Analysis of Students’ Conceptual Understanding of Grouped-Data Mean Based on APOS Theory in Grade X at SMA Negeri 1 Jayapura

Maria Novita Langoday (Cenderawasih University)

Journal of Education and Teaching Learning
Vol.4 No.2 October (2026)

Abstract content is typed in Arial Narrow, 11-point font, justified, italicized, and single-spaced. The abstract contains a summary of the research objectives, methods, and results. The abstract is limited to a maximum of 200 words. This study aims to analyze students' conceptual understanding based on APOS (Action, Process, Object, Schema) theory regarding grouped-data mean in Grade X at SMA Negeri 1 Jayapura. A descriptive qualitative approach was employed, with the researcher serving as the primary instrument. The participants were all 27 students in Grade X-11, who completed a constructed-response test on grouped-data mean to map the APOS stage they had attained. Based on the test results, six students were selected through purposive sampling using the principle of maximum variation sampling, with two students representing each of the Process, Object, and Schema stages, to participate in two Think Aloud sessions as a form of time triangulation. Data were analyzed through data reduction, data display, and conclusion drawing, and validity was examined through time triangulation and method triangulation. The results show that all participants had attained the Action and Process stages, as reflected in their ability to determine the class midpoint, calculate the frequency–midpoint product, and explain the steps for calculating grouped-data mean. For items 1 and 2, almost all participants consistently attained the Schema stage from the written test onward, whereas for the more complex item 3, some participants consistently attained the Schema stage only during the second Think Aloud session after initially being at the Process or Object stage. This difference was influenced more by nervousness and a lack of self-confidence during the interview than by instability in conceptual understanding. Thus, students' conceptual understanding of grouped-data mean varied between the Object and Schema stages, particularly for more complex contextual questions; therefore, teachers are advised to provide more varied contextual questions to encourage students to attain higher stages of understanding.