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Stages of Mathematical Development and Cognitive Growth by Virginia Arvizu-Calvillo

This discussion explores the three critical phases of mathematical development as described by Virginia Arvizu-Calvillo: the Embodied Objects stage, Proceptual/Symbolic stage, and the Formal/Axiomatic stage. Each phase reflects a progression from hands-on exploration of physical objects to abstract reasoning and advanced formal thinking. The insights underscore the importance of cognitive units in learning mathematics, highlighting that students who can transition from embodied concepts to abstract thinking demonstrate greater success in their mathematical abilities.

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Stages of Mathematical Development and Cognitive Growth by Virginia Arvizu-Calvillo

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  1. Mathematics and Cognitive Growth Virginia Arvizu-Calvillo

  2. Phases of Mathematical Development • Embodied Objects Stage • Proceptual /Symbolic Stage • Formal/Axiomatic Stage

  3. Embodied Objects • Exploration of Objects • Moving to the Symbolic

  4. Proceptual • Process/procedure and concept • Cognitive Unit- compressed piece of knowledge • Students who can move farther away from the conceptual (embodied objects) are more successful

  5. Formal/Axiomatic • Abstract Thinking

  6. Tall, D. (2004). Thinking Through Three worlds of Mathematics. Internaltional Group for the Psycology of Mathematics Education, 4, 281-288.

  7. Van Hiele’s Levels Of Geometric Thinking • Inquiry Phase • Direct orientation • Explication • Free Orientation • Integration

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