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The Development and Psychometric Modeling of an Embedded Assessment for a Data Modeling and Statistical Reasoning Learning Progression

  • Author(s): Schwartz, Robert Andrew
  • Advisor(s): Wilson, Mark
  • et al.

Data modeling is an approach that helps students to transform initial, and often misguided, understandings of variability and chance to forms of reasoning that coordinate chance with variability by designing learning environments that support this reasoning by allowing students to invent and revise models. The Assessing Data Modeling and Statistical Reasoning (ADMSR) project is a collaborative effort between measurement and learning specialists that has developed a curricular and embedded assessment system based on a framework of seven constructs that describe the elements of statistical learning. Taken together, the seven constructs described above form a single learning progression.

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 research applies different measurement models to the data from the ADMSR project. Unidimensional item response (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. Longitudinal and multilevel IRT models are applied to model the change in students' abilities to see if students improved on the constructs after instruction. Finally, 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.

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