Effects of the first year of a three-year CGI teacher professional-development program on grades 3–5 student achievement: A multisite cluster-randomized trial

A Description of the Cognitively Guided Instruction Professional Development Program in Florida: 2013–2020

“…It is important to recognize that the guide for CGI workshop leaders does not attempt to define the one and only way to support teacher learning through CGI. Subsequent CGI PD programs-including those created by the authors of the guide for workshop leaders-vary significantly, employing structures such as workshops (e.g., Carpenter et al, 1989;Fennema et al, 1996;Moscardini, 2014;Schoen et al, 2018;2020), teacher work groups (e.g., Franke & Kazemi, 2001), and university classes for preservice teachers (e.g., Philipp et al, 2007;Vacc & Bright, 1999). CGI PD models have also blended these approaches.…”

“…The frameworks addressed in the CGI 3-5 PD program implemented in Florida focus on children's thinking about: (a) multiplication and division on whole numbers, (b) fraction concepts, (c) operations on fractions, (d) base-ten number concepts involving whole numbers and decimals, (e) addition and subtraction on whole numbers, and (f) early algebraic ideas (Carpenter et al, 1999;2003;Empson & Levi, 2011;Schoen et al, 2018).…”

“…Cognitively Guided Instruction (CGI) is one of very few teacher PD programs that has been found to have a potentially positive impact on student learning in mathematics. Several experimental and quasiexperimental studies have found that CGI PD can have positive effects on student learning (Carpenter et al, 1989;Jacobs et al, 2007;Schoen et al, 2018;2020;2021b;Secada & Brendefur, 2000;Villaseñor & Kepner, 1993) 1 .…”

Comparing the frequency and variation of additive word problems in United States first‐grade textbooks in the 1980s and the Common Core era

“…This particular scheme emerged in the 1980s and 1990s. The taxonomy of problem types presented in Table 1 has influenced teacher professional-development programs in mathematics (see, e.g., Carpenter et al, 1996Carpenter et al, , 1999Fennema et al, 1996;Schoen et al, 2018Schoen et al, , 2020, further research on word-problem difficulty (see, e.g., Garcia et al, 2006;Olkun & Toluk, 2002;Stigler et al, 1986), and policy (see, e.g., NGA & CCSSO, 2010). Although it uses different terminology for the Join, Separate, and Part-Part-Whole semantic categories, the taxonomy of additive word problems in the CCSSM (see Table 2) is very similar to that in Table 1.…”

“…Starting with a randomized controlled trial that was conducted in the 1980s, Cognitively Guided Instruction (CGI) has had a far‐reaching impact on research, policy, and curriculum in mathematics education (Carpenter et al., 1989; Carpenter et al., 1996; Fennema et al., 1996; Jacobs et al., 2007; Schoen et al, 2018; Schoen et al, 2020). CGI is complex and multifaceted, but research‐based frameworks for types of word problems and strategies students use to solve problems are two of its more salient features (Carpenter et al., 1999).…”