(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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effect of different types of videos (‘own’ versus ‘public’ videos). Similarly, we know little about whether the PSTs’ noticing and reasoning skills are in line with those of experts. We explore both of these knowledge gaps in Study 1.
3.2 AN EMBEDDED STUDY: IDENTIFICATION OF EXPERT PHENOMENA To explore the PSTs’ expert-like noticing and reasoning, it was necessary to identify targets of such noticing and reasoning considered important by experts. We describe the process here in the form of an embedded study, the goal of which was to identify important moments in the lessons used for the pre- and post-tasks (see Section 3.5.1). These moments are subject-related and considered key to the quality of the teaching-learning situations, thus adding (or failing to add) to the fulfilment of the learning aims of the lesson. The resulting research question explored here is:
RQ1b.0: What are the phenomena in the lessons used in the pre- and posttasks, deemed important by experts for the fulfilment of the aims of the lessons? How do the experts interpret them?
3.2.1 PARTICIPANTS – EXPERTS The authors of this book performed three roles: course leaders designing and conducting the video-intervention, researchers conducting Studies 1 to 4 and experts setting the expert norm. They all educate teachers in their respective fields (art, biology, elementary social studies, English language and mathematics) by teaching them subject and subject education courses. They also supervise PSTs during their school practice placements and are supervisors of their diploma theses. When the video-interventions were organised, they had from 7 to 36 (mean = 21) years of university-level teaching experience. Five had also taught at elementary or secondary schools. All had experience with video-based tasks in their subject education courses and with research both in their respective field and on PSTs’ noticing (e.g., Vondrová & Žalská, 2015; Vondrová et al., 2016; Uličná et al., 2017; Pavlasová et al., 2018; Robová & Novotná, 2018; Simpson et al., 2018; Stará & Starý, 2018, 2019; Novotná, 2019).
3.2.2 DATA ANALYSIS To investigate PSTs’ professional vision, we asked them to view a whole lesson rather than a clip, as this would provide more context and enable the Focus on noticing and knowledge-based reasoning (Study 1) – 99 –
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PSTs to show their ability to “‘sift through’ the complexity of the classroom to identify important moments” (Stockero, 2014, p. 241) in the same way that in-service teachers do (Santagata, 2011). To ensure some equivalence between the lessons in different subjects, they were all self-contained (in that there was no need for further context), authentic (from Czech schools) and focused on new content familiar to the PSTs. Each course leader selected two videos of such lessons, mostly 45-minute lessons, though the EAE lessons were double lessons of 90 minutes. An overview of the lessons can be seen in Tab. 3.1. Tab. 3.1: Lessons used in the pre- and post-tasks Aim of the lesson Teaching methods and organisational form of work
Subject Grade/Code Topic
1/EAEf
Frottage Technique
To develop tactile perception and sensibility to material, to explore the surface of different objects and materials, to introduce the frottage technique, to develop the pupils’ ability to reflect on their own creative work Brainstorming, common perception, individual creation, group discussion, structured reflection
4/EAEo
Geometric Structure
To introduce the frottage technique and to create a structure using geometrical shapes, to observe and complete the shapes by drawing Brainstorming, individual creation, reflection
5/ESSp
Waste of Food
To explore the issue of food waste (cause and effect, consequences, possible solutions) Brainstorming, cooperative group work, group and whole class discussion, peer assessment
5/ESSf
Attainability of Food
To explore the origin of pupils’ food, to discuss attainability of food Cooperative group work, group and whole class discussion, searching for information in the text, comparing the information
9/BIg
Minerals and Rocks
To introduce differences between minerals and rocks Group work, work with a textbook and worksheet, whole class work, use of natural items
Mammals (insectivore)
To revise general characteristics of mammals, to introduce general characteristics of insectivores and typical representatives in the Czech Republic (Erinaceus, Talpa and Sorex) Common revision, work with textbooks, pupils asking questions, continuous writing on the blackboard
EAE
ESS
BI 8/BIs
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