Data-ing process with image-based data: variable identification and generation

Using photographs as data, which involves making observations from images and organizing them into variables to answer statistically investigative questions, is recommended for K-12 level statistics education. Research is needed to support pre-service mathematics teachers' experiences with exploring such image-based data. With this task-based interview study, the goal was to shed light on (1) the pre-service mathematics teachers' data-ing actions during identifying and generating variables in relation to data familiarization, question posing, and data organization components and (2) how pre-service mathematics teachers identified and generated variables in the process of data-ing. Data from video recordings, transcripts of the interview sessions for each pair, and their work with photos on the shared online document, that is, groupings and questions posed, were analyzed using a progressive focusing approach. The results showed that the data-ing actions during identifying and generating variables with data familiarization, question posing, and data organization included observing, interpreting, conjecturing, inferring, comparing, grouping, ordering, questioning/question posing, relating variables, categorizing variables, and measuring variables. The pairs used various combinations of multiple actions while data-ing. There were two types of variable identification: (1) observational variables based on visual judgment or metadata and (2) inferential variables based on personal interpretation. The latter type presented a tension between the variable defined and how to measure it objectively, as well as challenges in writing clearly defined variables when posing questions.