Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

TECHNOLOGICAL ADVANCEMENT IN REMOTE SENSING AND INNOVATIVE APPLICATION TO VOLCANOLOGY

The integration of remote monitoring techniques at different scales is of crucial importance for monitoring of volcanoes and assessment of the associated hazard. In this optic, technological advancement and collaboration between research groups also play a key role. Vhub is a community cyberinfrastructure platform designed for collaboration in volcanology research. Within the Vhub framework, this dissertation focuses on two research themes, both representing novel applications of remotely sensed data in volcanology: advancement in the acquisition of topographic data via active techniques and application of passive multi-spectral satellite data to monitoring of vegetated volcanoes. Measuring surface deformation is a critical issue in analogue modelling of Earth science phenomena. I present a novel application of the Microsoft Kinect sensor to measurement of vertical and horizontal displacements in analogue models. Specifically, I quantified vertical displacement in a scaled analogue model of Nisyros volcano, Greece, simulating magmatic deflation and inflation and related surface deformation, and included the horizontal component to reconstruct 3D models of pit crater formation. The detection of active faults around volcanoes is of importance for seismic and volcanic hazard assessment, but not a simple task to be achieved using analogue models. I present new evidence of neotectonic deformation along a north-south trending fault from the Mt Shasta debris avalanche deposit (DAD), northern California. The fault was identified on an airborne LiDAR campaign of part of the region interested by the DAD and then confirmed in the field. High resolution LiDAR can be utilized also for geomorphological assessment of DADs, and I describe a size-distance analysis to document geomorphological aspects of hummock in the Shasta DAD. Relating the remote observations of volcanic passive degassing to conditions and impacts on the ground provides an increased understanding of volcanic degassing and how satellite-based monitoring can be used to inform hazard management strategies in nearreal time. Combining a variety of satellite-based spectral time series I aim to perform the first space-based assessment of the impacts of sulfur dioxide emissions from Turrialba volcano, Costa Rica, on vegetation in the surrounding environment, and establish whether vegetation indices could be used more broadly to detect volcanic unrest.