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In the preface to On War, Clausewitz describes his work as a series of loosely connected pure nuggets of knowledge. He then states his hope that his nuggets would eventually be connected and consolidated into what he calls a “final casting without dross”. It is the goal of this work to begin that consolidation and take steps towards a final casting and a more comprehensive understanding of war, combining Clausewitz’s models with modern findings not available at the time of On War’s conception. Using Clausewitz’s combat equation as a foundation for a framework on the nature of war, this work will synthesize many of On War’s central concepts, while also expanding upon the terms and mechanics presented in Book One. It is hoped that the resulting model will combine the best of Clausewitz’s findings in a way that makes the sum of the parts greater than the whole, and allows previous findings which were isolated to a particular silo of study to be cross examined for exponential application to the study of war. This may in due time, with additional contributions, result in the ever desired revolution in military affairs and enhance the military sciences for years to come.
Traditional instruction of mathematics has relied predominantly on teacher-centered pedagogies or passive learning (e.g lecture). Active learning differs in that it includes student-centered approaches and has been shown to increase student understanding in STEM courses.
The purpose of this study is to explore and discover what elements lead to good problem-solving tasks in an active learning mathematics focused classroom. Elements were determined using interviews with mathematics instructors that currently use active learning techniques and problem-solving tasks in their classrooms. Instructors were asked to describe the process they use for creating tasks. An instructor’s guidebook will be created and made available based on the findings and discoveries of this study on how to create problem-solving tasks.
The three main categories of emergent themes were task structure, task development, and problem-solving environment. The emergent themes in task structure are useful for understanding what elements make a good problem-solving task. Knowing the particular challenges previous instructors faced in creating an active-learning environment will help instructors avoid common pitfalls. These elements of creating a problem-solving environment will also be included in the guidebook as a class cannot have good problem-solving tasks without an environment conducive to active learning.
lack of time pressure and urgency to the given situations. If these expected results hold, there may be implications for both undergraduate engineering curriculum and real-world engineering endeavors.