eNumeracy

OK, I've had a lot of discussions about this. Here's the scenario:

Kindergarten classroom, 9:30 A.M. Groups of kids sprawled on the floor with crayons, multi-colored manipulatives, and a blank worksheet supposedly meant for reproducing the pattern that they create with the manipulatives. The lesson goal appears to be "create an ABCA pattern." Figuring in transition time, to the full lesson, we're talking about close to 40 minutes. With regard to allocated time in instruction per day, we're now talking about more than 20% dedicated to this activity.

While I watch, I circulate around, asking each child what they are doing. They respond:

"Coloring," says Marcus.

"Patten-ing" says Brianna.

"My favorite color is green" says Michaela.

Now, without regard to basic issues of pedagogy, instructional classroom mangement, and generic lesson design, I didn't see much in the way of multiple opportunities to respond with immediate feedback that is corrective when necessary. As a matter of fact, each student seemed to get about 1 minute each with the teacher during this practice time. Something is wrong. A lot of somethings is wrong. Now, it's my turn to talk to the teacher.

I ask, "do you regard this lesson as a math lesson?" Unequivocally and emphatically, and with a quizzical look, she answers, "yes - patterning is fundamental." She goes on to indicate that they'll be doing this for another week. "Tomorrow is ABCAB," she adds.

Our number system is a base-10 redundant system with clear numerical patterns (seven groups of 3 is 21). This is not in doubt. However, the connection with fundamental ideas of number sense such as enumeration, domparing and ordering, partitioning, grouping, composing, and decomposing, where does he ABCA call home? OK, it's grouping. What if the kids engaged in the process haven't yet mastered the cardinality principle, which solidifies that they have a decent idea that a group is defined by the number in the set. Let's say they've got this figured out - what if they don't know that the cardinal "four" means two and two more things, or three and one more thing?

Without regard to the instructional management problems here - where exactly does ABCA patterning fit into the concept of number sense? What are the prerequisites? Where does it belong in the curriculum? Does it belong in the curriculum? What sort of supports and training does this teacher need?