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.

Is virtuality close enough to reality? A comparison of the effectiveness of simulations with traditional laboratory activities in a high school biology class

Some schools do not have ideal access to laboratory space and supplies. Computer simulations of laboratory activities can be a cost-effective way of presenting experiences to students, but are those simulations as effective at supplementing content concepts? This study compared the use of traditional lab activities illustrating the principles of cell respiration and photosynthesis in an introductory high school biology class with virtual simulations of the same activities. Additionally student results were analyzed to assess if student conceptual understanding was affected by the complexity of the simulation. Although all student groups posted average gain increases between the pre and post-tests coupled with positive effect sizes, students who completed the wet lab version of the activity consistently outperformed the students who completed the virtual simulation of the same activity. There was no significant difference between the use of more or less complex simulations. Students also tended to rate the wet lab experience higher on a motivation and interest inventory.

Assessment of a high school geological field course

Fieldwork is supportive of students’ natural inquiry abilities. Educational research findings suggest that instructors can foster the growth of thinking skills and promote science literacy by incorporating active learning strategies (McConnel et al, 2003). Huntoon (2001) states that there is a need to determine optimal learning strategies and to document the procedure of assessing those optimal geoscience curricula. This study seeks to determine if Earth Space II, a high school geological field course, can increase students’ knowledge of selected educational objectives. This research also seeks to measure any impact Earth Space II has on students’ attitude towards science. Assessment of the Earth Space II course objectives provided data on the impact of field courses on high school students’ scientific literacy, scientific inquiry skills, and understanding of selected course objectives. Knowledge assessment was done using a multiple choice format test, the Geoscience Concept Inventory, and an open-ended format essay test. Attitude assessment occurred by utilizing a preexisting science attitude survey. Both knowledge assessments items showed a positive effect size from the pretest to the posttest. The essay exam effect size was 17 and the Geoscience Concept Inventory effect size was 0.18. A positive impact on students’ attitude toward science was observed by an increase in the overall mean Likert value from the pre-survey to the post-survey.

Effect of implementing project-based education in high school physics : file folder bridge engineering

Project-based education and portfolio assessments are at the forefront of educational research. This research follows the implementation of a project-based unit in a high school physics class. Students played the role of an engineering firm who designed, built and tested file folder bridges. The purpose was to determine if projectbased learning could improve student attitude toward science and related careers like engineering. Teams of students presented their work in a portfolio for a final assessment of the process of designing, building and testing their bridges.

Benson's Theorem for Partial Geometries

In 1970 Clark Benson published a theorem in the Journal of Algebra stating a congruence for generalized quadrangles. Since then this theorem has been expanded to other specific geometries. In this thesis the theorem for partial geometries is extended to develop new divisibility conditions for the existence of a partial geometry in Chapter 2. Then in Chapter 3 the theorem is applied to higher dimensional arcs resulting in parameter restrictions on geometries derived from these structures. In Chapter 4 we look at extending previous work with partial geometries with α = 2 to uncover potential partial geometries with higher values of α. Finally the theorem is extended to strongly regular graphs in Chapter 5. In addition we obtain expressions for the multiplicities of the eigenvalues of matrices related to the adjacency matrices of these graphs. Finally, a four lesson high school level enrichment unit is included to provide students at this level with an introduction to partial geometries, strongly regular graphs, and an opportunity to develop proof skills in this new context.