A Hypothetical Learning Progression for Quantifying Phenomena in Science

In this article, we report on a three-pronged effort to create a hypothetical learning progression for quantification in science. First, we drew from history and philosophy of science to define the quantification competency and develop hypothetical levels of the learning progression. More specifically, the quantification competency refers to the ability to analyze phenomena through (a) abstracting relevant measurable variables from phenomena and observations, (b) investigating the mathematical relationships among the variables, and (c) conceptualizing scientific ideas that explain the mathematical relationships. The quantification learning progression contains four levels of increasing sophistication: level 1, holistic observation; level 2, attributes; level 3, measurable variables; and level 4, relational complexity. Second, we analyzed the practices in the Next Generation Science Standards for current, largely tacit, assumptions about how quantification develops (or ought to develop) through K-12 education. While several pieces of evidence support the learning progression, we found that quantification was described inconsistently across practices. Third, we used empirical student data from a field test of items in physical and life sciences to illustrate qualitative differences in student thinking that align with levels in the hypothetical learning progression for quantification. By generating a hypothetical learning progression for quantification, we lay the groundwork for future standards development efforts to include this key practice and provide guidance for curriculum developers and instructors in helping students develop robust scientific understanding.