Improving Learning: Using a Learning Progression to Coordinate Instruction and Assessment

Abstract

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We describe the development and implementation of a learning progression specifying transitions in reasoning about data and statistics when middle school students are inducted into practices of visualizing, measuring, and modeling the variability inherent in processes ranging from repeated measure to production to organismic growth. A series of design studies indicated that inducting students into these approximations of statistical practice supported the development of statistical reasoning. Conceptual change was supported by close coordination between assessment and instruction, where changes in students’ ways of thinking about data and statistics were illuminated as progress along six related constructs. Each construct was developed iteratively during the course of design research as we became better informed about the forms of thinking that tended to emerge as students were inducted into how statisticians describe and analyze variability. To illustrate how instruction and assessment proceeded in tandem, we consider progress in one construct, Modeling Variability. For this construct, we describe how learning activities supported the forms of conceptual change envisioned in the construct, and how conceptual change was indicated by items specifically designed to target levels of the construct map. We show how student progress can be monitored and summatively assessed using items and empirical maps of items’ locations compared to student locations (called Wright maps), and how some items were employed formatively by classroom teachers to further student learning.

Keywords

• learning progression
• data modeling
• statistical reasoning
• item response models
• Rasch models