The Analysis Process

Data analysis in educational design research is typically inferential, interpretative and cyclical (Reimann, 2011). This approach was reflected in the structure the analytic process. Both inductive and deductive approaches to data analysis were employed. A deductive approach was used because the research questions were determined deductively and so based on explicit theoretical frameworks underpinning and informing the study, the data analysis employed a partially deductive framework (Patton, 2002). From this perspective, the data were analysed deductively according to existing theoretical frameworks, which acted as ‘sensitising concepts’; categories or references that originated in the research

literature and were brought by the researcher to direct data exploration (Patton, 2002, p. 456). For example, as the theoretical framework for the study reasoned that the instructional innovations would trigger statistical reasoning and learning, data evidencing these processes was actively sought.

The study focus was the exploration of statistical reasoning through the models created by the children as they worked the modeling problem to a solution. The study was interested in the characteristics of the task contexts and the data contexts the children drew from as they engaged with the modeling tasks and developed their models. Accordingly, data analysis strove to reveal the substance of the contextual use and reasoning employed by the children (that is, what contextual knowledge they drew from and what reasoning they used). The theoretical

98 identification of the models developed by the children during the modeling activities. Data analysis strove to reveal the impact of key elements of the task contexts, that is, determine which elements of the design of the modeling activities impacted the children’s use of knowledge and reasoning to solve the statistical problem. The children’s use of contextual knowledge when engaging with data based reasoning were actively sought, as was evidence of the role of the design characteristics of the modeling activities on statistical reasoning processes and their development.

Data analysis also employed an inductive process, where important

dimensions were allowed to emerge from the patterns found in the data. The use of both inductive and deductive approaches helped organise and explain the data and find concepts to help make sense of and present the data (Miles & Huberman, 1994). For example, inductive analysis found patterns of difference in the children’s use of picture story book knowledge when reasoning between the design and analysis systems in data modeling and patterns of more abstract reasoning in task contexts with certain characteristics. Analysis repeatedly moved from verification to discovery, through deductive and inductive processes, as themes or categories for specific statistical processes such as instances of inductive reasoning were

established and tested (Patton, 2002).

Data were initially analysed chronologically. Repeated reading of the transcripts and viewing of the videotaping enabled the researcher to gain an

understanding of the data as a whole and to develop sensitivity to the data. Iterative refinement cycles for videotape analyses of conceptual change were a key tool. This technique enabled data interpretations to be validated through being repeatedly tested, refined and extended and to develop an adequate framework for interpretation that endeavoured to reduce bias (Lesh & Lehrer, 2000). Initial and subsequent

impressions were noted and diagrammed for logical ways to select sessions for closer analysis, in conjunction with data collected through other methods, including

ongoing collaboration with the participant teacher.

A content analysis was applied to the data, as a means of reducing and making sense of it and to identify core meanings that were theoretically based or emerging as patterns or themes (Patton, 2002). In conjunction with the interpretative framework already developed, content analysis provided usable units of analysis for

99 categorisation into emerging themes (Denscombe, 1998) which were described and summarised for more focused coding (Miles & Huberman, 1994). A provisional ‘start list’ of codes drawn from analysis at the time of data collection, based on the conceptual framework along with the research questions, also informed this. Topic coding (Richards, 2009) enabled a focus on construct validation through seeking agreement as to categories through other interpretations generated from other sources, and to avoid a tendency to view data through narrow or limited theoretical windows. The coding process itself was inherently subjective, however, sensitivity to context and theory were sought to bring balance to the process (Patton, 2002).

Data contributing to the research questions were progressively reviewed, and examined for patterns and trends using constant comparative strategies (Strauss & Corbin, 1990). Common themes through multiple perspectives were identified and refined through systematic comparison of similarities and differences between concepts to bring out possible properties and dimensions not otherwise evident (Strauss & Corbin, 1998). These themes were grouped for analytic coding to engage in contextualised interpretation (Richards, 2009) with recursive testing and affirming between the data and coding occurring for codes that did not fit the data until

verification of the analysis could be met. The themes reinforced many of the key categories proposed through the theoretical framework such as the children’s use of the picture story context in data based reasoning and inductive reasoning during data analysis, suggesting the conceptual framework as an acceptable model (Saldana, 2007).