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…”

“Cognitive activation is a teaching strategy that involves providing learners with experiences that challenge their thought processes by allowing room for discourse, questioning, critical thinking and problem-solving (Baumert et al., 2010; Fauth et al., 2014).”

“Some items that comprised teacher-level variables were adapted from previous studies (Baumert et al., 2010; Creemers & Kyriakides, 2015; Fauth et al., 2014; Klieme, 2008; Teodorović, 2011), the DaQS database (https://daqs.”

“Journal of Chemical Education, 63(10), 873-875.”

“It was interesting to discover that teachers who have content knowledge are not better than teachers who have pedagogical knowledge (Baumert et al., 2010).”

“…learning has attracted a global interest as new evidence has repeatedly illustrated the importance of early experiences with mathematics and the long-term implications of these over students’ mathematics learning and achievement (Baumert et al., 2010; Duncan et al., 2007; Ginsburg et al., 2008).”

“Journal of Agricultural Education 51 Volume 58, Issue 4, 2017 Research has indicated ways to strengthen PCK in teachers could lead to increased student progress and student learning (Baumert et al., 2010; Hill, Rowan, & Ball, 2005).”

“With regard to the classroom level, three basic dimensions of instructional quality have been proposed by several researchers: cognitive activation, classroom management, and student orientation (Baumert et al. 2010; Creemers and Kyriakides 2008; Klieme et al. 2009; Kunter and Baumert 2006; Kunter et al. 2008, 2013; P…”

“In contrast, Baumert et al. (2010) found sizable effects for teachers ’ “ pedagogical content knowledge ” ( d = 0.30) on mathematics achievement net of prior knowledge of mathematics, reading literacy test scores, mental ability, and SES (which had no effect).”

“The LPs and KPs have informed assessment design for both summative and formative tasks (Bennett, 2010; Graf & van Rijn, 2015; Deane et al., 2015).”

“Traditionally, a teacher for the upper elementary or lower secondary level of education in Slovakia and the Czech republic (and in fact in many other countries and regions, such as Germany [4] and Flanders [9]) specializes in two curricular domains (from now on called subjects), e.”

“Alice’s example imitates the findings by Baumert et al. (2010) that teachers without conceptual understanding are unable to present content logically to their students.”

“The sample comprised two (2) schools per Zone which came to a total number of eight (8) schools as the researcher selected four (4) Zones out of the eight (8).”

“This finding is in line with previous studies indicating that subject-specific knowledge is relevant for high-quality teaching and student learning (Baumert et al., 2010).”

“…ranging from non-significant (Begrich et al., 2020; Hugener et al., 2009; Krauss et al., 2020) to positive significant effects, yet of different magnitude (e.g., β = 0.10–0.12 in König et al., 2021, and Lipowsky et al., 2009, vs. β = 0.32–0.37 in Baumert et al., 2010, and Förtsch et al., 2016).”

“…mathematics, which could not prove any or only weak systematic relationships between teachers’ professional knowledge and students’ learning progress (Baumert et al., 2010; Blömeke et al., 2022; Krauss et al., 2020; for an overview, see Yang & Kaiser, 2022), indicating that corresponding effects…”

“Various authors have demonstrated that GPK can be conceptually distinguished from other knowledge components, particularly those that pertain to specific subjects (Shulman, 1987; Baumert et al., 2010; König et al., 2022b).”

“For example, some frameworks focus on teaching quality in the classroom (Baumert et al., 2010; Klieme et al., 2001; Lipowsky et al., 2009), and aspects of safety and relationships are built into the teaching practices.”

“…thinking and fostering in-depth learning through working on complex tasks, cognitive learning strategies have been suggested to be an effective method for high-quality education (Baumert et al., 2010; Klieme et al., 2009; Lipowsky et al., 2009; Teig et al, 2019; Von Kotzebue et al, 2020).”

“Previous research demonstrated that teachers’ professional knowledge contributes to instructional quality in the domain of mathematics (e.g., Depaepe et al., 2020; Baumert et al., 2010; Hill et al., 2008).”

“Moreover, examining the association between student achievement and supportive climates may assist in identifying factors that could improve educational outcomes (Baumert et al., 2010; Fauth et al., 2019; Krane et al., 2017).”

“…that knowledge-for-practice, knowledge-in-practice, and knowledgeof practice of teacher learning (Cochran-Smith & Lytle, 1999) influence academic progress of students, and Baumert et al. (2017a) revealed a substantial positive effect of pedagogical content knowledge on students’ learning gains.”

“In einigen Studien konnte das deklarative Professionswissen von Lehrkräften als Prädiktor für die Unterrichtsqualität und den Lernerfolg von Lernenden nachgewiesen werden (Baumert et al. 2010; Hill et al. 2005).”

“(Abell, 2008; Anderson & Freebody, 2012; Ball, Thames, & Phelps, 2008; Baumert et al., 2010; Findell, 2009; Shulman, 1986, 1987) (Findell, 2007; Voss, Kunter, & Baumert, 2011; Shulman, 1986, 1987) (Abell et al.”

“One of the recurring key findings is, however, that CK alone is not sufficient if teachers are to engage students and support their learning and that pedagogical content knowledge has substantial positive effects on students’ learning outcomes (Baumert et al., 2009).”

“International studies have found similar results: Teachers of 10th-grade German students (Baumert et al., 2010) and sixth-grade students in Peru (Metzler & Woessman, 2012) also found a significant relationship of teacher content knowledge to student learning in mathematics.”

“Die Skalen zur Erfassung der Unterrichtsqualität sowie beide Leistungstests wurden bereits mehrfach in Publikationen beschrieben (Baumert et al., 2010; Dubberke et al., 2008; Kunter et al., 2013).”

“Scholars agree that PCK is a major determinant that shapes teacher quality and consequently, influences student learning (Shulman, 1987; Baumert et al., 2010).”

“Content knowledge further includes the understanding of the curricular content (Baumert et al., 2010) and its scope and disciplines (Shulman, 1987).”

“…instructional strategies for creating effective learning environments (Voss et al., 2011), and 3) Pedagogical Content Knowledge (PCK), involving the application of subject-specific teaching methods to support effective instruction (Baumert et al., 2010; Hill et al., 2008; Shulman, 1986).”

“While some studies have demonstrated a direct positive correlation between teacher knowledge and student achievement (Baumert et al., 2010; Darling-Hammond, 2003; Darling-Hammond & Young, 2002), other studies (Akiri, 2013; Nye et al., 2004) have been inconclusive about the existence of such a…”

“…content comprehensible for students (Ball et al., 2008; Shulman, 1986), which involves the knowledge about students’ mathematical thinking and instructional strategies for effective mathematics teaching (Ball et al., 2008; Baumert et al., 2010; Copur-Gencturk & Tolar, 2022; Tatto et al., 2008).”

“…being taught; (2) pedagogical knowledge (PK), which involves domain-general instructional strategies that create effective learning environments (Baumert et al., 2010; Voss et al., 2011); and (3) pedagogical content knowledge (PCK), which refers to the knowledge about content-specific teaching…”

“The underlying model for pre-service physics teachers’ PCK considers different in-fluential conceptualisations of PCK in the Anglo-American tradition (e.g. Lee and Luft 2008; Magnusson et al. 1999; Park and Oliver 2008) and German tradition (e.g. Baumert et al. 2010; Riese and Reinhold 2012).”

“However, educators have noted that specialization is a precursor for interdisciplinarity, and interdisciplinary teaching builds upon well-established content knowledge from each component discipline (Baumert et al., 2010; You, 2017).”

“Dabei scheint gerade das Fachwissen eine zentrale Rolle für die Entwicklung fachdidaktischer Expertise einzunehmen (z.B. Baumert et al. 2010; Riese und Reinhold 2012; Schiering et al. 2022).”

“Regarding the relevance of teachers’ CK for the development of PCK and the teaching activities [55,58,68] as well as the difficulty level of the items, a dilemma of primary teacher education becomes apparent.”

“Indem sie kognitive Konflikte provozieren, regen Aufgaben Schüler*innen dazu an, ihr Vorwissen zu reaktivieren und in Frage zu stellen und vertiefend über die Inhalte nachzudenken (Baumert et al. 2010; Lipowsky et al. 2009).”

“Students’ performance is more affected from teachers’ PCK (Baumert et al., 2010).”

“These types of knowledge are considered to affect teaching and student learning [7,8].”

“Most studies on equity and teacher competence have been conducted in the US and Germany (e.g. Baumert et al., 2010; DarlingHammond, 2006).”

“Beyond challenging the students, the tasks should also be prepared in a way that they can be adapted to different learning prerequisites and abilities of the students (Baumert et al. 2010).”

“The same data were collected from these students and teachers at the end of the students’ tenth-grade year (Baumert et al., 2010).”

“With a special focus on mathematics teachers, especially the COACTIV-project (Baumert et al. 2010), the Michigan-Group (Ball et al.”

“Studies show that the quality of teachers' explanations strongly depends on their content knowledge, (Baumert et al. 2010, Riese 2010). It has to be flexible and adjusted to their students needs. An effective teacher is the single most important factor of student learning (DarlingHammond, 2000). Demtröder et al (2006)…”

“Moreover, it is not only the tradition of university mathematics but also recent research which emphasizes the role of teachers’ mathematical content knowledge for the successful classroom work (Baumert et al. 2010; Baumert and Kunter 2006; Darling-Hammond 2000; see also the discussion by Czerwenka and Nölle 2011).”

“This study emphasizes technology-enhanced constructive support, essential for a supportive class climate fostering motivation and engagement in challenges (Baumert et al., 2010; Klieme, 2020; Praetorius et al., 2018).”