This study is a part a Nordic centre of excellence for quality teaching in the Nordic countries, (QUINT). The centre adopts a broad interdisciplinary model including a systemic and differential framework for research on teaching quality that encourages study design and analyses at different levels of aggregation (teaching and learning processes, classroom and school environments, teacher-student interaction). QUINT is a leading international and Nordic environment for video-based studies of teaching quality and makes a significant contribution to international research on teaching quality.  The aim of the current study is to provide some insight into the quality of mathematics teaching in Icelandic elementary schools.  Specifically, the aim is to assess the quality of teaching within two domains (1) classroom discourse and (2) intellectual challenge. Classroom discourse refers to the opportunities within the classroom given to students for extended mathematics related conversations with their peers or with the teacher and intellectual challenge refers to the intellectual rigor of the activities in which students engage in mathematics.

It is widely accepted that students learning is affected by multiple factors, including factors at the student level, classroom level, school and system level (Muijs et al., 2014). However, recent reviews have highlighted that the classroom level, or more precisely, teaching quality is more important for student learning than several other factors, including socio-economic background, class size, classroom climate, and teacher’s years of experience and formal training (Hanushek et al., 2014). Although scholars from very different disciplinary traditions agree that teaching quality matters, teaching quality still lacks a clear and widely accepted definition (Ding & Sherman, 2006; Hanushek et al., 2014). Teaching quality is a complex and multidimensional phenomenon whose study requires a variety of complementary strategies (Croninger, Valli, & Chambliss, 2012).  Recent reviews of research on teaching quality (Howe & Abedin, 2013; Klette, 2015; Nilsen & Gustavsson, 2016) have focused on four dimensions proven critical for high-quality teaching; instructional clarity, cognitive activation, discourse features, and supportive climate. The analytical framework, the PLATO protocol (Grossman et al., 2013), which is used in this study, is organised around four instructional domains: Instructional scaffolding, disciplinary demand, representation and use of content, and classroom environment.  The current study is focused on the instructional domain of disciplinary demand that consists of the elements: intellectual challenge and classroom discourse. The former measures the intellectual demand of lesson activities, and can be related to theories of metacognition and analytical thinking (Schoenfeld, 2013). More demanding activities will promote analytical thinking by requiring students to justify their answers and provide reasoning. The PLATO protocol provides a framework for analysing the level of the quality of these elements in a given lesson (Grossman, 2020).  Classroom video-data is ideal for this kind of analysis for it allows for the evaluation of instructional practices from multiple perspectives and viewpoints (e.g. teachers, students and researchers). It also facilitates a grounded approach to dialogues between different theoretical positions and paradigms in educational research (Klette, Blikstad-Balas & Roe, 2017), that other observations systems do not necessarily allow for because of a limited overview of classroom activities (Bell at al., 2019).

Ten Icelandic compulsory schools participate in the study. The participating schools were purposefully chosen with the aim of to establishing heterogeneity of the sample and include different school types in terms of size, location and background of the students. The sample includes both rural and urban schools, schools with students of various social backgrounds, a school that had a greater proportion of multilingual students, schools with traditional classrooms as well as an open plan school. Two schools were selected in each group in case of the school chosen first would not accept participation. A total of 31 teachers in grade 8 participate in the study where eleven teach Mathematics. Twelve lessons in grade eight were video recorded in each of the ten schools, four consecutive lessons in three subjects, a total of 120 lessons. Of the 120 lessons, 40 were recorded in mathematics. A portable video lab was used for the recordings. Each recording required two cameras, one based at the back of the classroom and one in the front. Two microphones recoded the audio, one for the teacher and one was placed in the middle of each classroom, recording dialogue from students. The video data were coded by using PLATO (Protocol for Language Arts Teaching Observation). The PLATO protocol is an observation guide that was developed by Pamela Grossman at Stanford University (Grossman et al, 2013). The protocol was developed to observe Language Art lessons but has been tested and developed for other subjects as well (Bell, et al, 2019). Internationally, PLATO is one of the most widely recognized observation protocols, containing a detailed description of 12 indicators of quality teaching. This protocol is recommended by Bell et al. (2019) for several reasons; it covers a wide range of both teachers and student activities in the classroom, it is adaptive to different subjects and suits well for the analysis of video-data. PLATO elements are scored on a range from 1 to 4. Comparable data has been collected in each of the five Nordic countries. This sampling procedure and coding procedure in Iceland is comparable to those employed in the other Nordic countries participating in the study. All procedures about confidentiality, permission, storing and sharing the data have already been acknowledged by applicable authorities in each country. In Iceland, the Icelandic Data Protection agency were notified and the Institutional Review Board has reviewed the study with no objections.

In the past years, Icelandic mathematics teaching has been criticised for homogenous teaching methods, a narrow view of the curriculum and overall declining PISA results (Óskarsdóttir, 2014). Our findings show that students had limited possibilities to engage in elaborate and focused discussions where they had to clarify and specify their ideas. Furthermore, our findings show that much time in Icelandic mathematics teaching is devoted to procedural activities. In a large portion of the observed lessons, students worked individually on tasks at their own pace with limited interaction with other students, given little opportunity to engage in elaborative and focused discussions. However, there were some examples of intellectual challenge and student discourse at a high level. These findings are in line with a prior study that compared Icelandic mathematics teaching and Finnish teaching showed that, even though many Icelandic teachers used progressive-minded, learner-based instructional strategies. It was evident that students in Iceland spent much of their class time learning independently, without significant collaboration with others (Savola, 2010).

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