Theses Doctoral

An Examination of Three-dimensional Geometry in High School Curricula in the US and China

Cao, Mengmeng

Geometry is an essential branch in mathematics that helps students learn to grasp their environment and leverage that grasp into abstract understanding and reasoning. There has been an observable decrease in geometrical content in secondary education curricula, and particularly a “puzzling scarcity” in three-dimensional geometry, which has led to a decline in students’ geometrical abilities, spatial thinking and deductive reasoning abilities. This study addresses this issue by scrutinizing the enacted curriculum standards and the most influential textbooks related to three-dimensional geometry in two prominent countries, the US and China, both of which embrace the interplay of both conventional and innovative practices. This qualitative study used both content analysis and cross-cultural comparison methods to inquire about and to understand the current situation of three-dimensional geometry in high school. I focused on probing the communication types, objects, concepts, and spatial thinking abilities related to three-dimensional geometry in the standards and texts. To understand spatial abilities, I synthesized a spatial thinking abilities framework with six attributes and used this framework to exam the affordance of these abilities in the texts and requirements in the standards.
The result and analysis reveal the details of each text and standards individually and offer an examination of the alignment between the standards and texts. The comparison of the two countries’ different approaches also sharpens the understanding of the issue. I also worked to unveil students’ multiple ways of making sense of geometry concepts by two geometry learning models, Piaget’s model and van Hiele’s model, as well as spatial thinking abilities.

Geographic Areas


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More About This Work

Academic Units
Mathematics Education
Thesis Advisors
Wasserman, Nicholas Henning
Ph.D., Columbia University
Published Here
May 14, 2018