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…”

“…´ e, 2013; Morinaj & Hascher, 2022; Park, 2004), especially after they transition from elementary to secondary school (Coffey, 2013; Maaz, Gresch, McElvany, Jonkmann, & Baumert, 2010) and face the challenge of adapting to a new school environment (Knoppick, Becker, Neumann, Maaz, & Baumert, 2015).”

“…as the Mathematics Teaching and Learning to Teach project (Ball et al., 2005; Hill et al., 2005), the Cognitive Activation in the Classroom project (Baumert et al., 2010; Kunter et al., 2013), and the Teacher Education and Development Study in Mathematics (Blömeke et al., 2014; Tatto et al., 2012).”

“A predictor of student achievement (Baumert et al., 2010), cognitive activation focuses on students’ critical understanding of what they are learning.”

“Personal learning support practices are exemplified by teachers adapting their instructional approaches to build on students’ prior knowledge and cater to students’ learning needs, providing support to their students’ learning, and leveraging feedback to help students improve (Baumert et al., 2010).”

“Similarly, in the UK, Reynolds and Muijs (1999) found teacher knowledge plays a crucial role in effective teaching practices while in the U.S., Baumert et al. (2010) found a correlation to exist between MKT, classroom pedagogy and student achievement.”

“Pedagogical content knowledge is assumed to be a core facet of professional competence and has been found to signi fi cantly predict students ’ learning progress in other fi elds of study (Baumert et al. 2010).”

“…ways of thinking such as creativity, critical thinking, decision-making, problem-solving, and learning which further connects to the framework of education teachers’ professional development which is a key factor for learners’ achievement (Baumert et al., 2010; Bakkenes, 2010; and Parker, 2016).”

“In particular, teachers’ CK and PCK are important predictors of instructional quality (Baumert et al., 2010; Blömeke et al., 2008; Kunter et al., 2013).”

“Whether referred to as ‘‘cognitively activating’’ (Baumert et al. 2010) or ‘‘high cognitive demand’’ (Stein et al. 1996), there is general consensus regarding what constitutes low-versus high-levels of challenge.”

“Visions of graduating statistically thinking students can only be realized if the students are taught by competent statistical thinkers, as suggested by research that connects teacher knowledge with student achievement (Baumert et al. 2010; Hill et al. 2005).”

“(2004) and Schilling and Hill (2007) could not empirically distinguish CKC nor SKC (Baumert et al., 2010), but in this study a presupposition is that both sub-constructs are applicable to social studies teachers’ financial literacy CK.”

“Some empirical studies show that cognitive activation is a key variable that infl uences students’ achievements (Baumert et al. 2010 ).”

“…and subject matter knowledge necessary for meaningful mathematics teaching (Coenen et al., 2018; Gustafsson & Nilsen, 2016) promoting student outcomes (Baumert et al., 2010; Blömeke et al., 2016; Coenen et al., 2018; Hill et al., 2019; Kunter et al., 2013; Lee & Lee, 2020; Toropova et al., 2019).”

“Then it is important to stimulate the teachers’ pedagogical content knowledge (PCK) since their initial training (Baumert et al. 2010; Kind, 2009, 2017; Nilsson & Loughran, 2012).”

“(2010), the breadth and depth of teachers‟ KSM determine the variety of teaching strategies and the types of alternative mathematical representations teachers will use in their teaching of a particular topic to students (Baumert et al., 2010) as well as how they will link topics across different grades (Walsh et al.”

“Adding to these findings, Baumert et al. (2010) found that teachers’ domain-specific instructional knowledge seemed to be of key significance for student progress in mathematics.”

“…example, across content areas the literature substantiates that general content knowledge, such as what might be taught in a college-level math course, provides an insufficient knowledge base for teaching content to children (Baumert et al., 2010; Hill & Ball, 2009; Morine-Dershimer & Kent, 1999).”

“Ultimately, ways to strengthen PCK in beginning teachers could lead to increased student progress (Baumert et al., 2010).”

“Cognitive activation is achieved by implementing instructional strategies that present students with challenging tasks and stimulate higher-level thinking processes (Baumert et al., 2010; Klieme et al., 2009).”

“Given that CK and PCK are important indicators of the quality of teachers’ instruction and students’ learning (Baumert et al., 2010; Hill et al., 2005; Kersting et al., 2012) and they are distinct elements of the content-specific expertise needed in teaching (e.g., Copur-Gencturk & Tolar, 2022),…”

“characterized by respect and support, that is tailored to the (emotional) needs of students (Baumert et al., 2010; Reyes et al., 2012).”

“[13] also revealed that secondary mathematics teachers’ PCK positively affected students’ learning gains.”

“Wie die Hattie-Studie (Hattie 2010) sowie die CoActivStudie (z.B. Baumert et al. 2010) zeigen, hat die Lehrkraft durch ihr Wissen, ihr Verhalten und ihre Kompetenzen entscheidenden Einfluss auf die Lernleistung der Schülerinnen und Schüler.”

“Whereas, what teachers know and can do individually is an important element in improving schools (Baumert et al., 2010), it is clearly not enough (Gess-Newsome, 2013; Leana, 2011).”

“Empirische Belege für den Effekt des kognitiven Aktivierungspotenzials von Unterricht auf die Schüleroutcomes lassen sich bereits in vielen Studien, u. a. zum Lehrerprofessionswissen, finden (z. B. Baumert et al. 2010; Cauet et al. 2015; Kunter et al. 2005; Lenske et al. 2015; Pauli et al. 2008).”

“…to continuous interaction between environmental, behavioral, and cognitive elements (Parcel & Baranowski, 1981), learning gains in mathematics (Baumert et al., 2010), and student motivation to absorb class material being impacted by the instructor’s ability to present desirable outcomes…”

“Although the terminology used varies [36], the three basic dimensions are (1) classroom management, (2) supportive climate, and (3) cognitive activation.”

“Such teachers may also reduce the achievement gap between students (Baumert et al., 2010).”

“In a study, researchers (Baumert et al., 2010) evaluated both elementary teachers’ mathematical content knowledge and pedagogy content knowledge on student performance and found pedagogical content knowledge was more predictive of student learning than teachers’ content knowledge level.”

“Third, components such as learning sessions, coaching, and the cycles of collaborative learning sought not only to increase teachers’ content knowledge but also their pedagogical content knowledge, which is a critical competency for improving student learning (Baumert et al., 2010; Hill et al., 2008).”

“Teacher training in the academic track focuses on subject-speci fi c content knowledge and scienti fi c outreach procedures, while teacher training in the nonacademic school track emphasizes a more practical approach with a strong pedagogical orientation (Baumert et al. 2010).”

“Several studies have mentioned the importance of CK and PCK particularly for mathematics (Baumert et al., 2010; Goe, 2007; Shulman, 1986; Wayne & Youngs, 2003). Some of the strongest evidence comes from Baumert et al (2010) for mathematics, and Sancassani (2021) for science, who employs a within student approach and f…”

“Moreover, some scholars included curriculum and media [21], math tasks and cognitive demands [22], and context knowledge [23] as components of PCK.”

“Ähnlich wie im COACTIV-Kompetenzmodell besteht eine wesentliche Weiterentwicklung in der Berücksichtigung von Einflussfaktoren auf den Übergang vom potenziellen Können der Lehrkräfte zur Realisierung im Unterricht, die als amplifiers and filters zusammengefasst werden.”

“Hence, there is no evidence that in countries with a higher tracking degree, the attraction of less qualified teachers or the provision of a less demanding curriculum in lower tracks reduces school performances (Baumert et al., 2010; Brunello and Checchi, 2007), at least when it comes to the influence on immigrant chi…”

“For Germany, Baumert et al. (2012, Table S1) reported correlations around 0.5 for IQ with both reading and mathematics.”

“…developed a framework that in addition to teachers’ deep understanding of mathematics (i.e., CK), included three dimensions of PCK made up of knowledge about multiple solution strategies for a task, student ideas, and representations and explanations (Baumert et al., 2010; Krauss et al., 2008).”

“Moreover, these facets directly relate to students’ understanding and learning in the classroom (e.g., Author(s), 2007 – removed for blind review; Baumert et al., 2010).”

“…evidence on teaching effects is at odds with the theory and evidence reported in national longitudinal studies as well as in qualitative research (eg Baumert et al., 2010; Klieme, Pauli, & Reusser, 2009; Kyriakides, Christoforou, & Charalambous, 2013; Muijs et al., 2014; Seidel & Shavelson, 2007).”

“…knowledge (PK), which is regarded as generic knowledge for designing meaningful learning environments that support students’ learning processes (Baumert et al., 2010; Voss et al., 2011); and (3) pedagogical content knowledge (PCK), which is knowledge about content-specific teaching and…”

“For example, this kind of benchmark was used to evaluate the impact of teachers ’ pedagogical content knowledge on student learning (Baumert et al., 2010), and to provide context for data on performance gaps in achievement between countries (OECD, 2014, p. 46) and between students with and without…”

“Meanwhile, the significantly positive effect of pedagogical content knowledge on student performance agrees with the findings of relevant research, which confirms the correlation between teacher expertise as well as high-quality teaching and student learning [25].”

“For example, several studies that investigated PCK focused on mathematics teachers (Baumert et al., 2010; Hoover, Mosvold, Ball, & Lai, 2016; Tatto et al., 2012).”