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…”

“The COACTIV study showed that the MCK and MPCK of secondary mathematics teachers could be separated empirically, although both dimensions of knowledge correlated strongly (Baumert et al., 2010).”

“These tools provide interactive and personalized learning experiences, crucial for practical instruction and student progress in secondary-level mathematics (Baumert et al., 2010).”

“These knowledge domains are separable but correlated, as empirically demonstrated for several disciplines, including early literacy (König et al., 2022), mathematics education (Baumert et al., 2010), physics education (e.g., Sorge et al., 2019a), or biology education (e.g., Großschedl et al., 2019).”

“Considering that subject knowledge is a basis for subject didactic knowledge (Baumert et al., 2010), the relevance of teacher training–also on the Wadden Sea ecosystem–becomes clear.”

“Zahlreiche Studien widmeten sich bereits dem Professionswissen als Wissensbasis für das Unterrichten (z.B. Baumert et al. 2010; Großschedl et al. 2015).”

“Other studies have shown that increased subject matter knowledge does not necessarily correspond to more effective instruction [64, 65].”

“Special attention has been directed toward teachers’ PCK since it predicts both the quality of teaching as well as student learning (e.g., Baumert et al., 2010; Iserbyt et al., 2020).”

“Studies in this line of research have focused on explaining relationships between these newer conceptualizations of mathematical knowledge needed for teaching and student learning (e.g., Baumert et al., 2010; Hill, Rowan, & Ball, 2005; Kleickmann et al., 2013).”

“Baumert et al., (2010) identified Mathematical Content Knowledge (MCK) is mathematical abilities at school level up to the university level where individuals considered being mathematically literate (Reid & Reid, 2017).”

“As a result, their students will acquire high academic achievements [2, 3, 4].”

“…about mathematics they will teach, as well as their ability to critically reflect on their classroom instruction and improve student Appova & Taylor, p. 678 learning (e.g., Baumert et al., 2010; Burton et al., 2008; Capraro et al., 2005; Carpenter et al., 1988; Tirosh et al., 2011; Vale, 2010).”

“Teachers’ content knowledge is crucial to the initiation of meaningful teaching and learning processes (Baumert et al., 2010; Zlatkin-Troitschanskaia et al., 2019a) and correlates with other facets of professional knowledge, for instance, pedagogical content knowledge (Holtsch et al.”

“, (2015); Baumert et al., (2010) detecting students' misconceptions can be used open-ended questions.”

“Studies have observed and explored PCK in various educational contexts (Baumert et al., 2010; Borowski et al., 2012; Lee & Luft, 2008; Loewenberg Ball et al., 2008).”

“There are significant results that show the importance of MKT framework in order to connect the effect of teachers’ mathematics teaching on students obtained mathematical knowledge (Baumert et al. 2010; Charalambous 2010; Hill, Rowan, & Ball, 2005; Tchoshanov 2011).”

“They defined CK as “a conceptual understanding of the mathematics taught” (Baumert et al., 2010, p. 166) and PCK as “the knowledge that makes mathematics accessible to students” (p. 142).”

“Lessons which are very cognitively activating may, for instance, contradict what students already know, offer numerous solutions, or demand that students expand their previous knowledge to come to a solution (Baumert et al., 2010; Kunter & Trautwein, 2013).”

“Many findings indicate that these facets of knowledge have a significant effect on the designing and outcomes of learning environments (Baumert et al., 2010; Shulman, 1986): Professionals who have a deep and connected content knowledge have an advance in selecting appropriate methods or in using…”

“In recent research based on a large sample of German secondary school students, Baumert et al. (2010) reported that, while both CK and PCK affect student outcomes in mathematics and are highly correlated, CK was less predictive of instructional quality and student progress than PCK.”

“In fact, recent results presented by Baumert et al. (2010) show that secondary school mathematics teachers’”

“This framework had a significant influence on the advancement of teacher education students and professional development (Baumert et al., 2010).”

“On the other hand—inspired by Baumert et al. (2010), who concretized mathematical PCK—we interpret Mathematical TPCK as the knowledge about the purposive use of tools for effective teaching and learning mathematics.”

“…of individualized learning opportunities that cater to all students according to their prerequisites seems desirable (Brophy, 2000; Lipowsky et al., 2009), class-average prerequisites such as average achievement may be easier for teachers to diagnose and react to (Baumert et al., 2010).”

“This domain is considered to be one of the fundamental domains for the teaching profession (Shulman, 1987), as it enables teachers to provide high-quality instruction (Voss et al. , 2011; Gess-Newsome et al. , 2017) and can foster students’ achievement (Baumert et al. , 2010).”

“However, strong empirical evidence to support this claim is still missing (for an exception see Baumert et al., 2010).”

“Das kognitive Potenzial von Klausuraufgaben ist zwar im Bereich des Argumentierens und Modellierens am Gymnasium etwas höher als an den anderen Schulformen, ist aber insgesamt als gering einzuschätzen (Baumert et al. 2010).”

“It is necessary to understand the causes of this lack of knowledge about PA and HRE, so that actions can be taken to reverse this trend and optimise student learning through a good knowledge of PE teachers 13,22 .”

“As the tasks used in mathematics classrooms are crucial for students’ enjoyment, boredom, and interest, teachers can shape these by selecting appropriate tasks for classroom instruction (Baumert et al., 2010).”

“According to Baumert et al., (2010) it is intolerable to teach without teaching and learning resources; the teaching and learning resources help in catching learners' attention as well as sustaining their interest, and they also allow learners to discover themselves and their abilities, an opinion supported by Capper…”

“The hypothesized relations could repeatedly be supported by data with respect to a broad range of knowledge, including GPK, cognitive skills, and performance facets for both primary and secondary school teachers (Baumert et al., 2010; Nehls et al., 2020).”

“…the United States (e.g., Ball, Thames, & Phelps, 2008; Hill, Rowan, & Ball, 2005), the Cognitive Activation in the Classroom Study in Germany (e.g., Baumert et al., 2010; Kunter et al., 2013), and Teacher Education and Development Study in Mathematics in seventeen countries (e.g., Senk et al.,…”

“Unterstützt wird diese Annahme durch verschiedene Untersuchungen, die zeigen, dass das FDW der Lehrkraft sowohl für kognitiv aktivierenden Unterricht (Ball et al. 2001; Keller et al. 2017) als auch das Lernen der Schülerinnen und Schüler bedeutsam ist (Baumert et al. 2010; Keller et al. 2017).”

“In support of this view, Baumert et al. (2010) indicated that in the United States and Europe, concerns have been raised on whether pre-service and in-service training succeeds in equipping teachers with the professional knowledge they need to deliver consistently high-quality instruction.”

“Higher tracks are also associated with more positive teacher beliefs about students (Hallam & Ireson, 2003), teachers having more pedagogical content knowledge, and teachers having more content knowledge (Baumert et al., 2010).”

“Mathematical problems play an important role in mathematics classrooms all over the world (Hiebert et al. 2003) as teachers can shape students’ learning by selecting appropriate problems for classroom instruction (Baumert et al. 2010).”

“The frequency scale is the Likert Scale (always or almost always, often, sometimes, never or rarely), which is derived from the psychometric scale proposed by Baumert et al. (2010). The questionnaire on cognitive activation strategies is presented in Table 6.”

“Baumert et al. (2010) found that the PCK of mathematics teachers is inconceivable without CK, and that CK alone is not a sufficient basis for teachers to be able to deliver cognitively activating instruction that, at the same time, provides individual support for students’ learning.”

“Das aufgezeigte Forschungsdesiderat zu Fragen nach Möglichkeiten der Unterstützung von Lehrkräften bei der Entwicklung von Expertise aufgreifend untersucht das DFG-Forschungsprojekt Co2CA2 im Rahmen einer Lehrerfortbildungsstudie die Wirksamkeit von Fortbildungen für Lehrkräfte im Schuldienst auf deren spezifischfachd…”

“Con posterioridad al informe del Panel se publicó el trabajo de Baumert et al. (2010) acerca de los resultados del proyecto COACTIV en Alemania, que evaluó la ganancia de aprendizaje de 4.353 alumnos a lo largo de un año (final de 9.º a final de 10.º), medidos con dos pruebas PISA, y tres tipos de…”

“…on task and content coverage to more qualitative aspects of teaching— e.g., the extent to which classes are well-managed, teachers foster student cognitive engagement, or students feel emotionally, physically, and intellectually safe (Baumert et al., 2010;Klieme et al., 2009; Pianta&Hamre, 2009).”

“While scholars broadly agree that mathematics teachers require professional knowledge for effective teaching (Baumert et al., 2010; Blömeke et al., 2022), recent developments in the mathematics teacher cognition agenda-driven research have prompted a shift toward the inclusion of facets that are…”

“These strategies foster students ’ complex thinking abilities, such as critical analysis, problem-solving, and creativity, by actively involving them in the learning process (Baumert et al., 2010).”

“Fauth and colleagues (2019) found a positive correlation between the degree of cognitive activation in classrooms and teachers ’ pedagogical content knowledge (see also Baumert et al., 2010).”

“Scholars have emphasized the importance of teachers’ subject matter knowledge in teaching and student learning (e.g., Ball et al., 2008; Baumert et al., 2010; Copur-Gencturk, 2015; Copur-Gencturk et al., 2024a, 2024b).”

“…educational administration researchers, educational policymakers, and practitioners have highlighted the need to focus on teachers ’ instructional and professional practices to improve the quality of student learning outcomes (Baumert et al., 2010; Marsh et al., 2012; Wagner et al., 2016).”

“Plenty of studies adopted this model and set forth empirical evidence to ground the three dimensions (e.g., Baumert et al., 2010; Bellens et al., 2019; Fischer et al., 2019; Künsting et al., 2016; Praetorius et al., 2014).”

“Some researchers have found a close relationship between PCK and teaching practices (e.g., Baumert et al., 2010), yet others have noted the limitations of this standpoint and found no relation (Yang et al., 2020) between PCK and classroom practitioners ’ approaches to teaching.”

“CK is a teacher’s own mastery of the content he or she wants to teach (Baumert et al., 2010); it comprises subject-specific knowledge and skills, including knowledge about how relevant information is interconnected (Loewenberg Ball et al.”

“[40,46], the results of the interviews in this study PVCK2: The content I read on social media helps me make different interpretations of subject-specific knowledge.”

“The quality of instruction and teacher knowledge, both content and pedagogical, are related (e.g., Baumert et al., 2010; Carlsen, 1992), and Harry ’ s case demonstrates this connection.”