2009 Projects:
 |  | Biomathematics |
| Project Directors: Robert Edwards, Peter Salamon, Imre Tuba |
The team of students will build on recent successes in analyzing metabolic activity of a microbial ecosystem [Dinsdale et al]. The project will forge new tools to characterize the chemical conversions taking place in the system. The mathematical prerequisites are linear algebra and discrete mathematics. Requisite topics in statistics and bioinformatics will be covered in the first two weeks of the project.
The characterization of ecosystems in Dinsdale et al. is based on canonical discriminant analysis. The project will explore alternative characterizations using various vector space methods including principal component analysis, maximum information components analysis, and related approaches. Abundant metagenomic data for use by the project is freely available (http://metagenomics.nmpdr.org).
 |  | Mathematics Education |
| Project Directors: Andrew Izsák, Joanne Lobato |
The Diagnosing Teachers' Multiplicative Reasoning (DTMR) project is developing a new kind of test that can be used with large samples of teachers and that measures teachers' capacities to reason about fractions, decimals, and ratios in ways that support students' thinking. We are combining results from case study research on students' and teachers' reasoning about these topics with a new class statistical models for tests called cognitive diagnosis models (CDMs). We are using the case-study research base to identify core components of reasoning and are using those components to build and validate one test form of 30 to 40 items. A strong research base exists regarding CDMs, but researchers have yet to develop instruments for these models from the ground up within the CDM framework. As a result, the project promises to interest both mathematics educators and psychometricians. Furthermore, our approach to test development could serve as a model for developing further instruments that diagnose reasoning in other areas of multiplicative reasoning and reasoning in other STEM content areas.
