An Examination of Variability: Using Construct Measurement to Develop an Interdisciplinary Assessment

Abstract

In an increasingly data-driven society, making decisions with data is a requirement not only for research scientists but also for navigating life more generally (Kjelvik & Schultheis, 2019). An informed citizenry must be prepared to discover patterns, predict outcomes, make decisions with data, and evaluate data-based claims for legitimacy and applicability (Franklin & Bargagliotti, 2020). In United States K-12 classrooms, the expectation of using data to support claims is an essential part of research methods at each level of science instruction. In fact, NGSS standards include analyzing and working with data at every grade level. Usiskin and Hall suggested that for most K-12 students, making decisions based on statistics is discussed more often in science than in mathematics (2015). Statistics instruction, however, has been primarily the responsibility of mathematics teachers. Consequently, conventional instruction of statistics in K-12 mathematics often presents computational aspects of statistics and stops short of experiences that allow students to explore and apply statistical ideas of measuring variability in context. Independent of instructional support, it can be difficult for students to knit together these ideas of calculations and context across disciplinary boundaries of math and science (Lehrer & Schauble, 2004; Makar & Confrey, 2003). Assessments are a tool that could support developing statistical literacy, revealing students’ construction and integration of knowledge and skills acquired across multiple subjects when focused on interdisciplinary ideas, such as variability. Using the four building blocks of Wilson’s (2005) framework for constructing measures, I developed assessment instruments to assess patterns of student thinking about variability for 6th-grade mathematics and science teachers. The assessment instruments were designed to collect evidence of connections students make between quantitative and qualitative descriptions of variation by prompting students to utilize statistical and scientific ideas. These assessments encouraged student thinking rooted in both mathematics and science and provided teachers in both disciplines with a more complete representation of students’ growing understanding. Thoughtful completion of the items required integration between science content knowledge and the understanding of the phenomenon arising from the data as students interpret and explain based on the contextualized data rather than simply focusing on computation or data manipulation (Ben-Zvi et al., 2012).