Mapping a Data Modeling and Statistical Reasoning Learning Progression using Unidimensional and Multidimensional Item Response Models.

There are different ways to conceive and measure learning progressions. The approach used by the ADMSR project followed the "four building blocks" approach outlined by the Berkeley Evaluation and Assessment Research (BEAR) Center and the BEAR Assessment System. The final building block of this approach involves the application of a measurement model. This paper focuses on the application of unidimensional and multidimensional item response theory (IRT) measurement models to the data from the ADMSR project. Unidimensional IRT models are applied to aid in construct development and validation to see if the proposed theory of development presented by the construct map is supported by the results from an administration of the instrument. Multidimensional IRT measurement models are applied to examine the relationships between the seven constructs in the ADMSR learning progression. When applying the multidimensional model, specific links between levels of the constructs are analyzed across constructs after the application of a technique to align the seven dimensions.