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The objective of this section is to move beyond visualization and articulate the data necessary to research learning within a CAS. Utilizing visuals of an educational CAS clarifies and separates different data into appropriate units of analysis. For example, utilizing Poth and Bullock’s (in press) visualization to examine the NCLM allowed for the articulation of necessary data sources to systematically study mathematics teacher learning at different levels within the CAS phenomena. See Table 1 for example of utilizing a visualization of a complex educational phenomena as a way to justify data sources and sampling.
Through the process of investigating phenomena using visualizations of CAS, such as Poth and Bullock’s (in press), the NCLM, and the ones participants begin to create during the workshop, different and important parts of a CAS can be illuminated. This allows for a more complete and truthful articulation of variables within an education CAS. A more complete understanding of the data allows for clearer sampling plans within and/or across different units of analysis within the CAS. Using models of educational CAS forces the user to sample more authentically because the visualizations are built around the unit(s) of analysis.
Participants will use the models they have started to create during the workshop to begin to interrogate their phenomena and identify appropriate data sources and sampling techniques. Using guiding questions 4-6 from section 1 participants will consider:
4) What data sources are necessary to capture influences on and from the unit of analysis within and across hierarchical levels?;
5) What sampling techniques are needed to capture both individual and organizational emergent properties relevant for the research question?; and
6) How do the emerging understandings of the educational CAS, the chosen unit of analysis, and the selected data sources inform study procedures?
This workshop will provide time for participants to engage in the iterative inquiry process needed to develop visualizations of a CAS. Through investigating their educational phenomena, their visualizations, and their data sources and sampling techniques, participants will begin to develop a deeper understanding of the CAS they are studying and how to model the CAS. Using their visuals participants will also engage in effectively utilizing visualizations of CAS as a way to justify data sources and sampling.