The use and application of geometric transformations is a fundamental standard for the Common Core State Standards. This study was developed to determine current high school teachers’ prior mathematical content knowledge and develop their content knowledge of transformations and their applications. The design of this study was guided by the questions: “Why is there a level of reluctance amongst secondary teachers when it comes to teaching geometric transformations?” and “How can their content knowledge become deepened to apply geometric transformations to prove that two figures are congruent?” The study provided teachers a chance to gain experience with transformations and use transformations to develop an understanding of congruence and similarity. The teachers’ work with transformations also enhanced their understanding of how transformations are the foundation for Euclidean geometry and begin to lay a foundation for the basics of rigid motion in the plane, with or without the use of coordinates. The results supported the claim that teachers’ transformation content knowledge needs to be deepened overall and in particular with respect to the application of transformations to prove that two figures are congruent. The results also showed that, with an increase of understanding of the mathematical properties of transformations, teachers are better prepared to teach them in their classrooms.
","abstract_html":"<p>The use and application of geometric transformations is a fundamental standard for the Common Core State Standards. This study was developed to determine current high school teachers’ prior mathematical content knowledge and develop their content knowledge of transformations and their applications. The design of this study was guided by the questions: “Why is there a level of reluctance amongst secondary teachers when it comes to teaching geometric transformations?” and “How can their content knowledge become deepened to apply geometric transformations to prove that two figures are congruent?” The study provided teachers a chance to gain experience with transformations and use transformations to develop an understanding of congruence and similarity. The teachers’ work with transformations also enhanced their understanding of how transformations are the foundation for Euclidean geometry and begin to lay a foundation for the basics of rigid motion in the plane, with or without the use of coordinates. The results supported the claim that teachers’ transformation content knowledge needs to be deepened overall and in particular with respect to the application of transformations to prove that two figures are congruent. The results also showed that, with an increase of understanding of the mathematical properties of transformations, teachers are better prepared to teach them in their classrooms.</p>","abstract_has_math":false,"creators":["Bonn, Tamara V"],"institution":null,"degree_name":"Master of Arts in Teaching, Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Dr. John Sarli"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-06-01T07:00:00Z","date_published":"2015-06-01T07:00:00Z","updated_at":"2026-07-24T01:52:45Z","subjects":["geometric transformations","application","Science and Mathematics Education"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/150","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. John Sarli"]},{"key":"dc:creator","label":"Author","values":["Bonn, Tamara V"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-05-16T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Teaching, Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["geometric transformations","application","Science and Mathematics Education"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/150"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The use and application of geometric transformations is a fundamental standard for the Common Core State Standards. This study was developed to determine current high school teachers’ prior mathematical content knowledge and develop their content knowledge of transformations and their applications. The design of this study was guided by the questions: “Why is there a level of reluctance amongst secondary teachers when it comes to teaching geometric transformations?” and “How can their content knowledge become deepened to apply geometric transformations to prove that two figures are congruent?” The study provided teachers a chance to gain experience with transformations and use transformations to develop an understanding of congruence and similarity. The teachers’ work with transformations also enhanced their understanding of how transformations are the foundation for Euclidean geometry and begin to lay a foundation for the basics of rigid motion in the plane, with or without the use of coordinates. The results supported the claim that teachers’ transformation content knowledge needs to be deepened overall and in particular with respect to the application of transformations to prove that two figures are congruent. The results also showed that, with an increase of understanding of the mathematical properties of transformations, teachers are better prepared to teach them in their classrooms.
"]},{"key":"dc:title","label":"Title","values":["Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity"]}]}],"canonical_facts":{"dc:contributor":["Dr. John Sarli"],"dc:creator":["Bonn, Tamara V"],"dc:date.available":["2015-05-16T07:00:00Z"],"dc:description.abstract":["The use and application of geometric transformations is a fundamental standard for the Common Core State Standards. This study was developed to determine current high school teachers’ prior mathematical content knowledge and develop their content knowledge of transformations and their applications. The design of this study was guided by the questions: “Why is there a level of reluctance amongst secondary teachers when it comes to teaching geometric transformations?” and “How can their content knowledge become deepened to apply geometric transformations to prove that two figures are congruent?” The study provided teachers a chance to gain experience with transformations and use transformations to develop an understanding of congruence and similarity. The teachers’ work with transformations also enhanced their understanding of how transformations are the foundation for Euclidean geometry and begin to lay a foundation for the basics of rigid motion in the plane, with or without the use of coordinates. The results supported the claim that teachers’ transformation content knowledge needs to be deepened overall and in particular with respect to the application of transformations to prove that two figures are congruent. The results also showed that, with an increase of understanding of the mathematical properties of transformations, teachers are better prepared to teach them in their classrooms.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/150"],"dc:subject":["geometric transformations","application","Science and Mathematics Education"],"dc:title":["Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Teaching, Mathematics"]},"updated_at":"2026-07-24T01:52:45Z"}