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.]
- What did you do?
- So what new knowledge did you build?
- Now what problem solving strategies might you apply to make further progress?