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.

Using a Prediction and Option Generation Paradigm to Understand Decision Making

In many complex and dynamic domains, the ability to generate and then select the appropriate course of action is based on the decision maker's "reading" of the situation--in other words, their ability to assess the situation and predict how it will evolve over the next few seconds. Current theories regarding option generation during the situation assessment and response phases of decision making offer contrasting views on the cognitive mechanisms that support superior performance. The Recognition-Primed Decision-making model (RPD; Klein, 1989) and Take-The-First heuristic (TTF; Johnson & Raab, 2003) suggest that superior decisions are made by generating few options, and then selecting the first option as the final one. Long-Term Working Memory theory (LTWM; Ericsson & Kintsch, 1995), on the other hand, posits that skilled decision makers construct rich, detailed situation models, and that as a result, skilled performers should have the ability to generate more of the available task-relevant options. The main goal of this dissertation was to use these theories about option generation as a way to further the understanding of how police officers anticipate a perpetrator's actions, and make decisions about how to respond, during dynamic law enforcement situations. An additional goal was to gather information that can be used, in the future, to design training based on the anticipation skills, decision strategies, and processes of experienced officers. Two studies were conducted to achieve these goals. Study 1 identified video-based law enforcement scenarios that could be used to discriminate between experienced and less-experienced police officers, in terms of their ability to anticipate the outcome. The discriminating scenarios were used as the stimuli in Study 2; 23 experienced and 26 less-experienced police officers observed temporally-occluded versions of the scenarios, and then completed assessment and response option-generation tasks. The results provided mixed support for the nature of option generation in these situations. Consistent with RPD and TTF, participants typically selected the first-generated option as their final one, and did so during both the assessment and response phases of decision making. Consistent with LTWM theory, participants--regardless of experience level--generated more task-relevant assessment options than task-irrelevant options. However, an expected interaction between experience level and option-relevance was not observed. Collectively, the two studies provide a deeper understanding of how police officers make decisions in dynamic situations. The methods developed and employed in the studies can be used to investigate anticipation and decision making in other critical domains (e.g., nursing, military). The results are discussed in relation to how they can inform future studies of option-generation performance, and how they could be applied to develop training for law enforcement officers.