TABLE 2.

Categories in the MRC and their definitions and connections to this study

Categories in the MRC	Definitionsa	Connection to this study
Invention	The underlying skills and abilities that allow students to conceive novel representations	Competency with graph choice, construction, and knowledge of variables is vital for conjuring new graphical representations (Leonard and Patterson, 2004; Tairab and Al-Naqbi, 2004; McFarland, 2010; Webber et al., 2014). In the think-aloud interviews, participants were asked to construct a graph from raw data.
Critique	Critical knowledge that is essential for assessing the quality of representations	Assessing the strengths and weaknesses of various graphs exposes students’ critical knowledge (McFarland, 2010; Angra and Gardner, unpublished data) Although the interviewer did not explicitly probe the participants to critique their graphs, we wanted to see whether participants spontaneously generated a critique.
Functioning	Providing reasoning for understanding the purpose of different representations, their usage, and limitations	Functioning unearths students’ reasoning for understanding the purpose of different types of graphs and the usage being dependent on the type of data present (McFarland, 2010; Webber et al. 2014; Angra and Gardner, unpublished data) In the think-aloud interviews, students were asked to articulate their graph choice.
Learning/reflection	Strategies for fostering understanding of representations	Reflection, reveals students’ awareness of their own understanding of graphs and gaps in their knowledge (Tanner, 2012) Several times in the think-aloud interviews, participants were probed to reflect on their graph choice and construction.

^a See diSessa and Sherin (2000).