wrestling with students to 'prove' solutions with 'work,' simply increase the complexity of the problem so they must do the work out to get it right."
In Texas, we spend a great deal of time leaving no child behind, but that really means that we spend a disproportionate amount of time with the low-ability students. In itself, that's not a bad thing--if a student can learn but takes five-times as long to do it, we remain patient and do our job. Did we sign up to teach kids or to teach bright kids? Unfortunately, in spending that time and effort, we tend to neglect other types of students. So, like me, you vow to give as much time and effort to the high-end students. Therefore, for every lesson, we must be prepared to push those students, having problems or challenges ready to go. Heck, we're smart enough to anticipate the ease with which some students learn the material, so we owe it to them to have something ready.