After providing my preservice elementary teachers with this coffee-stained Rosetta Stone, and giving them time to try to solve the place value problem, I begin pulling out other artifacts found in the Wumanian student's lab. These are intended to reinforce the efforts of those learners who are on the right track and redirect those who are still floundering. My rule of thumb is to pull out a new artifact whenever a learner asks, "Is this right?" (Please don't give away my little secret.) The idea is that the artifacts will enable them to monitor their own progress without relying on me to validate their work.
I might start with something simple like the ruler shown below. Except, I do not tell them its function - only that it was found in the lab. Therefore, it contributes to the mystery while reinforcing the place value emphasis in the Wumanian system.
The next artifact would be the clock. It does not add anything new to the exploration of the system. However, it does represent a familiar object to which they can connect. It suggests that their prior knowledge and experience will be of help in solving this problem.
The calendar offers the most support in completing the numeric portion of the Wumanian system. While it is a familiar object to the preservice teachers, its structure continues to hide some of the patterns necessary to completely understand the place value system. In other words, it does not completely solve the problem for them.
When the preservice teachers see the cards and the coins, the alien nature of the story becomes clear. One of the hardest things to avoid is constantly trying to translate from our system to the Wumanians' system. I believe this part of the story allows them to look at the new system from a different perspective. These artifact also provide certain clues to the structure behind the system and the numerals.
Finally, I introduce the lyrics to a song using the Wumanian words associated with the numbers. I have considered including a recording of the Wumanian student singing the song. The repetition in the language is another pattern that helps the preservice teachers to complete the Rosetta Stone worksheet. It also highlights one of the problems with the language associated with our system.
Once the preservice teachers have broken the code for the Wumanian system, we begin to consider how Wumanian children might learn how to add, subtract, multiply, and divide in their new system. This provides me the opportunity to introduce centers that might be used to develop operational fluency. A few of these centers will be shared in the next post.
I'm enjoying these posts. I've used base 3 and base 8 'alien' systems with math groups.ReplyDelete
Odd bases seem unlikely to evolve from creatures counting on two hands. I've used the justification that my aliens were almost always holding a baby in one arm, and so could only use one hand to count.
I'm glad you are enjoying this series. It's been a good reminder of how much fun I had developing this unit. There certainly is a desire on my part to be creative in my lessons but I want to steer clear of being entertaining.
As for the odd bases, a couple of thoughts: Who said the Wumanians have two hands? And if they do have two hands, then perhaps the Wumanians are more advanced and have developed a way to count on their hands all the way to yiwuwu-yiwu.