This research proposes that the explicit incorporation of spatial thinking into teacher preparation programs is an effective and efficient way to foster and develop a spatially literate populace. The major objective of this study was to examine the effect of explicit instruction in spatial thinking on the development of preservice teachers' knowledge, skills, and dispositions toward teaching it. A one-day workshop - Teaching Spatial Thinking with Geography - for preservice geography teachers was developed as the intervention of this study. The primary focus of the workshop was to provide an explicit opportunity to learn about spatial thinking and to practice skills required to incorporate spatial thinking into participants' classrooms. Three assessments were used to examine changes in participants' knowledge, skills, and dispositions, before and after the workshop: the spatial concepts test, the teaching spatial thinking disposition survey, and participant-produced lesson plans. Individual interviews were conducted to obtain a deeper understanding of participants' learning experiences during the workshop. A mixed-method research design was adopted in which both quantitative and qualitative methods were used to offset the weaknesses inherent within one method with the strengths of the other. The major findings of this study include: 1) explicit instruction about spatial concepts is necessary to the development of preservice teachers' knowledge required for teaching spatial thinking through geography; 2) the skills development required to teach spatial thinking should be approached as the development of pedagogical content knowledge; 3) dispositions toward teaching spatial thinking should be differentiated from dispositions toward teaching general thinking skills; 4) although explicit instruction about teaching spatial thinking contributed substantially to the preservice teachers' acquisition of knowledge and skills and the development of positive dispositions toward teaching spatial, each of these components develops at a different rate but affect each other; and 5) a promising approach to the development of preservice teachers' pedagogical content knowledge would be to offer geography education courses, not general geography or methods courses, in which the focus is explicitly on teaching geography with an emphasis on spatial thinking.

abstract: Recent advances in geo-visualization technologies, such as Google Earth, have the potential to enhance spatial thinking. Google Earth is especially suited to teaching landforms and geomorphological processes in traditional, online, or hybrid college classroom settings. The excitement for the technology as a learning tool, however, must be tempered by the need to develop sound and supportive pedagogies. A fundamental gap in the geoscience education literature exists because learning experiences with Google Earth, from the perspective of the student, are not completely understood. This dissertation analyzes three case studies in college introductory physical geography (Chapters 2 and 4) and teacher education (Chapter 3) courses at Arizona State University where students completed an online (Chapter 2 and 3) laboratory that used Google Earth as the main tool for landform identification and interpretation, and a hardcopy laboratory and in-field exercise (Chapter 4) that compared Google Earth oblique with traditional stereopair air photo and planimetric perspectives. Gauging student performance in these tasks, along with their formative and summative opinions for `what it was like to learn this way', provide information as part of a feedback loop to develop and improve instructional scaffolding and best practices so that the focus remains on the content-to-be-learned and not the tool. These case studies show that, in general, prior use of Google Earth is usually not a limiting factor; multiple perspectives and supplemental visualizations of landforms with Google Earth's may enhance the learning experience; the hands-on nature of structured Google Earth exploration in these labs are virtual field trips that increase enjoyment and fit within a learner-centered curriculum; scaffolding landform-learning exercises for aspiring elementary school teachers linked to children's literature assists the development of content knowledge for teaching physical geography and spatial thinking; and, finally, despite a virtual globe's high-quality visualizations and promising potential for learning, there is still a role for stereopair images in the geomorphology classroom. / Dissertation/Thesis / Doctoral Dissertation Geography 2014

O autor deste trabalho parte pressupõe que a articulação entre a Educação Geográfica e a Cartografia Escolar possui grande relevância para o desenvolvimento do pensamento espacial dos estudantes da escola básica. Essa dimensão da inteligência é essencial para a cidadania consciente e para o exercício das mais diversas atividades profissionais e cotidianas. Considerando esse cenário, o objetivo central desta pesquisa é avaliar qual é o nível de contribuição da Educação Geográfica e da Cartografia Escolar no segmento do 6º ao 9º anos do ensino fundamental para que os alunos sejam capazes de ampliar sua capacidade de pensar espacialmente em situações que envolvem representações espaciais, sobretudo as cartográficas, aplicadas a contextos geográficos. Para isso, recorremos ao campo de pesquisas do pensamento espacial (spatial thinking), desenvolvido principalmente nos Estados Unidos no decorrer das últimas décadas. Dessa forma, adotamos como definição do pensamento espacial a que foi apresentada no relatório do National Research Council (2006) e que tornou-se a referência nessa seara de investigação: Pensamento espacial um tipo de pensamento é baseado na amálgama de três elementos: conceitos espaciais, instrumentos de representação e processos de raciocínio (NRC, 2006, ix). Nossa metodologia envolveu dois caminhos distintos, mas articulados. Realizamos a análise das três coleções de livros didáticos de Geografia mais adotadas no segmento de 6º ao 9º anos do ensino fundamental brasileiro, com a finalidade de avaliar em que medida os exercícios e atividades presentes nessas obras contribuem para o desenvolvimento do pensamento espacial discente. A título de parâmetro comparativo, fizemos o mesmo com uma coleção de didáticos franceses destinados à mesma faixa de escolaridade. Para realizar essa avaliação das atividades utilizamos a Taxonomia do Pensamento Espacial de Jo e Bednarz (2009), criada exatamente para essa finalidade e replicada por Scholz et al. (2014). O levantamento identificou não apenas a proporção de questões demandantes do pensamento espacial, mas o nível dos processos de raciocínio envolvidos e o tipo de representação espacial utilizado. O segundo caminho metodológico foi a aplicação do Teste de Aptidão do Pensamento Espacial (STAT, em inglês), desenvolvido por Lee e Bednarz (2012), a 268 alunos brasileiros do 9º ano do ensino fundamental, em seis escolas diferentes. Após a tabulação dos dados realizamos uma análise comparativa entre os resultados dos alunos brasileiros e os números resultantes das aplicações do mesmo teste em dois contextos internacionais: uma escola estadunidense (LEE e BEDNARZ, 2012) e os de três escolas em Ruanda (TOMASZEWSKI et al., 2014). A análise incluiu tanto os resultados globais do teste quanto os resultados dos alunos de cada instituição em cada um dos oito grupos de modalidades do pensamento espacial considerados pelos elaboradores do STAT. Nossas conclusões finais resultaram do cotejo das informações obtidas a partir dessas duas linhas metodológicas. / The author of this thesis believes that Geography Education and School Cartography have both great importance for the development of spatial thinking among students in K-12. This dimension of intelligence is crucial for citizenship and for the practice of many professional and daily activities. Considering such a framework, the main goal of this research is to assess the contribution of Geography Education and School Cartography in Brazilian middle school to enhance students capacity to think spatially in situations that encompass spatial representations, specially cartographic ones, in geographical contexts. To answer this question we decided to betake the field research known as spatial thinking, developed mostly in the U.S. during the last two decades. As a consequence we adopted the definition of spatial thinking that was presented in the report of the National Research Council (2006), which has become the main reference in the field: Spatial thinkingone form of thinking is based on a constructive amalgam of three elements: concepts of space, tools of representation, and processes of reasoning (NRC, 2006, ix). Our methodology was based on two interconnected paths. We analyzed the three most adopted Geography textbooks collections for the four years of Brazilian middle school (6th to 9th grades) with the purpose of assessing in which extent the exercises in those books are capable of fostering students spatial thinking. In order to stablish a comparison with Brazilian textbooks we also assessed a French textbook collection destined to the same grade levels. To perform such an assessment, we used the Taxonomy of Spatial Thinking (Jo and Bednarz, 2009) designed for this particular purpose and replied by Scholz et al. (2014). The study identified not only the ratio of questions demanding spatial thinking but also the processes of reasoning involved. The second methodological path was based on the use of the Spatial Thinking Ability Test (STAT), designed by Lee and Bednarz (2012). We have administered the STAT to 268 students of six different Brazilian schools, all of them in the end of the 9th grade. After organizing all the data, we compared the Brazilian results with those of two international studies where the same test was administered: one school in the United States (LEE and BEDNARZ, 2012) and three schools in Ruanda (TOMASZEWSKI et al., 2014). Our analysis included both the global results of students overall performance in the test and their accomplishments regarding the eight modes of thinking spatially defined by the authors of the STAT. Our final conclusions were the results of the comparison between the outcomes obtained from our two methodological paths.

O pensamento espacial é uma atividade cognitiva desenvolvida no cotidiano e pode ser sistematizado pelas mais diversas disciplinas escolares, principalmente pela Geografia. Os conceitos, as representações e habilidades espaciais são componentes dessa forma de pensamento. A compreensão do conceito de pensamento espacial e a investigação de como pode ser desenvolvido de forma sistematizada na escola torna-se ponto central na contemporaneidade, composta pelas mais diversas linguagens que representam o espaço. Reconhecendo tal importância, constatamos a ausência de referenciais para o seu desenvolvimento por crianças em atividades escolares, com o enfoque geográfico, na Educação Infantil. Como objetivo principal, destaca-se a proposição de referenciais teóricometodológicos para o conhecimento espacial de crianças de quatro a seis anos. Parte-se da seguinte pergunta de pesquisa: quais habilidades e conceitos espaciais podem ser abordados em atividades para o desenvolvimento do pensamento espacial de crianças de 4 a 6 anos? Para respondê-la e alcançarmos o objetivo principal, os objetivos específicos constituem pauta de trabalho para o desenvolvimento da investigação: sondar e analisar a pertinência, as possibilidades e a abordagem das noções espaciais na Educação Infantil; desenvolver situações de ensino, com base nas teorias norteadoras sobre pensamento espacial, desenho infantil e construção de conceito sob a perspectiva histórico-cultural; compreender os padrões estabelecidos nas representações gráficas realizadas pelas crianças; compreender os diálogos entre as crianças. As sequências de atividades são instrumentos da investigação, cada uma apresenta seus objetivos próprios, com base na representação, no conceito e nas habilidades do pensamento espacial. As três sequências de atividades têm como conceito central a Localização. A primeira trata especificamente do espaço próximo, aquele de vivência, enquanto as outras duas mobilizam o conhecimento geográfico a partir de aspectos distantes de suas vivências imediatas. Para analisarmos a expressão do pensamento espacial, narramos os acontecimentos principais da atividade, transcrevemos as vídeo-gravações e mapeamos os registros de acordo com o nosso interesse: verificar os conceitos e habilidades espaciais. Compreendemos que o desenho consiste em uma linguagem que concretiza e reflete o raciocínio espacial, envolvendo importantes princípios da cartografia e da geografia. A concepção assumida é a da infância enquanto categoria social e a criança enquanto sujeito de direito ao conhecimento e, neste caso, espacial. A criança é pensada nesta pesquisa como ser capaz de aprender, refletir, criar, trocar, dialogar e ensinar sobre o espaço. Ao longo da análise dos dados de pesquisa, concluímos que as palavras são elementos fundamentais que concretizam o modo de pensar, no caso, a habilidade do pensamento espacial, e o desenho é parte da iniciação cartográfica. Afirmamos nesta tese a relação direta da Geografia no desenvolvimento do pensamento espacial, tendo em vista a própria natureza desta ciência, e também da Cartografia enquanto linguagem que materializa essa forma de pensar. Defendese, assim,o conhecimento geográfico na Educação Infantil, por meio do pensamento espacial, pois as crianças podem ampliar seus conhecimentos espaciais. / Spatial thinking, comprised of concepts, representations and spatial abilities, is a cognitive activity developed in everyday living, and can be systematized through different school disciplines, mainly Geography. The comprehension of this concept and the investigation of how it can be developed and systematized in schools are critical points, involving different languages that represent the space. Considering this, we noticed the absence of references in geography-focused school activities for the development of spatial thinking. Our main objective is to propose theoretical and methodological references for the spatial knowledge of children aged between 4 and 6 years old. The research is based on the following question: Which spatial abilities and concepts can be addressed in activities aimed at developing spatial thinking in children aged 4 to 6 years old? To answer this question and achieve the main objective, the specific objectives were: a) to investigate and analyze the pertinence, possibilities and approaches regarding the spatial notions in childrens education; b) develop teaching situations based on guiding theories about spatial thinking, childrens drawing and the concept construction under a historical and cultural perspective; c) understand the patterns in childrens graphic representations; and d) analyze the childrens dialogues. Three series of activities with distinct objectives were proposed and analyzed as investigation instruments, based on the spatial thinking representation, concept, and abilities. All the activities addressed the central concept of Location. The first activity series deals specifically with the space nearby, the existence space, while the two other series are related to the geographic knowledge regarding distant aspects. In order to analyze spatial thinking expression, we narrated the main outcomes of the activities, transcribed the video recordings, and mapped the resulting data according to our interests; i.e., verify the spatial concepts and abilities. Drawing consists in a language that concretizes and reflects spatial reasoning, involving important principles of Cartography and Geography. The present research adopted the conception of childhood as a social category, and the child is the subject of the right to acquire knowledge, in this case, spatial knowledge. In this research, children are considered capable of learning, reflecting, creating, exchanging experiences, dialoguing, and teaching about the space. The analysis of the research data allowed us to conclude that drawing is part of the cartographic initiation, and words are fundamental elements that concretize the way of thinking, in this case, spatial thinking ability. In this thesis, we reaffirm the direct relationship between Geography and the development of spatial thinking, considering the very nature of this Science, and Cartography as the language used to materialize this way of thinking. The present thesis defends the development of spatial thinking in childrens education as a way to broaden the spatial knowledge and the construction of spatial concepts by the children.

Master of Arts / Department of Geography / J. M. Shawn Hutchinson / Information dashboards are decision-support tools that pull data from multiple sources and display those data on a single screen. Information dashboards are becoming common in fields such as medicine, computer science, and business, given their perceived ability to facilitate faster and more accurate assessments by users. However, there is very little peer-reviewed research on information dashboards that support this assumption. This research focuses on applying the concept of an information dashboard visualization within the spatial sciences and evaluating the effectiveness of a geographic information dashboard, or GID, on improving user performance related to spatial thinking tasks. A review of literature from multiple disciplines highlights what is, and what is not, understood about dashboard visualizations. Borrowing from ideas such as Cognitive Fit Theory and past work in evaluating the effectiveness of map animations, an appropriate method for evaluating the GID is proposed. A Web-based GID and an alternative “tabbed” visualization were developed using the R Shiny package to support an analysis of grassland vegetation development for a site located in northeastern Kansas. A controlled experiment was conducted using a survey completed by volunteer student participants who responded to a series of benchmark tasks related to the interpretation of 6 related maps and graphs. Data for three dependent variables (task completion time, task response accuracy, and an integrative measure of performance accounting for both time and accuracy) were collected directly from the survey or post-survey grading of responses. Three independent variables and their impact on spatial task performance were analyzed, including the type of visualization, assessed spatial thinking ability, and cognitive task type. Results showed that participants using the GID completed the benchmark tasks faster and more accurately, but that a users’ spatial thinking ability had the most significant influence on performance regardless of visualization. Evidence was found to support the idea that the GID improved spatial thinking performance, especially for users with more experience in spatial reasoning, and that the GID format may improve user performance beyond what is expected based on an independent assessment of spatial thinking ability.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-10-23T12:50:00Z No. of bitstreams: 2 Dissertação - Leovan Alves dos Santos - 2015.pdf: 847118 bytes, checksum: 9be773f7bde2dda9e8f7ec3881bbc738 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-23T13:33:39Z (GMT) No. of bitstreams: 2 Dissertação - Leovan Alves dos Santos - 2015.pdf: 847118 bytes, checksum: 9be773f7bde2dda9e8f7ec3881bbc738 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-23T13:33:39Z (GMT). No. of bitstreams: 2 Dissertação - Leovan Alves dos Santos - 2015.pdf: 847118 bytes, checksum: 9be773f7bde2dda9e8f7ec3881bbc738 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-04-16 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / This research analyzes, through a teaching experience, teaching Geography in the survey with the aim of building a spatial thinking by students. For this, it has been an object of research a Didactic sequence (SD) in Geography teaching for elementary school, planned, implemented and evaluated by two teachers, in order to understand how the teaching of Geography from the research can collaborate for the student to meet their everyday spatial practices, and their place of experience as a reference to analyze the geographic space. To make feasible what was proposed, methodologically, this research was based on action research assumptions, with elements of ethnographic research. Many questions permeate the intention and the development of this research, such as research can make a methodological approach to the teaching of school geography? How the teaching of Geography from research can contribute to the development of spatial concepts by students? To what extent the local student can contribute to be an analysis of the scale of the research Geography teaching? Thus, we sought to initially conduct a literature review of the theoretical basis for teaching Geography from pesqusia the papers presented at the National Meeting of Geography Teaching Practice (Enpeg) and Core forums Teaching and Research in Geographical Education (Nepeg) . Were analyzed, then theses and dissertations of the last decade that address the theme of research in school geographical education. Later, it was made a semi-structured interview with the teacher and I were observed their practices. Was also examined the expression of perceptions of teacher II from the questions asked Professor I. At the end, we proceeded to the analysis of some documents, such as the National Curriculum Parameters (PCN), the National Curricular Guidelines (DCN) the pedagogical projects of the main courses that form Geography teachers in Goiás and the Pedagogical Political Project (PPP) of schooling field of research. Teaching Sequence started from a dialectical conception of education, focusing on the questioning, organization and synthesis of knowledge. The activities were aimed at students, while researching his subjects, could question the content from its initial social practice and could count on the teacher in mediating the geographic content and the orientation of their research. Finally, the activities sought to promote a return to the initial social practice of these students, in which the initial notion of them were already processed and forwarded to the formation of a spatial thinking and a geographic look. There was the intention on the part of teachers I and II, that students could build their spatial concepts according to the specific contents of Geography, when making a significant offer to students and act in their classrooms to develop and create potential, not just limited to expect the capabilities necessary for the understanding of a particular concept ever to develop. / presente investigação analisa, por meio de uma experiência pedagógica, o ensino de Geografia pela pesquisa com o objetivo de construção de um pensamento espacial pelos alunos. Para isso, tem-se como objeto de investigação uma Sequência Didática (SD) em ensino de Geografia para o ensino fundamental, planejada, aplicada e avaliada por dois professores, com a finalidade de compreender de que forma o ensino de Geografia pela pesquisa pode colaborar para que o aluno possa conhecer suas práticas espaciais cotidianas, tendo seu local de vivência como referência para analisar o espaço geográfico. Para tornar viável o que fora proposto, metodologicamente, esta pesquisa foi baseada nos pressupostos da pesquisa-ação, com elementos da pesquisa etnográfica. Muitos questionamentos perpassam a intenção e o desenvolvimento desta investigação, como: a pesquisa pode compor uma abordagem metodológica para o ensino da Geografia escolar? De que forma o ensino de Geografia pela pesquisa pode contribuir para o desenvolvimento de noções espaciais pelos alunos? Em que medida o local do aluno pode contribuir para ser uma escala de análise do ensino de Geografia pela pesquisa? Assim, buscou-se inicialmente realizar um levantamento bibliográfico das bases teóricas para o ensino de Geografia pela pesqusia nos trabalhos apresentados nos Encontros Nacionais de Práticas de Ensino de Geografia (Enpeg) e nos fóruns do Núcleo de Ensino e Pesquisa em Educação Geográfica (Nepeg). Analisaram-se, em seguida, teses e dissertações da última década que tratam a temática da pesquisa na educação geográfica escolar. Posteriormente, foi feita uma entrevista semiestruturada com o professor I e observaram-se suas práticas. Examinou-se também a expressão das percepções do professor II a partir das perguntas feitas ao professor I, tais percepções foram registradas logo após a entrevista com este professor. Ao final, procedeu-se à análise de alguns documentos, tais como os Parâmetros Curriculares Nacionais (PCN), as Diretrizes Curriculares Nacionais (DCN), os projetos pedagógicos dos principais cursos que formam professores de Geografia em Goiás e o Projeto Político Pedagógico (PPP) da escola-campo da pesquisa. A Sequência Didática partiu de uma concepção dialética de ensino, tendo como foco a problematização, sistematização e síntese do conhecimento. As atividades estiveram voltadas para que os alunos, ao pesquisarem seus temas, pudessem problematizar o conteúdo a partir de sua prática social inicial e pudessem contar com o professor na mediação dos conteúdos geográficos e também na orientação de suas pesquisas. Por fim, as atividades desenvolvidas buscaram promover um retorno à prática social inicial desses estudantes, em que a noção inicial deles estivesse transformada e já encaminhada para a formação de um pensamento espacial e de um olhar geográfico. Houve a intencionalidade, por parte dos professores I e II, de que os alunos pudessem construir suas noções espaciais de acordo com os conteúdos específicos da Geografia, ao apresentarem uma proposta significativa aos discentes e atuarem em suas respectivas salas de aula no sentido de desenvolver e criar potencialidades, e não somente se limitar a esperar que as capacidades necessárias à compreensão de um determinado conceito algum dia se desenvolvessem.

Geography education is undergoing change in K-12 education due in part to the introduction of geospatial technologies, including geographic information systems (GIS). Although active engagement in GIS mapping would seem to enhance students’ spatial thinking, little is known about the mapping strategies that students employ or about changes in their geographic knowledge that would result. This study, set in a high school Advanced Placement human geography class, sought to contribute to these areas of inquiry. Participants performed a web-based GIS task focused on global population and migration. Attention in the study was on (a) the strategies students employed when investigating geographic phenomena using GIS, (b) changes in their cognitive maps, as assessed through sketch maps, resulting from the activity, (c) the relationship between GIS maps and sketch maps, and (d) the ways in which a subset of students serving as case studies explained the nature of their mapping. The study employed screen-captures, video-recordings, observations, pre- and post-study sketch maps, and interviews. Analyses of the GIS process revealed that, in creating their maps, the students used a number of strategies, which included searching, layering, removing layers of data, adjusting transparency, editing, and noting. Although searching and layering were employed by all students, there was variability across students in use of the other strategies. With respect to changes in their spatial thinking, analyses of the sketch maps showed increases in elaboration and accuracy in terms of migration patterns. When GIS maps were compared to sketch maps, analyses showed relations for many students. The six students who served as case studies revealed major connections between personal interests and the reasoning employed in mapping. They also described their entry points into the process. The study shows how real-time data collection, including screen captures, as well as more static measures, specifically sketch maps, can provide insights into the spatial thinking of students while using GIS. It provides some support to educational approaches to geography in which students become creators of maps, not simply users of maps, and suggests that, through their own mapping process, students expand their cognitive maps and enhance their spatial thinking.

<p>  </p> <p>Radian angle measure is central to learning trigonometry, with researchers providing evidence that a coherent understanding of radian contributes to a coherent understanding of trigonometric and inverse trigonometric functions. However, there are few opportunities for students to engage with curricular situations that involve radian angle measure. The purpose of this dissertation is to explore and provide insights into preservice mathematics teachers’ (PMTs’) conceptions of radian angle measure using three curricular situations. The first chapter reviews the relevant literature, which reported that PMTs’ conceptions of radian angle measure involve angles measured in terms of π, in relation to degrees, and in relation to the unit circle. In chapter two, I explored PMTs’ conceptions of radian angle measure using textbook representations. Seven PMTs participated in a think-aloud semi-structured interviews, where they defined radian angle measure from six textbook diagrams of radian, including a diagram of the unit circle. In chapter three, building on literature that reported that PMTs’ conceptions of radian angle measure involve relating radian to degrees, I explored how PMTs conceptualize this relationship. Five PMTs participated in semi-structured interviews, where they described radian angle measure given the angle measure in degrees. In chapter four, I explored the PMTs’ conceptions of radian angle measure given a novel context. Four PMTs participated in semi-structured virtual interviews, where they engaged with a digital activity that involves radian angle measure in the context of light reflection. Some of the dissertation’s findings align with previous research, where PMTs’ conceptualized radian angle measure in relation to the unit circle. However, this dissertation provides empirical evidence of why the PMTs refer to the unit circle. The PMTs acknowledged knowing the unit circle from memorization, but also explained that the purpose for using the unit circle is efficiency. At the same time, the PMTs acknowledged limitations in the unit circle and in their conceptions of it. Overall findings from the dissertation demonstrate the complexity of PMTs’ conceptions of radian angle measure. The PMTs’ conceptions were reported as concept definitions, ways of thinking, and spatial ways of thinking. The PMTs demonstrated flexibility with reasoning about radian angle measure using foundational conceptions in learning higher mathematics topics (e.g., proportional reasoning concepts, spatial ways of thinking). By positioning the PMTs as knowers and thinkers with valuable insights to provide, I was able to uncover and report a collection of conceptions that were demonstrated by PMTs when a curricular situation involved radian angle measure. The findings from this dissertation extend existing research that explored conceptions of angle measure and radian angle measure by reporting PMTs’ conceptions of radian angle measure given three different curricular situations. While there is still much that needs to be investigated about complexities in PMTs’ conceptions of radian angle measure, this dissertation represents one step toward providing insights about those complexities. </p>