(2015) introduced a Mathematical Quality of Instruction framework (MQI), which focused “on topics most salient to mathematics instruction: mathematics pedagogy and student work with mathematics, rather than classroom management or general pedagogy” (p. 558). Stockero and van Zoest (2013) focus on pivotal teaching moments, i.e., instances “in a classroom lesson in which an interruption in the flow of the lesson provides the teacher with an opportunity to modify instruction in order to extend or change the nature of students’ mathematical understanding” (p. 127). Leatham et al. (2015) introduced Mathematically Significant Pedagogical Opportunities to Build on Student Thinking (MOST), referring to situations which occur at the intersection of pupils’ thinking, significant mathematics, and pedagogical opportunities, and which meet six criteria also identified by the experts. To sum up, the norm-based studies employ experts to prepare a norm for use in assessing the quality of the participants’ noticing and knowledge-based reasoning. Conclusions are then formulated in terms of the ‘expert-likeness’ of their observations. Most frameworks, including those of Sherin and van Es (2009) and Stockero (2008), can distinguish some levels of knowledge-based reasoning (see Section 1.1) but do not differentiate between comments in terms of the plausibility of the reasoning itself. Thus, two comments may be coded ‘theorise’, as both include elements of theory to support their reasoning, but one may not be plausible in expert terms. Alternatively, two PSTs may make opposing evaluative comments about the same teaching-learning situation, one of which is preferred by the experts. Obviously, whether any interpretation is plausible or not is to an extent subjective, even if it is based on the views of experts in the field. Nevertheless, alignment between PSTs’ views of what they see in the lesson and what is considered appropriate by experts is essential. As Schäfer and Seidel note: a teacher might notice an event and reason that student thinking was encouraged in the video (which would be classified as student thinking) but an expert in the field of teaching and learning viewing the same video would reason that student thinking actually was not being encouraged. (Schäfer & Seidel, 2015, p. 36)
Only a few studies to date focus on the compatibility of the views of experts and PSTs or practising teachers (e.g., Blomberg et al., 2011; Stürmer et al., 2013; Mitchel & Marin, 2015; Schäfer & Seidel, 2015; Stockero et al., 2017). To avoid repetition, their findings are presented in Section 3.7.2, and discussed in relation to our own. To sum up, while there are many video-intervention studies with PSTs of different subjects56 documenting how the use of videos develops their noticing and knowledge-based reasoning, there is a shortage of research exploring the 56 Though mathematics and science predominate. – 98 –
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