Data Analysis

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).

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Universitas Sriwijaya used to select the focus group, in such a way that students in the focus group should vary in their level of knowledge observed from the result of this pretest. Meanwhile, to analyze the video recordings of the students‟ explanations during the interview, we first replayed the video and transcribed interesting segments. Qualitative data on students‟ prior knowledge of the prerequisite materials and the topic of the lesson were critically gathered. This was reflected on the starting points of the HLT.

3.3.2.Preliminary Teaching Experiment (Cycle 1)

Generally, the preliminary teaching experiment aims to improve the design before it was used in the second cycle. Analysis to the data gathered was done by observing how a small group of students react to it. In this phase, data collected were video recordings of the learning process, observation notes, and students‟ written works. The data were analyzed with task oriented approach, that is, by analyzing in the level of activities (Van Eerde, 2013). HLT was used as a guideline to analyze the data.

The analysis was done in each micro cycle and macro cycle. The data analysis performed as in the following steps:

Analysis of the micro cycle Video recordings

The video of one lesson was watched along with the HLT to make a comparison between the students‟ actual learning and the proposed HLT. Here, we focused on analyzing the conjectures in the HLT, whether it covered all the possibilities of the students‟ ideas, and whether the suggestions we gave for the conjectures really helped the students in learning.

Observation notes

Observation notes were made by an observer during the class session. These notes were used to help the analysis of the video recording. The observation notes told the researcher crucial learning moments that should be reviewed in the recordings.

Students’ written work

The students‟ written works were gathered by collecting worksheets and exercises given to students during the class. Analysis of these works was done by interpreting

the students‟ answers; observing whether their works and explanations in the video recording confirmed each other.

The video recordings, observation notes, and the students‟ written works in one lesson were compared each other to see how and what the students have learned during the lesson. This gave us ideas about the students‟ end points after one lesson, which will be used as a starting point for the next lesson. Adjustments to the HLT of the following meeting were done according to this result.

Analysis of the macro cycle

The analysis of the macro cycle of the preliminary teaching was performed after the posttest. Here, reflections on every micro cycle were taken into account to re-build the new version of the HLT. Thus, modifications toward the design can be performed.

3.3.3.Teaching Experiment (Cycle 2)

Data analyses of the teaching experiment in the second cycle were mainly the same as those applied in the first cycle. Special concerns were given to the performance of the focus group. However, the overall classroom performances were also looked to gain information about the classroom condition. The result of the analysis of this cycle was used to answer the research questions and to generate a local instruction theory of algebra learning. Therefore, in analyzing the macro cycle of this phase, we looked carefully not only to the HLT but also to the research questions.

3.3.4.Posttest

Analysis of the posttest was similar to that of the pretest. Qualitative analysis was done by interpreting the students‟ written works. This interpretation was confirmed to the students through an interview after the test. The result perhaps enriched the conclusion and answers to the research questions.

3.3.5.Validity and Reliability

The reliability of data analysis and the validity of the conclusions drawn in a study is a key to a good quality study. Therefore, these issues become essential.

Bakker and Van Eerde (2015) mentioned that in data analysis, the researcher must pay

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Universitas Sriwijaya attention to the soundness of the conclusion (internal validity), generability and transferability of the results (external validity), the independency of the researcher in data analysis (internal reliability), and the transparency of the analysis (external reliability).

Internal validity

Data triangulations were performed by comparing data from different sources to ensure the credibility of the result. Reflections toward conjectures of a specific episode were also tested over the other episodes. This ensured whether the interpretations toward the data were accurate. Comparison between the HLT and the actual learning will also improve the internal validity, as it provided evidence to draw a conclusion.

External validity

Efforts to ensure the transferability of the analysis were done by presenting transparent explanations about the classroom situations, students‟ characteristics, and conclusion drawings in every stage of analysis. This should be enough for readers to justify the suitability of the study in their environment, and how the HLT could be adjusted in their situation.

Internal reliability

Internal reliability in data analysis is kept by minimizing subjectivities in interpreting data. This was done by discussing important episodes of the lesson with the supervisors, and fellow researchers. Thus, the final conclusions covered the combination of multi-interpreters, instead of the researcher‟s own interpretation.

External reliability

To improve the traceability of the data analysis, transparent reports on how the researchers come up with the interpretations or conclusions were provided. Here, we provided the readers with evidences and steps on how the data were treated.