Mathematical Knowledge for Teaching and its Specificity to High School Geometry Instruction

This paper documents efforts to develop an instrument to measure mathematical knowledge for teaching high school geometry (MKT-G). We report on the process of developing and piloting questions that purported to measure various domains of MKT-G. Scores on a piloted set of items had no statistical relationship with total years of experience teaching, but all domain scores were found to have statistically significant correlations with years of experience teaching high school geometry. Other interesting relationships regarding teachers’ MKT-G scores are also reported. We use these results to propose a way of conceptualizing how instruction specific considerations might matter in the design of MKT items. In particular, we propose that the instructional situations that are customary to a course of studies, can be seen as units that organize much of the mathematical knowledge for teaching such course.Research reported had the support of the National Science Foundation through grant DRL-0918425 to P. Herbst. All opinions are those of the authors and don’t necessarily reflect the views of the Foundation. Some of this material was presented at the 2012 Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. This is an expanded version of the conference paper.http://deepblue.lib.umich.edu/bitstream/2027.42/98833/1/MKT_and_geometry_instruction_herbst&kosko.pd