Data Collection

research, this activity aims to develop the local instruction theory and improve the interpretative framework. Besides, Edelson (2002) also mentioned that this phase is important in terms of generalization of the theory developed in a study. Practically, this phase is done by comparing the hypothesized students‟ learning with the actual conditions during the teaching experiments. In this case, the HLT and research questions play important roles as guidelines for the analysis.

To conduct the retrospective analysis in this study, the researcher follows a task oriented approach (as described in Van Eerde, 2013). In this approach, the researcher will first have a look at the video of the lesson with the HLT and research questions as guidelines. During this process, the researcher will give remarks on interesting fragments. The role of the teacher and classroom dynamics are used to explain inconsistencies between the hypothesized and the observed learning. To help the process of analysis, Van Eerde (2013) suggested making a data analysis matrix comparing the HLT and the actual learning trajectory (ALT), like in table 3.1:

Table 3.1 Data analysis matrix for comparing HLT and ALT

Activity Hypothetical Learning Trajectory (Conjectures of students‟ thoughts)

Actual Learning Trajectory (Observed class events)

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Universitas Sriwijaya with the initial step in our HLT. There are several techniques that we employed in this phase, such as, interview with the teacher, classroom observation, and conducting a pre-test.

Classroom observation and interview with teacher

The classroom observation generally aims to reveal the classroom norms, teachers‟ ways of teaching, and general overview of students‟ ability. Observation notes were made to record important information during the observation. To help the data gathering, an observation sheet was employed (see appendix).

Meanwhile, in the interview, the researcher tried to collect data on teacher‟s beliefs on algebra teaching, Pendidikan Matematika Realistik Indonesia (PMRI), and some technical matters related to the implementation of the study. This interview was semi-structured with some guiding questions provided (see appendix). The interview was audio recorded. An illustration of the data collected during the classroom observation and teacher‟s interview can be observed in table 3.2:

Table 3.2 Summary of data collection in the preparation phase

Topics

Data Sources Classroom

observation

Interview with teacher Students‟ prior knowledge of the prerequisite topics √ √

Classroom norms √

Pedagogical matters √ √

Familiarity with PMRI (Indonesian RME) √ √

Teacher‟s personality (teaching philosophy and beliefs, experiences in teaching the current level, educational background)

√ Classroom conditions (including the availability of

learning materials) √ √

Flexibility (how strict the school and the teacher with the following the curriculum, textbook, and

innovation in teaching)

√

Pre-test

The pre-test mainly aims to reveal two things, that is, the student‟s understandings of the prerequisite knowledge, and the students‟ understandings toward

the topic of the lesson. This test was organized in a form of written test (see appendix C). After the test, we would have the students‟ written works to analyze. In addition, an interview was also done to some students to clarify their answers and to get a deeper knowledge about the students‟ understandings toward the given problems.

Interviews to students were video recorded.

Information on the students‟ mastery of the prerequisite knowledge is reflected on the starting point of our HLT. Meanwhile, the students‟ initial understandings toward the topic of the lesson were compared with their knowledge after the learning implementation, to see whether the learning really occurred.

3.2.2.Preliminary Teaching Experiment (Cycle 1)

In this phase, the design and the instruments were field tested to a small group (4 students). This field test perhaps provides suggestions to improve the design, the conjectures, and the instruments before they were used in a larger classroom. Data gathered during this phase included the students‟ written works, video recordings of classroom observation, and field notes. The learning session was handled by the researcher. A static camera was used to record the lessons. An observer also joined the class, made notes about the lessons, and watched over the camera. The result of the analysis of this phase would contribute to improvement of the HLT.

3.2.3.Teaching Experiment (Cycle 2)

The second teaching experiment was conducted in a larger group, which is different from the class of the students involved in the cycle 1. The class was handled by the regular teacher of the class. The revised HLT was used as a guideline for the teacher to conduct the lessons. The data gathered during this phase were expected to describe how the students learned during the 6 series of lessons, how the teacher facilitated students‟ learning, and how the designs helped students to learn.

To collect the data, the same techniques as in the first cycle was applied, that is, by utilizing video recordings, field notes on teacher‟s and students‟ performances, and the students‟ written works. Due to the large number of students involved in this phase, two cameras were employed to record the classroom activities; a static and a dynamic camera. The static camera was used to record the overall classroom activities, while the dynamic camera was used to zoom in a specific event during the class, for instance,

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Universitas Sriwijaya the students‟ presentations or in their group‟s discussion. The classroom situation, including social norms and socio-mathematical norms were also observed during the class, particularly during the classroom‟s discussion and in the interaction between the teacher and her students and among the students themselves.

To collect more focused data, four students were chosen to be the focus group.

The choice was made in a discussion with the teacher by considering the students‟

performances during the classroom observations, the pretest, and teachers‟

suggestions. The members of the groups were moderate (not too high and not too low in mathematics), but having a relatively good communication skill. During the class, the teacher gave no special interventions to the group.

3.2.4.Posttest

The posttest was given to students after the sixth lesson to ensure whether the students experienced a progress after attending the overall lessons. Therefore, some items in the posttest were made the same as in the pretest; some others are different, particularly those asking for students‟ higher level thinking. These different items perhaps showed if the students achieved higher than the expected learning goals. It is important to highlight that the students‟ performances in the posttest would not be the major data to reflect; it will just give insights about the progress of the students.

3.2.5.Validity and Reliability of Data Collection

To guarantee the quality of the data collected, issues related to validity and reliability will also be explained. The validity of the data collection tells its accuracy (internal) and its interventionist nature (ecological). Meanwhile, the reliability tells the independency of the researcher (internal) and the replicability (external) of the data collection (Bakker & Van Eerde, 2015).

To guarantee that the data we collected are valid internally, a number of data collections were employed, such as, interview, observation, field notes, and students‟

assignments. These different data collections perhaps strengthened each other in informing about the observed characteristics of the subjects. Thus, the explanations could be more accurate. Another effort to increase the internal validity was to increase the quality of the instruments. This was done through consultation with experts, in this

case, the supervisors and some fellow researchers. A good-quality instrument merely impacted the quality of the data collected.

Meanwhile, the ecological validity was maintained by conducting the study in a normal classroom. In this case, the class was handled by the regular teacher, and the students involved are in one regular class. The general classroom norms will also be maintained, for example, greeting to teacher to start and end the lesson.

To ensure the internal reliability of the data collection, we used cameras instead of relying only on the observer‟s notes. This use of technology perhaps minimized the intervention of the researcher in the data gathering. The video recordings indeed also maintain the external reliability of the data collection, since it provides virtual data that are replicable (Bakker & Van Eerde, 2015).