A schematic–Theoretic view of problem solving and development of algebraic thinking

By D. Steele, D. Johanning. 2004

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Visual templates in pattern generalization activity (2010, background): “On the basis of recent findings at the K-9 and preservice elementary undergraduate levels involving generalization in patterning activity, we still need further research in terms of how such coordination could take place more effectively in a systematic manner (Mulligan & Mitchelmore, 2009; Warren &”
Schema-Based Instruction for Mathematical Word Problem Solving: An Evidence-Based Review for Students With Learning Disabilities (2020, background): “Schemas are assembled by continuously adding new layers of knowledge to form deeper and broader understanding of concepts (Steele & Johanning, 2004).”
The Effect of the Differentiated Teaching Approach in the Algebraic Learning Field on Students’ Academic Achievements (2016, background): “Algebraic thinking periods refers to periods of recognizing and analyzing mathematical structures, understanding and identifying mathematical relations, making generalizations, and analyzing changes (Steele & Johanning, 2004).”
Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns (2008, background): “Steele and Johanning (2004) developed a teaching experiment in which eight US 7th graders were asked to generalize five linear and three quadratic problem situations that pertained to growth, change, size, and shape.”