Visualizing Mathematics pp 195-228 | Cite as

# Analyzing the Relation Between Spatial and Geometric Reasoning for Elementary and Middle School Students

## Abstract

Numerous studies have found that spatial ability and mathematical ability are positively correlated. But specifying the exact nature of the relation between these types of reasoning has been elusive, with much research focused on understanding correlations between mathematical performance and specific spatial skills as measured by spatial tests. We attempt to deepen understanding of the relationship between spatial and mathematical reasoning by precisely describing the spatial processes involved in reasoning about specific topics in geometry. We focus on two major components of spatial reasoning. *Spatial visualization* involves mentally creating and manipulating images of objects in space, from fixed or changing perspectives on the objects, so that one can reason about the objects and actions on them, both when the objects are and are not visible. *Property-based spatial analytic reasoning* decomposes objects into their parts using geometric properties to specify how the parts or shapes are related, and, using these relationships, operates on the parts. Spatial analytic reasoning generally employs concepts such as measurement, congruence, parallelism, and isometries to conceptualize spatial relationships.

## Keywords

Mathematics Geometry Spatial visualization Analytic Reasoning Mental model Learning progression Structure Shape Isometries Reflections Rotations Measurement Length Angle Area Volume## References

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