Using Work Samples from the National Assessment of Educational Progress (NAEP) to Design Tasks that Assess Statistical Knowledge for Teaching

Abstract

Statistics courses for prospective teachers are being developed in response to recent K-12 curriculum recommendations. As these courses are developed, it is important to design accompanying assessments. This manuscript describes a strategy for assessing aspects of statistical knowledge for teaching. The strategy involves analyzing and responding to children's work samples from the National Assessment of Educational Progress. An example is provided to illustrate how such an assessment task can serve to reveal different aspects of respondents' subject matter knowledge as well as their pedagogical content knowledge. Thoughts are provided on how to use the assessment tasks to identify levels of statistical knowledge for teaching.

The Look Of Pedagogical Content Knowledge In Middle School Statistics

“…Only 26% of their participants were able to make general statements and suggest improvements. Groth (2014) found that 85% of his participants were able to identify a student with a more sophisticated response about which measure of center to use; however, the majority of his participants were not able to give specific suggestions to the less sophisticated students on improving his understanding. Ijeh (2013) found that most of his participants taught the subject of statistics, particularly graphical representations of data, in a step-wise procedural fashion and linked that teaching to student misconceptions about graphical displays, analysis, and interpreting of scatter plots.…”

“…Like Godino et al (2008), Groth (2012Groth ( , 2014, Mercimek and Erbas (2017), and Sorto and White (2004) also worked with PSTs. Groth (2012) used writing prompts to help asses and develop content and pedagogical knowledge of his students.…”

“…Although scholarship on different embodiments of MKT is vast, there also exists research on the understanding of SKT. SKT became a subject of research projects with in-service teachers outside of the United States (Burgess 2007(Burgess , 2009a; Estrella, Olfos, & Mena-Lorca, 2015;Watson, 2001;Watson, Callingham, & Donne, 2008;Watson & Nathan, 2010) as well as research done with preservice teachers (PSTs) in the United States (Groth, 2014). Much of the research on SKT with in-service teachers outside of the United States is concentrated around Australia with Watson and colleagues (Watson, 2001;Watson et al, 2008;Watson & Nathan, 2010), who have developed, and validated, different assessments in understanding teacher knowledge including pedagogical content knowledge (PCK) (Hill, Ball, and Schilling, 2008) within statistics.…”

“…As previously mentioned, research in SKT has been lacking, with most of the work done with PSTs and little work done with in-service teachers especially in the United States. The work done in the United States has concentrated mostly on PSTs (Groth, 2014). Because the CCSSM (NGA & CCSSO, 2010) has been adopted as the new implemented curriculum in most states, there is a need for research to be done with in-service teachers to understand their knowledge of pedagogy.…”

“…However, when it comes to presenting evidence of what teacher knowledge looks like the research is fragmented at best (pre-and in-service teachers; Estrella et al, 2015;Groth, 2014;Ijeh, 2013;Mercimek & Erbas 2017;Sorto & White, 2004;. In this section, I introduce some of the most prevalent frameworks hypothesized and used in understanding and explaining PCK within statistics, and then I discuss some of the research that shows what teachers' PCK looks like within SKT.…”