## Tuesday, April 17, 2012

### What comes after erwu-si?

In last week's post, I introduced the story of Wumania's struggle to find an efficient number system. This context, used during the first few weeks of a mathematics education course for preservice elementary teachers, provides learners with a fresh perspective with which to explore place value concepts. The previous lesson asks learners to predict the number system developed in Wumania given that it uses only the symbols found on their flag.

Problem Solving Workshop
Goal: The learner will use patterns found in various representations to identify the underlying structure of an unknown number system.

Scheme Activation: Sharing Our Predictions
Learners post the number systems they developed using the five symbols.
As the examples above show, the systems they create typically reflect an additive model - like those found in ancient cultures.

Focus: Problem Solving (from NCTM Process Standards)
• Build new mathematical knowledge through problem solving;
• Solve problems that arise in mathematics and in other contexts;
• Apply and adapt a variety of appropriate strategies to solve problems; and
• Monitor and reflect on the process of mathematical problem solving.
Activity: Part of the Picture
I introduce an artifact of the Wumanian number system with the following story:
Good news! We have found more artifacts from the lab of the student who solved the number system problem for Wumania. As they are cleaned and catalogued, they will be made available to you. Maybe the most exciting is this sheet containing various representations of the system. Unfortunately, there seems to have been some sort of accident in the lab. A major portion of the sheet is covered by what we are assuming is a coffee spill. Still, this is an amazing find and ought to support us in our quest to understand this new Wumanian number system.

[I created the artifact based on the ideas presented in the article, Using Language and Visualization to Teach Place Value. It is meant to immerse learners in multiple representations. This allows them to choose which information to focus on. Some learners focus on the patterns vertically, in a particular column, while others look for relationships horizontally.]

Reflection: Recount
• What did you do?
• So what new knowledge did you build?
• Now what problem solving strategies might you apply to make further progress?

1. Fun and important work for PD. So a Starbucks in Wumania would charge me \$11 for a tall mocha latte? Thanks!

1. I stopped by Starbucks and it looks like a Wumanian would pay between san and si dollars for a tall mocha latte. It would be around yiwu dollars for a venti. I hope this helps. (Are you thinking of franchising a Starbucks there?)

2. Thanks, David. My "\$11" was meant as yiwu-yi. No Starbucks, but The Coffee Bean though.

3. This is a really interesting idea David. I really like it. As a follow-up activity, constructing a numeral system that makes more sense than our current English language system would be very interesting, as would doing research into how other cultures do numeral systems.

1. Thanks, David. I tried to design a number system that has both symbols and language that make it easier to use than our system. Typically, each year at least one learner notices that the symbols' "nodes" represent its worth. And the language was written to take advantage of the strengths of some Asian systems which say 21 as "two-ten one."

2. Yeah, and the considerations that go into constructing a number system are pretty important, and obviously require mathematical reasoning. I know that you have developed this number system with those considerations in mind, what I'm suggesting is that the activity of constructing a number system (that is consistent and useful) is a powerful learning opportunity for students.