Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress

“…affect students’ learning gains and motivational development (Bransford, Darling-Hammond, & LePage, 2005; Bransford, Derry, Berliner, & Hammerness, 2005; Grossman & McDonald, 2008; Grossman & Schoenfeld, 2005; Hiebert, Morris, Berk, & Jansen, 2007; Munby, Russell, & Martin, 2001; Reynolds, 1989).”

“In contrast to Hill and colleagues (Hill et al., 2004; Hill et al., 2007), who conceptualized mathematical knowledge for teaching as an amalgam of the mathematical everyday knowledge that all educated adults should have, a purely mathematical understanding of topics typically taught at school, and mathematical knowled…”

“On the one hand, we expect differences between pre-service teachers, who aspire to teach for the non-academic and the academic track due to the differences in content courses (Baumert et al., 2010; Riese & Reinhold, 2010).”

“constructs; teachers’ CK is an essential precondition for development of PCK; and PCK is most important for cognitively activating instruction in class (Baumert et al., 2010).”

“Surprisingly, 20 years later, there are only a few paper-and-pencil tests on teachers’ PCK available (Baumert et al., 2010; Hill et al., 2005; Rohaan et al., 2009; Schmidt et al., 2007), especially in the field of biology (Gardner & Gess-Newsome, 2011).”

“Studies have found a relationship between (1) mathematics teachers’ PCK and the cognitive demand of learning activities (Baumert et al., 2010), which links to IP#2 in the STEM Common Measurement System, (2) science teachers’ PCK and their”

“The ability to find different solutions is part of pedagogical content knowledge, which is an important predictor of students’ academic achievements in mathematics (Baumert et al. 2010).”

“Stimulating cognitive activation requires PSTs to have the capacity to focus on students’ individual learning needs (Baumert et al., 2010; Tas et al., 2018).”

“…professional knowledge of mathematics teachers (e.g., Hill et al. 2004), on effects of professional knowledge on student learning outcomes (e.g., Baumert et al. 2010), and on the development of professional knowledge during the course of mathematics teacher education (e.g., Blömeke et al. 2014).”

“…learning and that this one factor is more important than class size, classroom climate, and teachers’ years of experience and formal training (Baumert et al., 2010; Bryk, Sebring, Allensworth, Easton, & Luppescu, 2010; Hattie, 2009; Konstantopoulos & Chung, 2011; Seidel & Shavelson, 2007;…”

“Cognitive activation has proven to be an effective tool for stimulating students’ learning and interest in other subjects (e.g., mathematics: Baumert et al., 2010; science learning: Fauth et al., 2014; Biology: Förtsch et al., 2016), while empirical evidence about its potential role in civic…”

“Teacher knowledge as part of teachers’ professional competence has become an important research topic during the last decades (e.g. Baumert et al., 2010; Gitomer & Zisk, 2015; Tatto et al., 2012).”

“Another effort to measure teachers’ content-specific knowledge was the COACTIV study (Baumert et al., 2010), in which teachers of students who took the 2003–2004 Program for International Student Assessment (PISA) were given assessments of both their CKT and their common content knowledge (Krauss, Brunner, et al.”

“It has been confirmed that students whose teachers have a high level of PCK exhibit better academic performance and a higher level of motivation [99,100].”

“This finding is supported by studies showing links between teachers’ knowledge of mathematics subject matter and how to teach it, and student achievement (e.g., Baumert et al., 2010; Goulding, Rowland, & Barber, 2002; Hill, Rowan, & Ball, 2005; Ma, 1999).”

“Only subject-speci fi c planning decisions may enable in-depth elaborations, as student learning of a school subject takes place in a particular domain (König et al. 2018; Baumert et al. 2010; Weinert 1994).”

“[6] found a significant positive effect of teachers’ CK and PCK on instructional quality (assessed by means of student ratings, teacher self-reports, and analyses of tasks) and on student progress in mathematics education (measured through an achievement test).”

“empirical support for the separation of these dimensions and their association with student learning comes from the german extension to the Timss 1995 video study (Klieme, schümer and Knoll, 2001), a german large-scale study on mathematics teachers (Baumert et al., 2009), a swiss-german video study on math instruction…”

“In order to determine which different aspects of school quality are related to student achievement, we would rather need a modeling approach that determines meditational mechanisms between aspects of quality and student achievement (for an example of such an approach, see Baumert et al., 2010).”

“Among researchers, there is a common assumption that a high level of PCK will predict a high level of student achievement (e.g. Rollnick et al., 2008), and some researchers (e.g. Baumert et al., 2010) stress that PCK makes the greatest contribution to explaining student progress.”

“…a positive relationship not only between direct measures of teachers’ knowledge of mathematics content and pedagogy and student achievement (Baumert et al., 2010; Hill, Rowan, & Ball, 2005) but also between teachers’ beliefs about mathematics teaching and learning and student achievement…”

“The analytic approach of Baumert et al. (2010) decomposes professional competence into distinct prerequisites for performance: subject-specific professional knowledge and further components, including subject-unspecific ones (beliefs, motivation, and self-regulation).”

“Correlational studies remain prominent in the field (e.g., Baumert et al., 2010 Hill, Rowan, & Ball, 2005; Kersting et al., 2010), but in the 1980s and 1990s studies began using teacher interviews to investigate teacher knowledge (see Ball, Lubienski, & Mewborn, 2001).”

“Although recent studies utilizing well-established instruments have provided some evidence that teachers’ mathematical knowledge is related to students’ mathematics achievement and the mathematical quality of instruction (Baumert et al., 2010; Hill et al., 2008; Hill, Rowan, & Ball, 2005; Rockoff, Jacob, Kane, & Staig…”

“…are designed to measure a specialized type of content expertise used in teaching, including analyzing students’ work, determining the validity of a mathematical argument, or using proper representations for teaching particular math ideas (Ball, Thames, & Phelps, 2008; Baumert et al., 2010).”

“(Baumert et al., 2010; Krauss, Baumert, & Blum, 2008; Krauss, Brunner, et al., 2008; Kunter et al., 2007).”

“Other researchers have found that the development of content knowledge and of the pedagogy of the content, in particular, is highly dependent on ‘formal training at the university level, supervised internships, and reflective teaching experience’ (Baumert et al., 2010, p. 143).”

“…environments that encourage students to think, solve problems, make decisions, select, or integrate knowledge, and thus to develop an elaborated, content-related knowledge base are more likely cognitively activating (Baumert et al., 2010; Brophy, 2000; Klieme et al., 2009; Lipowsky et al., 2009).”

“For instance, focusing on mathematics instruction, some researchers emphasized aspects such as activating prior knowledge and working on challenging tasks as key elements of CAS (Klieme et al., 2009; Baumert et al., 2010), while others focused on engaging students in thoughtful discourse or using instructional scaffol…”

“…and end of the school year of the intervention) was 5.6% in our sam- educational literature, they have been found to capture real information on effective classroom teaching (Tschannen-Moran and Hoy 2007; Hattie 2009; Klieme, Pauli, and Reusser 2009; Pianta and Hamre 2009; Baumert et al. 2010).”

“This finding was anticipated, and is concordant with previous research which points to the importance of teacher content knowledge for student achievement, particularly in mathematics (Baumert et al., 2010).”

“The project COACTIV (Baumert et al. 2010) has proved that the content knowledge of mathematic teachers and their pedagogical content knowledge together are important for the quality of their teaching.”

“Studies in secondary schools indicate that cognitive activation is especially relevant to student achievement (Baumert et al., 2010; Kunter et al., 2013), whereas support seems to be more closely associated with student motivation (Klieme, Lipowsky, Rakoczy, & Ratzka, 2006; Kunter et al.”

“On the other hand, it is widely known in the tracking literature that teachers in low tracks provide lower-level instruction (Baumert et al., 2010; Oakes, 1985) and have lower expectations of their students (Brophy, 1983), which in turn influences students’ own perceptions of their abilities (Good, 1987).”

“The bigger picture that frames this work is that high-quality instruction requires mathematical content knowledge that is acquired in university-level training and can be further cultivated through systematic reflection on classroom experience (Baumert et al. 2010; see also Ball et al. 2001).”

“…to an elaboration of competencies characterizing effective teachers (Blömeke et al. 2011, 2012; Kunter et al. 2013) and of the processes that mediate the transformation of these competencies into classroom practice (Baumert et al. 2010; Blömeke et al 2015) which in turn influences research on CPD.”

“…of three instructional behaviors similar to those that have been found to have positive relations with student outcomes in previous studies (Baumert et al., 2010; Dubberke et al., 2008; Kunter, Baumert, et al., 2007; Tsai et al., 2008): (a) teachers’ classroom management skills, (b) the…”

“2017), continuing professional development (Desimone 2013; Harris and Sass 2011), mathematical knowledge (Baumert et al. 2010), and teachers’ self-efficacy (Fung et al.”

“Enhancing a deep understanding of the concepts is a continual focus (e.g., Baumert et al., 2010; Fauth et al., 2014; Klieme et al., 2009; Lipowsky et al., 2009; Praetorius et al., 2018).”

“Teachers’ knowledge, in turn, translates into higher student achievement (Ma 1999; Baumert et al. 2010; Sadler et al. 2013).”

“3) and for students’ learning progress (Baumert et al. 2010).”

“Recent research seems to share the assumption that three different dimensions are important to describe teachers’ professional knowledge, which includes most of Shulman’s ideas (e.g. Abell, 2007; Baumert et al., 2010; Blömeke, Felbrich, et al., 2008; Gess-Newsome, 1999; Grossman, 1990):”

“These domains include supportive classroom climate, classroom management, and cognitive activation (Baumert et al., 2010; Klieme, Pauli, & Reusser, 2009).”

“This results in cognitively more activating instruction, for example by encouraging students to discuss and validate different solution paths of a specific task instead of training one correct solution (Baumert et al., 2010; Klusmann et al., 2008; Retelsdorf et al., 2010).”

“For instance, a closer examination of the items, ‘I can craft good questions for my students’ and ‘I can help students think critically’ [12, 19], which were assigned to ‘Self-Efficacy in Instruction’ and ‘Self-Efficacy in Student Engagement’ respectively, suggests that they may not refer to only one factor, because t…”