Classroom Observation

In recording the lesson observation, I adapted and used the systematic classroom analysis notation (SCAN). Amongst several lesson observation schedules, I preferred SCAN since it focused on the major categories of teachers’ and students’ actions, and the features of the classroom activities that are central to my research. My rationale for observation, for my choice of SCAN and for its adapted form are discussed in more detail on page 53.

To address the research questions, SCAN was adapted in such a way as to enable me to address RQs 1.1, 2.1, 2.2, 3.1, 3.2, and 3.3 (presented on page 7). Table 3-3, p. 57 shows the SCAN shorthand codes for understanding the recording of the observation.

Below I include a scanned sample of the actual classroom observation as a means of

77 understanding how the codes were used and collated. The observation notes were taken roughly every 10 minutes during the lesson. Figure 4-1 is a sample of the record of a lesson taught by Kitty to Year 11 on ‘Algebraic expressions and proofs’ observed on 20/11/2015.

Figure 4-1. Scanned sample of a SCAN schedule in use

Figure 4-1 above shows a sample of SCAN schedule divided into six rows indicating time interval for recording the observation, resources used by teachers or students in the lesson, activity, episodes of interest and my immediate comments on the lessons.

The comment columns enabled me to commence initial descriptive coding while collecting the data. There are also five columns of data item focused on.

The mathematics teachers employed a variety of classroom seating arrangements.

These included the whole class facing the board, students sitting in a horseshoe shape facing each other and the board to the side, and other instances of students all sat in pairs and groups. Usually, the set-up of the class informed where I sat to observe the

78 lesson. My working principle in the lesson observations was to take a position where I could observe the entire class with minimal obstruction to lessons while maximising the opportunities to capture as much as possible of the lesson activities.

Having mastered the SCAN shorthand codes, I took notes as the lesson went on, trying to record as much as I could to observe. In the resources used column, I recorded all the digital and non-digital resources observed during the lessons and in a few instances where I was not sure what the resources were or the sources, the post-lesson interview was the opportunity to seek clarification. Whenever a conversation was not possible because the teacher is moving on to another duty, email exchanges were used to supplement the data. The data elicited through this column were used, in most part, to address the question on teacher’s resources and this was triangulated by the other methods of data collections used.

The Activity and Episodes columns capture the layers of the actual ongoing interactions, the whole of the lesson delivery and students’ engagement with tasks.

For instance, an activity level in this sense could be C – that is, the teacher’s exposition to the whole class, or O – teacher circulates in the class. An episode is a specific subunit of the classroom activities; this is an incident occurring that forms a part of the sequence of lesson activities. Episodes referred to what the teachers were doing during the lesson, such as facilitating or explaining. I defined mathematical and technological emphases in the episodes. Hence, Fi, refers to ‘facilitating mathematical ideas’ while Ft refers to ‘facilitating technology’ and Ei denotes ‘explaining’

mathematical ideas. Another included in the episode descriptors is I – meaning teacher initiating the lesson or a task. These various parsing of the lesson helps to create an evidence-based narrative for the case reports in the subsequent Chapters 6-8.

The events of interest are those teachers’ or students’ actions or interactions which I considered of interest to the research purpose and that could enable me to address the research questions. These could be incidents that reinforce an emerging theme or an outlier to the regular instances of lesson observation. For example, I considered

79 students’ use of an iPad with the diagnostic questions as an event of interest and elsewhere I highlighted students taking a timed test with background music as an event of interest. These events provide me with the opportunity to further seek clarifications from a specific teacher – say, Kitty or Emilia – as to why music was used during the test. In Table 4-4 below, I show the frequencies of the activities and episodes.

80 Table 4-4. Frequencies of the pre-defined SCAN descriptors for the seven teachers

The codes are explained in more detail in the following pages. The activity levels relate to what the teachers and students where observed to be doing during the lessons. The episodes focus on teacher-led activities.

15 This shows the number of distinct digital/ non-digital resources identified during the lesson observations.

16 This indicates the number of times Kitty’s classroom activities were observed (13 times).

Teachers Resources¹⁵

Lesson Activity Levels Episodes

C L Wo O D2-2 Dt-1 AwTt AwTs SS/ST Co Fi Ei Ft D R I Kitty (13)¹⁶ 18

44 9 32 28 16 11 18 8 13 40 28 34 3 5 12 20

Emilia (9) 10

39 3 35 25 11 8 11 4 9 28 18 19 0 3 14 10

Jimmy (8) 8

35 7 17 11 10 13 12 9 8 28 17 17 0 2 8 7

Jose (7) 9

29 11 16 13 4 9 8 5 7 16 13 9 0 0 7 10

Gray (8) 11

37 19 19 20 10 15 10 4 8 32 22 24 1 6 9 11

Gavin (8) 12

32 16 20 22 8 14 12 3 8 26 20 23 1 7 9 13

Richelle (8) 8

34 15 23 19 10 8 13 7 8 36 18 29 4 2 12 9

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Analysis of SCAN Datasets

The adapted SCAN schedule, in a sense, plays a double role, as an instrument for data collection and concurrently as a form of data analysis. Thus, as data is collected, a first level of data analysis takes place. The frequencies of resources used in class enabled me to identify distinct digital and non-digital resources used in the course of the lessons (e.g. Kitty - 18; Gray - 11; Richelle – 8, as shown in Table 4-4). I was able to match these resources with those the teachers had mentioned in their interviews and accessed on the screen capture data. In collating and classifying the resources in the case study report in Chapters 6-8, these identified resources in the lesson formed a large part of the teacher’s resource system, the set of resources drawn from the collective and how the teachers modify them. This observation confirms, on several levels, the teacher’s claim on resources as discussed in the case study reports. I found a range of different digital resources, non-digital resources and tools in classrooms in all three school contexts. All classrooms were equipped with interactive whiteboards and teachers had regular access to computers. The IWB has become a common feature in most UK secondary school classrooms (Kearney, Schuck, Aubusson, & Burke, 2018; Umameh, 2012). All teachers also had access to a range of resources available through the Internet and dedicated sites. This in part aided me in addressing one aspect of RQ 1.1 (In what ways are mathematics teachers accessing, adapting and creating resources for classroom practices?) and RQ 2.1 (What resources do mathematics teachers access and use?)

In terms of structuring the analysis of the observation dataset, the pre-defined SCAN descriptor codes which are applied, enabled me to organise the dataset in such a way as to make closer examination and analysis possible in a structured manner: for example, by examining relationships between SCAN descriptor codes as shown in Table 4-4 (AwTt - teachers’ activity with technology and AwTs - students activity with technology during the lessons). I deduce from the frequencies of the SCAN descriptors (AwTt vs AwTs) that technologies were used more often by the teachers than the students. For instance, as shown in Table 4-4 above, while Kitty was observed using the digital resources 18 times, her students were observed using

82 similar resources eight times. This approach was used for all the teachers and their students.

With regards to the forms of interactions under the activity level columns (D2-2 – students in pairs/group and Dt-1 - student-teacher interaction), Table 4-4 shows that all seven teachers regularly used these forms of interaction with their students: Emilia (8), Gray (15) and Richelle (8 times).

In terms of the episode level, what the teacher was seen doing (Co, Ei, Fi), there is a substantial amount of evidence in the data to argue that the lessons were largely teacher-led, though a counter-argument could be that the frequencies are so because the research is primarily focused on the mathematics teachers and not so much on the students’ activity. The episode levels enabled me to address RQ 3.1 (What tasks do mathematics teachers give to their students?) and to build a plausible narrative in the classification and presentation of the tasks as presented in the context of the lessons.

How the tasks were identified using SCAN and the logic of tasks classifications are discussed in a subsequent subsection, 4.2.3.

I now present a table of the number of observations made in the three schools (schools A=37 B=16 and C= 8) and the cumulative number of observations (61) in this study.

Number of Classroom Observations School A School B School C

For each school 37 16 8

Total for A, B and C 61

Table 4-5. Total number of classroom observations

Table 4-5 shows the individual total for each school and the total number of observations undertaken between October 2015 and June 2016.

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