Page 19 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

children’s achievement (Seidel & Shavelson, 2007). The associations between teaching behavior and children’s mathematics achievement are nevertheless not clear-cut across studies for the reason that the studies do not address the same aspects of teaching behavior and often emply different measures of teaching behavior and mathematics achievement (Seidel & Schavelson, 2007).
In a large-scale observational study, Van de Grift (2007) found the following variables related to the quality of teaching: a safe and stimulating learning climate; clear instruction; adaptive teaching; use of modeling, explanation, scaffolding (i.e., type of teaching strategies); and efficient classroom management. Follow-up research by Van der Lans et al. (2018) found that relevant teaching behaviors could be ranked according to level of complexity and thus from the simple provision of a safe learning climate and efficient classroom management to differentiation of learning needs and adaptation of lessons on the basis of identified needs. These complexity levels provide insight of how effective teaching develops and can also support teachers with feedback about how they can approve their effectiveness (Van der Lans et al., 2018).
Mathematical knowledge for teaching
The mathematical knowledge for teaching includes the specific mathematical knowledge and skills of teachers that are needed to effectively teach mathematics. Based on the mathematical knowledge for teaching framework of Ball et al. (2008), subject matter knowledge and pedagogical content knowledge can be distinguished. Subject matter knowledge includes common content knowledge (i.e., mathematical knowledge that is not unique to teaching and thus also useful in other professions), horizon content knowledge (e.g., seeing connections between early and later mathematics), and specialized content knowledge that is thus specific to the teaching of mathematics (e.g., understanding children’s solution methods, accurately use of representations). Pedagogical content knowledge includes knowledge of content and children, knowledge of content and teaching, and knowledge of content and curriculum (Ball et al., 2008). Inconsistent results have been found for the associations of mathematical knowledge
1
General introduction
17