“…his colleagues (1986, 1987) aptly named it "pedagogical content knowledge," which significantly advanced the field. Researchers around the world probed the mathematical knowledge needed for teaching and began to find better answers (e.g., Adler & Davis, 2006;Ball, Thames, & Phelps, 2008;Baumert et al, 2010;Blömeke et al, 2015;Bruckmaier, Krauss, Blum, & Leiss, 2016;Carrillo, Climent, Contreras, & Muñoz-Catalán, 2013;Herbst & Kosko, 2014;Hill, Schilling, & Ball, 2004;Knievel, Lindmeier, & Heinze, 2015;McCrory, Floden, Ferrini-Mundy, Reckase, & Senk, 2012;Rowland, Huckstep, & Thwaites, 2005;Saderholm, Ronau, Brown, & Collins, 2010;Senk et al, 2012;Tatto et al, 2008;Tchoshanov, 2011). Studies have ranged from investigations of what teachers (and preservice teachers) know (or lack) (e.g., Ball, 1990;Baumert et al, 2010;Hill, 2007;Rowland et al, 2005;Thompson, 1984); what teachers learn from interventions, or other opportunities to learn mathematics (e.g., Borko et al, 1992;Hiebert, Morris, & Glass, 2003); to articulating positions about what teachers should know (e.g., Conference Board of Mathematical Sciences, 2001Sciences, , 2012McCrory et al, 2012;Silverman & Thompson, 2008).…”