Abduction–induction (generalization) processes of elementary majors on figural patterns in algebra

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Visual templates in pattern generalization activity (2010, background): “5 that I inferred from clinical interviews in two earlier studies I conducted with preservice elementary majors (Rivera & Becker, 2007) and the cohort 1 students over two consecutive years of constructivist-driven design experiments on pattern generalization (Rivera, 2008).”
Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns (2008, background): “A constructive generalization of a linear figural pattern refers to those direct or closed degree-1 polynomial forms which learners easily abduce or induce from the available cues as a result of cognitively perceiving figures that structurally consist of non-overlapping constituent gestalts or parts”