Technology as a tool for integrating high school algebra and geometry

David Jay Hebert

Abstract

The NCTM Standards call for an increase in relating the various fields of mathematics. Further, the NCTM Standards call for an increase use of functions as a connector between these fields of mathematics. This dissertation used these ideas developed an activity that related high school algebra and geometry. The activity was using the orthocenter of a triangle as a function of a triangle. The activity goes on to investigate the locus of orthocenters as two vertices of a triangle remaining fixed and the third vertex traversing the line. The researcher looked at the students beliefs about the relatedness of algebra and geometry both before and after the activity. The researcher then compared these beliefs to see if they differed. Further, the researcher pointed out a relationship between triangles and conic sections via the orthocenter.