Reflective Reflection

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Originally, I thought that I would group the articles by themes to complete my weekly reflections. For instance, the Week 12 reflection would incorporate the theoretical and/or philosophical underpinnings of conceptual understandings as discussed in the works of Simon (1995) and Samara & Clements (2004). Then, Week 13 would explore the affordances and constraints of learning trajectories highlighted in the work of Daro, Mosher, & Corcoran (2011), Empson (2011), and Myers, Sztajn, Wilson, & Edgington (2015). But, as I finished the Simon article, and then the Daro article, I realized that I was really struggling to make sense of the importance of the Simon article. As with all other articles, (and maybe this is a flaw of mine), if I spend…show more content…
I need to get clear in my mind what the field considers a learning trajectory and then consider what has been identified in the literature as learning trajectory pros and cons.
The report produced by Daro et al. provides a definition of trajectories (or progressions) that is accessible to many levels and applicable to many areas. According to Daro et al, “trajectories or progressions are ways of characterizing what happens in between any given set of beginning and endpoints and, in an educational context, describe what seems to be involved in helping students get to particular desired endpoints” (2011, p. 23). While this appears to be a non-biased approach to describing or categorizing the learning paths of students, with the underlying goal of aiding educators and researchers in instructional decisions and explorations, not all see learning trajectories as beneficial. From the reading, it is obvious that educators may not agree that all learning trajectories are beneficial. In the table below, I have identified some of the pros and cons discussed in the literature.

Through the readings, it was fairly easy to categorizes the benefits of trajectories. Trajectories can aid in focusing on children’s thinking (Daro et al., 2011; Empson, 2011; Myers et al., 2015; Olive, 2000; Turner et al., 2016), guide instructor’s anticipation of student responses (Daro et al., 2011), improve mathematical
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