Students understand and can evaluate the role of proof in geometry and in mathematics in general, the theories of how students progress through the van Hiele levels in learning geometry and how these two topics are related. They can use this knowledge to evaluate current instructional, curricular, and policy recommendations of leaders in mathematics education regrading the teaching of geometry in the public schools.
Students can apply principles of quality research to analyze and critique research on the teaching and learning of geometry, and understand the affordances and constraints of research paradigms and methodologies in this body of research.
Students understand the central concepts, conditions, definitions, theorems, assumptions, structure and extensions of high school (Euclidean) geometry. They can use these understandings to prove general cases of geometric theorems and apply these theorems to solve problems in Euclidean geometry.
Students can assess the van Hiele level at which their students are operating and design tasks and lessons to move learners to a higher van Hiele level, eventually to the level of deduction and proof. Throughout the instruction at different van Hiele levels, students can continually evaluate the role that proof is playing for the learners and understand how to adjust their instruction to ensure that proof activities are meaningful. Students can use their knowledge of the van Hiele levels, proof, and the NCTM Standards to evaluate geometry curriculum for appropriate sequencing.
Students recognize the key role that geometry should play in school mathematics and the valuable insights provided by the literature on the teaching and learning of geometry, and feel a desire to continually seek opportunities to improve their own teaching of geometry and promote better instruction of geometry in the schools by seeking to adapt the instruction to the van Hiele level of the students.
Students strive to follow the example of Jesus Christ in both their personal and professional lives, seek consistency between their understanding of the restored gospel of Jesus Christ and principles of geometry teaching and learning, and use this enriched understanding of teaching and learning to nurture the divine potential of all in their spheres of influence.