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In all three lessons, PTs' representations and explanations were the targets of class discussion.
In fact, representations and explanations are not disjoint (e.g., one may explain the connections between representations).
Each lesson was first segmented into small chunks, which was analyzed from the aspects of representations and explanations.
Venkat (2015) argued that a focus on representations and explanations can simultaneously support teachers' mathematical learning and their learning about mathematics teaching.
By the time of lesson 1, the instructor had read PTs' responses to the pretest and was aware of the PTs' difficulties in representations and explanations.
It is assumed that teachers' competencies (e.g., choosing appropriate representations and explanations or providing challenging tasks) have a crucial impact on students' learning processes (Hattie 2009; Kunter et al. 2013; Lipowsky et al. 2009).
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A common conceptualisation of this construct does not exist so far (an overview of different conceptualisations was given by Schmelzing et al. 2013), but knowledge of students' conceptions and knowledge of multiple representation and explanations (both identified by Shulman 1986), could be seen as prevalent facets.
These findings suggest the need for national policies governing PADDD that are analogous to policies governing the initial establishment of PAs, including public consultation, technical studies, compensatory measures, and visual representation and explanation of the proposed changes.
After this, relevant excerpts were compared in terms of PTs' representation uses and explanations, respectively.
To support PTs' learning, the instructor provided interventions that aimed to enhance PTs' representation uses and explanations.
Based on the above SCK framework, we expect PTs to situate the teaching of AP of multiplication in word problem contexts, which can be unpacked through representation uses and explanations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com