Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns

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A Learning Trajectory in 6-Year-Olds' Thinking about Generalizing Functional Relationships. (2015, background): “Additionally, although we focused on children’s functional thinking in the context of their analysis of function tables, there is also important research regarding how students reason about functions figurally and geometrically (e.g., Moss & McNab, 2011; Rivera & Becker, 2008).”
Students' Mathematical Noticing. (2013, background): “Specifically, research on the generalization of patterns has identified a tendency for students to notice recursive rather than functional relationships (Lannin, Barker, & Townsend, 2006; Lee, 1996; Rivera & Becker, 2008).”
Algebraic Thinking with and without Algebraic Representation: A Pathway for Learning (2011, background): “Finally, students who have worked successfully with quasi-variables might be further challenged to use the symbols of algebra to represent and work with mathematical generalizations drawn from a range of numerical and measurement situations as well as figural representations (see Rivera 2006; River”