March 12, 2009
Binary codes were used to create messages using an alphabet trimmed to the letters-
B D G H I J K L M N P R S T U V
The challenge was to design efficient codes which include "check bits" so that the codes not only detect coding errors, but also identify where the errors are.
Participants worked in groups to pose potential code strategies and to test conjectures. Mathematical connections were made to binomial expansions, matrices, and vectors.
The ideas and strategies presented were beyond the norm of high school mathematics, yet numerous standards were addressed.
Some of the AIMS Standards included are:
2.1.1 Display data as lists, tables, and matrices; make predictions and observations about patterns or departures from patterns.
2.1.2 Draw inferences about data sets from lists, tables, and matrices.
2.1.6 Evaluate the reasonableness of conclusions drawn from data analysis.
2.3.2 Apply appropriate means pf computing the number of possible arrangements of the items in each case to solve problems by distinguishing between situations where order matters.
2.3.3 Determine the number of possible outcomes of an event.
3.1.2 Describe and model patterns.
3.1.3 Determine a specific term of a pattern.
5.1.2 Select an algorithm that explains a particular mathematicsl process; determine the purpose of a simple mathematical algorithm.
5.2.2 Write an appropriate conjecture given a seet of circumstances.
5.2.3 Investigate conjectures by:
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| Bill McCallum introduces notation to model coding issues. | Ginger Ververelli, Jan Liston, and Melissa Hall share conjectures. |
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| Ron Hopley shares his code solution with John Willy, Ramarao Cheepurupalli, and Janice Takagi. | Crystal Bartels presents her conjecture to Joanna Stevens and Anne Chen. |
