Supporting Spatial Reasoning: Identifying Aspects of Length, Area, and Volume in Textbook Definitions

Length, area, and volume share structural similarities enabling flexibility in reasoning for real-world applications. Deep understanding of structures can help teachers connect these concepts to support their students’ mathematical practices involving situations. In mathematics textbooks designed future teachers, definitions length, vary from procedural (e.g., use a ruler measure side lengths, formulas calculate measures) conceptual construct appropriate n-dimensional units that tessellate the space) formal function mapping qualitative size quantity units). Most describe as quantitative measurements provide examples standard units. Definitional aspects such describing an attribute or measurement, identifying dimensionality space, constructing nonstandard are inconsistently acknowledged across textbooks. Attending definitional spatial attributes quantification open conversations about structure essential meanings volume.