Date of Award

Spring 2015

Document Type



Mathematics, Engineering & Computer Science

First Advisor

Joe Helbling

Second Advisor

Kelly Cline

Third Advisor

Eric Sullivan


Geometry is a complex and visual discipline. Because geometry includes abstract concepts, geometry teachers often use manipulatives to make concepts visible and tangible. In this thesis, the question is proposed: which types of manipulatives are most beneficial to which age groups based on student achievement, student engagement and the Common Core State Standards. This thesis analyzes the existing research about the use of different types of manipulatives with different age groups. The research was separated into age group brackets, kindergarten through second grade, third grade through fifth grade, sixth grade through eighth grade, and ninth grade through twelfth grade. The types of manipulatives were categorized into one of four types of manipulatives: Physical Designated (use determined by teacher), Physical Non-Designated (use left for the student to decide), Virtual Designated, and Virtual Non-Designated. For the age group including students in kindergarten through second grade, Physical Designated and Virtual Designated manipulatives were suggested based on research. For the age group including students in third through fifth grade, Physical Designated, Physical Non-Designated, and Virtual Designated manipulatives were suggested. For the age group sixth through eighth grade all four types of manipulatives were suggested. For the ninth through twelfth grade age group, Physical Non-Designated, Virtual Designated, and Virtual Non-Designated manipulatives were suggested.