S*NLS as the linking mechanism between spatial structuring and numerical structuring¶

Theory · All theories
Evidence · 3 claims (3 for) · 2 studies (1 causal, 1 theoretical), q2 · 0 of 2 report an effect size · 3 claims rest on one study

Description¶

S-numerical linked structuring (SNLS) is a form of reasoning coordinating S-structuring, the mental construction of organization for sequences of physical/mental actions on perceptual or imagined material, with N-structuring, the construction of organization for numerical/algebraic symbols. The article defines it as "a form of reasoning that coordinates S-structuring and N-structuring consistent with a learner's understanding of the relevant spatial/numerical properties". In the elaborated CF account, S*NLS links the two parallel sets of levels of abstraction and supports students in directly connecting reasoning on each new problem to reasoning on the previous problem via recursion.

Design Implications¶

Context¶

Requirements¶

• Students need opportunities to act on sensory materials when forming initial combinatorial conceptualizations

Constraints¶

• Developed and illustrated in the context of permutation enumeration with cube towers

Target Learners¶

• undergraduate preservice middle school teachers

Target Learning Objectives¶

• linking concrete spatial reasoning to symbolic computational formulas

Claims¶

• Cube Tower Sequence Elaborated Cf Instantiation [+M]
• Spatial Skills Improve Through Block Building [+W]
• Students transferred cube-based permutation reasoning to permutation tasks not involving cubes [+W]

Related Theories¶

• Elaborated theory of levels of abstraction with a parallel set of levels for computational operation schemes
• Steffe's Number Sequences and Multiplicative Double Counting

Examples¶

• Cube-tower permutation enumeration task sequence
• Accomplish concreteness fading by incrementally increasing task size until physical manipulation becomes impractical

Key Sources¶

• Joseph Antonides, Michael T. Battista. (2022). Towards an Elaboration of Concreteness Fading: Reflections on a Constructivist Teaching Experiment. Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. https://eric.ed.gov/?id=ED630441