For the final blog post in this series, I wanted to address one of the questions that was asked at the October colloquium regarding ways to implement these types of tasks in the classroom. The Coordinating Units team has presented the tasks in stations within actual classrooms, and Ron Tzur’s research speaks of whole class settings in which the tasks can be presented.
This year, we worked in a second and a third grade classroom, running a rotating station. We grouped students based upon the level of task that was within their ability to learn. There were six students per group, and they worked in pairs. We set up large cups with connectable blocks a few feet behind the table which allowed the students to go build their towers. One student was the sender and one was the bringer. There was a cover for the towers to be hidden behind between each pair of students. We made printouts of the questions to be asked, which the students recorded their answers to, as well as a place for them to draw their scenario. We also created cards within sheet protectors in which there were printed the problem prompts. On the card, the number of towers and cubes per tower was a blank space where we would write in quantities. This allowed us to change problems quickly, giving the sender prompts for sending the bringer. We created these cards for each level, and it allowed us to change contexts easily just by changing a couple of words on a document.
The other possibility, described by Ron Tzur during his visit to the AIMS Center, was utilizing the towers task within a whole class setting. In this version of the task, the students line up with their partner facing them. There are blocks on the opposite side of the room. Students then perform the task in a similar manner as above, but the whole class would be working in pairs at the same time.
Either way, the students are given an opportunity to have hands-on experiences with real life scenarios in which composite units are tangible. Ron Tzur has seen students develop multiplicative concepts, similar to what we at the AIMS Center have seen in classrooms. One thing I want to stress is that the task itself is not important; the value comes from giving students meaningful opportunities to make sense of the structure behind multiplication. This series of blog posts that have described some ways to do that are just an example of opportunities we have used that have helped the students we have worked with.
If you try a variation of the tasks, we would love to hear about it. Please comment and feel free to ask questions as well. It would be great to hear stories from all of you teachers out there.