Learning Progression-based and NGSS-aligned Formative Assessment for Using Mathematical Thinking in Science

Purpose: The goal of this four-year project was to develop and validate an NGSS-aligned and Learning Progression-based assessment tool for Mathematical Thinking in Science (MTS) at the high school level. MTS refers to abstracting relevant measurable variables from 'messy' phenomena, identifying mathematical relationships among the variables, and using scientific ideas to explain the mathematical relationships. Learning progressions (LPs) are 'descriptions of the successively more sophisticated ways of thinking about a topic that can follow one another as children learn about and investigate a topic over a broad span of time' (National Research Council [NRC], 2007, p. 219). The assessment tool contains: 1) a mathematics component, where mathematics items and associated rubrics are used to measure students' baseline understanding in 'pure' mathematics; 2) a science component, where an MTS LP, associated items, and associated rubrics are used to measure students' MTS in two NGSS core ideas (energy in physical sciences and ecosystems in life sciences); 3) and a score reporting component that uses the automated scoring engine to generate real-time reports on students' performance in mathematics and MTS.