Sarah Rizzo

Date of Award


Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Science (MS)




Natasha Speer

Second Committee Member

Robert Franzosa

Third Committee Member

Eisso Atzema


Geometric transformations are difficult for students to perform. Often known as shifts, flips, turns, and stretches, transformations include translations, reflections, rotations, and dilations. Research indicates that pre-school through high school students have great difficulty performing and constructing transformations. Common strategies students use to construct the answers they give have also been documented by researchers. Little is known, however, about why students give the answers they do. The goals of this study are to understand how college students, some of whom are pre-service elementary, middle and high school teachers, perform transformations and to determine if a change of phrasing of the questions changes students’ performance. Student performances as well as verbalized thought process were utilized during analysis to investigate the research questions. Categories were developed based upon participant rationale for the placement of the transformed triangle. A group of students’ performances were compared when given directions in formal mathematical language and when given directions in informal mathematical language. Although more students correctly transformed the object when given directions in informal mathematical language the change in students’ performances was not significant for all cases. Students tended to be more successful translating a triangle when presented with informal mathematical language than any other transformation.