{"id":{"repo_id":"columbia-diss","oai_identifier":"oai:academiccommons.columbia.edu:10.7916/D8Z03G5W"},"canonical_url":"https://search.dev.ndltd.org/etd/columbia-diss/oai:academiccommons.columbia.edu:10.7916/D8Z03G5W","repository":{"repo_id":"columbia-diss","name":"Columbia University","base_url":"https://academiccommons.columbia.edu/oai"},"display":{"title":"Diagrammatic Reasoning Skills of Pre-Service Mathematics Teachers","abstract":"This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers\"™ content knowledge for teaching. However, there is no course in the mathematics curriculum that systematically develops diagrammatic reasoning skills, except Geometry. In the course of this study, a group of volunteers in the last semester of their teacher preparation program were presented with \"visual proofs\" of certain theorems from high school mathematics curriculum and asked to prove/explain these theorems by reasoning from the diagrams. The results of the interviews were analyzed with respect to the participants\"™ attained van Hiele levels. The study found that participants who attained higher van Hiele levels were more skilled at recognizing visual theorems and \"proving\" them. Moreover, the study found a correspondence between participants\"™ diagrammatic reasoning skills and certain behaviors attributed to van Hiele levels. However, the van Hiele levels attained by the participants were consistently higher than their diagrammatic reasoning skills would indicate.","abstract_html":"This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers"™ content knowledge for teaching. However, there is no course in the mathematics curriculum that systematically develops diagrammatic reasoning skills, except Geometry. In the course of this study, a group of volunteers in the last semester of their teacher preparation program were presented with "visual proofs" of certain theorems from high school mathematics curriculum and asked to prove/explain these theorems by reasoning from the diagrams. The results of the interviews were analyzed with respect to the participants"™ attained van Hiele levels. The study found that participants who attained higher van Hiele levels were more skilled at recognizing visual theorems and "proving" them. Moreover, the study found a correspondence between participants"™ diagrammatic reasoning skills and certain behaviors attributed to van Hiele levels. However, the van Hiele levels attained by the participants were consistently higher than their diagrammatic reasoning skills would indicate.","abstract_has_math":false,"creators":["Karrass, Margaret"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-24T01:44:16Z","subjects":["Mathematics--Study and teaching","Mathematics teachers","Mathematics teachers--Training of"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.7916/D8Z03G5W","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Karrass, Margaret"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012"]},{"key":"dc:type","label":"Dc Type","values":["Theses"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics--Study and teaching","Mathematics teachers","Mathematics teachers--Training of"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7916/D8Z03G5W"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers\"™ content knowledge for teaching. However, there is no course in the mathematics curriculum that systematically develops diagrammatic reasoning skills, except Geometry. In the course of this study, a group of volunteers in the last semester of their teacher preparation program were presented with \"visual proofs\" of certain theorems from high school mathematics curriculum and asked to prove/explain these theorems by reasoning from the diagrams. The results of the interviews were analyzed with respect to the participants\"™ attained van Hiele levels. The study found that participants who attained higher van Hiele levels were more skilled at recognizing visual theorems and \"proving\" them. Moreover, the study found a correspondence between participants\"™ diagrammatic reasoning skills and certain behaviors attributed to van Hiele levels. However, the van Hiele levels attained by the participants were consistently higher than their diagrammatic reasoning skills would indicate."]},{"key":"dc:title","label":"Title","values":["Diagrammatic Reasoning Skills of Pre-Service Mathematics Teachers"]}]}],"canonical_facts":{"dc:creator":["Karrass, Margaret"],"dc:date":["2012"],"dc:description":["This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers\"™ content knowledge for teaching. However, there is no course in the mathematics curriculum that systematically develops diagrammatic reasoning skills, except Geometry. In the course of this study, a group of volunteers in the last semester of their teacher preparation program were presented with \"visual proofs\" of certain theorems from high school mathematics curriculum and asked to prove/explain these theorems by reasoning from the diagrams. The results of the interviews were analyzed with respect to the participants\"™ attained van Hiele levels. The study found that participants who attained higher van Hiele levels were more skilled at recognizing visual theorems and \"proving\" them. Moreover, the study found a correspondence between participants\"™ diagrammatic reasoning skills and certain behaviors attributed to van Hiele levels. However, the van Hiele levels attained by the participants were consistently higher than their diagrammatic reasoning skills would indicate."],"dc:identifier":["https://doi.org/10.7916/D8Z03G5W"],"dc:language":["English"],"dc:subject":["Mathematics--Study and teaching","Mathematics teachers","Mathematics teachers--Training of"],"dc:title":["Diagrammatic Reasoning Skills of Pre-Service Mathematics Teachers"],"dc:type":["Theses"]},"updated_at":"2026-07-24T01:44:16Z"}