Can a Number Be Both Even and Odd? Discuss

I wrote a few weeks ago about a math teacher and professor that was profiled in the NY Times magazine for showing that teachers who know and are comfortable with math are better able to teach it (as measured by how well their students do). The magazine article highlighted an example of a discussion in that teachers' class of 3rd graders about whether the number 6 could be both even and odd at the same time. In case you didn't find the video on your own, here it is. Check it out, its a pretty remarkable discussion (it would be remarkable even in many college math classes).

One thing this discussion highlights is the difference between what a virtual laboratory, e-textbook, online tutorial, or other computer activities can do, and what a good teacher is capable of. The computer-based activities could certainly help the students distinguish between even and odd, and understand the difference between even and odd. But only the good teacher can get a discussion going that makes the students think hard about what even and odd really mean. That's a deeper conceptual learning and a way of thinking hard about a problem that will serve these students well in many potential future careers and in life in general. Ideally, I would hope the kinds of biology labs we build make it faster and easier for the teacher to get to those kinds of discussions, but this is a perfect example of why computers cannot and should not replace teachers.