Research has found that students are not adequately prepared to understand the concepts of geometry, as they are presented in a high school geometry course (e.g. Burger and Shaughnessy (1986), Usiskin (1982), van Hiele (1986)). Curricula based on the National Council of Teachers of Mathematics (NCTM) Standards (1989, 2000) have been developed and introduced into the middle grades to improve learning and concept development in mathematics. Research done by Rey, Reys, Lappan and Holliday (2003) showed that Standards-based curricula improve students' mathematical understanding and performance on standardized math exams. Using van Hiele levels, this study examines 20 ninth-grade students' levels of geometric understanding at the beginning of their high school geometry course. Ten of the students had been taught mathematics using a Standards-based curriculum, the Connected Mathematics Project (CMP), during grades 6, 7, and 8, and the remaining 10 students had been taught from a traditional curriculum in grades 6, 7, and 8. Students with a Connected Mathematics project background tended to show higher levels of geometric understanding than the students with a more traditional curriculum (NONcmp) background. Three distinctions of students' geometric understanding were identified among students within a given van Hiele level, one of which was the students' use of language. The use of precise versus imprecise language in students' explanations and reasoning is a major distinguishing factor between different levels of geometric understanding among the students in this study. Another distinction among students' geometric understanding is the ability to clearly verbalize an infinite variety of shapes versus not being able to verbalize an infinite variety of shapes. The third distinction identified among students' geometric understanding is that of understanding the necessary properties of specific shapes versus understanding only a couple of necessary properties for specific shapes.

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Doctor of Philosophy / Curriculum and Instruction Programs / Gail Shroyer / David Allen / This study was designed to gather input from early career elementary teachers with the goal of finding ways to improve elementary mathematics methods courses. Multiple areas were explored including the degree to which respondents’ elementary mathematics methods course focused on the NCTM Process Standards, the teachers’ current standards-based teaching practices, the degree to which various pedagogical strategies from mathematics methods courses prepared preservice teachers for the classroom, and early career teachers’ suggestions for improving methods courses. Both qualitative and quantitative methodologies were used in this survey study as questions were of both closed and open format. Data from closed-response questions were used to determine the frequency, central tendencies and variability in standards-based preparation and teaching practices of the early career teachers. Open-ended responses were analyzed to determine patterns and categories relating to the support of, or suggestions for improving, elementary mathematics methods courses. Though teachers did not report a wide variation in the incorporation of the NCTM Process Standards in their teaching practices, some differences were worth noting. Problem Solving appeared to be the most used with the least variability in its frequency of use. Reasoning, in general, appeared to be used the least frequently and with the most variability. Some aspects of Communication, Connections and Representation were widely used and some were used less frequently. From a choice of eight methods teaching practices, ‘Observing in actual classrooms or working with individual students’ and ‘Planning and teaching in actual classrooms’ were considered by early career teachers to be the most beneficial aspects of methods courses.

The emergence of Grid computing infrastructures enables researchers to shareresources and collaborate in more efficient ways than before, despite belongingto different organizations and being geographically distributed. While the Gridcomputing paradigm offers new opportunities, it also gives rise to newdifficulties. This thesis investigates methods, architectures, and algorithmsfor a range of topics in the area of Grid resource management. One studiedtopic is how to automate and improve resource selection, despite heterogeneityin Grid hardware, software, availability, ownership, and usage policies.Algorithmical difficulties for this are, e.g., characterization of jobs andresources, prediction of resource performance, and data placementconsiderations. Investigated Quality of Service aspects of resource selectioninclude how to guarantee job start and/or completion times as well as how tosynchronize multiple resources for coordinated use through coallocation.Another explored research topic is architectural considerations for frameworksthat simplify and automate submission, monitoring, and fault handling for largeamounts of jobs. This thesis also investigates suitable Grid interactionpatterns for scientific workflows, studies programming models that enable dataparallelism for such workflows, as well as analyzes how workflow compositiontools should be designed to increase flexibility and expressiveness. We today have the somewhat paradoxical situation where Grids, originally aimed tofederate resources and overcome interoperability problems between differentcomputing platforms, themselves struggle with interoperability problems causedby the wide range of interfaces, protocols, and data formats that are used indifferent environments. This thesis demonstrates how proof-of-concept softwaretools for Grid resource management can, by using (proposed) standard formatsand protocols as well as leveraging state-of-the-art principles fromservice-oriented architectures, be made independent of current Gridinfrastructures. Further interoperability contributions include an in-depthstudy that surveys issues related to the use of Grid resources in scientificworkflows. This study improves our understanding of interoperability amongscientific workflow systems by viewing this topic from three differentperspectives: model of computation, workflow language, and executionenvironment. A final contribution in this thesis is the investigation of how the design ofGrid middleware tools can adopt principles and concepts from softwareengineering in order to improve, e.g., adaptability and interoperability.

Doctor of Education / Department of Educational Leadership / Gerald Bailey / The purpose of the study was to research, develop, and validate a step-by-step guide for museum and public school partnerships that wish to create motivational standards-based curriculum materials in high school social studies. Museum and Public School Partnerships: A Step-by-Step Guide for Creating Motivational Standards-Based Curriculum Materials in High School Social Studies was developed using the research and development methodology of Borg and Gall (1989). The research and development process used in this study included seven steps: 1) research analysis and proof of concept, 2) product planning and design, 3) preliminary product development, 4) preliminary field testing, 5) revision of the prototype, 6) main field testing, and 7) revision of the final product. A prototype of the guide was produced and then evaluated by museum and public school experts in the preliminary field test. Revisions were made to the guide based on their feedback. The guide was then distributed to practitioners in the main field test. The reviewers in the main field test were museum staff or high school history educators; or museum, curriculum, or technology directors in the United States. Feedback from the main field test was used to create the final product. Major conclusions of the study were: a) there was a lack of literature specifically for museum and public school partnerships that wished to create motivational standards-based curriculum materials for high school social studies, b) museum and public school personnel benefit from quality resource step-by-step guides, c) educational guides developed through research and development methodology offer museum and public school personnel practical and valuable products for improving education, d) a step-by-step guide is a useful tool when museums and public schools partner to create motivational standards-based curriculum materials for high school social studies, e) this study produced the first step-by-step guide for museums and public schools that wish to partner to create motivational standards-based curriculum materials for high school social studies.

This thesis examines pupils’ justice conceptions regarding educational assessment. Due to the context-dependency of norms and values as well as of assessment, the study compares the justice conceptions of pupils in two different’socio-educational’ contexts: Sweden and Germany. The main interest of the study is to understand and to reconstruct pupils’ own relevance structures and what just assessment means from a pupils’ point of view. Here, the study aims to reach beyond the level of mere description by providing theoretical conceptualisations of pupils’ justice conceptions regarding assessment. Thus, the study´s methodological foundation is characterised by a combination of a context-sensitive comparative approach on the one hand, and on the other hand a pragmatist Grounded Theory approach. Data were mainly generated through focus group interviews with pupils attending the last year of the lower secondary level in the Swedish comprehensive school as well as in different school types in the German school system. In total, the sample consists of 95 pupils, who were interviewed in 21 focus group interviews. In addition, other sources of data were included, such as regulations and guidelines that supported a context-sensitive analysis of pupils’ conceptions. The theoretical conceptualisation that explains pupils’ justice conceptions is ‘meta-assessment’. ‘Meta-assessment’ refers to pupils’ evaluation of the assessment they experience in terms of justice and represents the shared, abductively derived and overlying analytical category regarding pupils’ conceptions. Pupils’ ‘meta-assessment’ is based on normative justice conceptions as well as on justice conceptions that are related to pupils’ situation and context-bound experiences with assessment. The first ones are about the ethico-moral character of pupils’ justice conceptions. The second shed light on the contextual conditions and consequences of the logics and practices underlying educational assessment as experienced by pupils on an everyday basis. This implies that just assessment from a pupils’ perspective needs to be understood in its wider contextual embedment; and in relation to teaching and learning in order to understand the complex interrelations of what just assessment ‘is’, and ‘should be’ from the perspective of those, who are mainly affected by it.

The goal of this study was to examine the professional development experiences of two participants while they were creating standards-based individualized education plan (IEP) goals using a virtual world called TeacherSim. The focuses of the study were how did special educators engage with the task of creating standards-based IEP goals using TeacherSim and how did TeacherSim support or hinder this? This research used a descriptive case study selecting two participants from the larger data set of seven participants. The data was analyzed using qualitative coding which compared the observed experiences with the case propositions. This case study demonstrated that special education professionals can work at a distance to learn the process of creating standards-based IEP goals while using the technology of a virtual world. Similarly, the use of virtual world technology appeared to facilitate feelings of physical and social presence, which aided in online collaborative activities.

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