It's been a long time since I posted about the Numeracy class, mainly because I am not teaching it this year, so it's no longer at the front of my mind. But, this year's Numeracy teachers are struggling with the same concepts that I did. One of these killer concepts is rounding. This does not seem like a very difficult idea, but for our students, learning how to round a number is a huge challenge. We've tried all sorts of scaffolding, conceptual development, practice with the algorithm, and some kids just can't get it.
Ultimately, we think it comes down to a continued lack of understanding of the base-10 system. These students missed out on some very important mathematics in their first few years of school, and this is making everything else inordinately difficult for them. This week, one of the classes is piloting an activity where the students have the goal of collecting one million pennies. Each day, students will have to count how many pennies there are so far (pennies will initially be collected in a big jar). The idea is that students will eventually lose patience with this, and propose the idea of some sort of stacking or grouping. The teacher will then magically produce a container that has slots to divide the pennies into groups! When groups of 10 are no longer enough, then bigger groups of 100 will be used, and so forth.
Aside from learning more about the base-10 system, and the relative sizes of the different places, we hope that this activity will help students understand more about large numbers. We do an activity in the class where the whiteboard is divided into categories (thousands, millions, billions, trillions), and teams are given strips of paper with a quantity and a number, anad they must stick it to the board in the right column. For example, a strip might read "Number of people in San Jose (1)", or "The average income of a family of four (50)". It should come as no surprise that students usually have no idea where to put the strips of paper. In any case, this year's students seem to really doubt that there are about a million people in San Jose - they think the number is bigger by orders of magnitude. With the pennies activity, students will hopefully see that reaching a million is a bit harder than they think. But if they do reach a million, they will definitely earn their pizza party!
Wednesday, October 25, 2006