Galen E. Turner

A model for high-school teacher professional development and student learning

This paper describes a model for high-school teacher professional development and student learning that can be readily adapted by other universities seeking meaningful partnerships with K-12 schools. In this program, university engineering and science faculty work collaboratively with high school teachers to present challenging engineering design projects to high school students. Our program consists of a series of Teacher Workshops for high school teachers, each followed by a Discovery Weekend with their students, and culminating in a challenge weekend. Each project includes a thorough integration of mathematics, science and engineering, thereby leading to a much deeper understanding of how the mathematics and science topics taught in high school are related to engineering design. This approach has led to increased confidence in the high school teachers, increased interest in STEM topics among the students, and a heightened awareness of the role engineering can play in meeting the challenges facing our society. The collaboration between university faculty and high school teachers maximizes the benefit to the students by having both their regular teachers and university faculty directly involved in their projects. It also effectively demonstrates to the students how diverse teams can often provide better solutions to problems.

A novel method for characterization of peripheral nerve fiber size distributions by group delay measurements and simulated annealing optimization

The ability to determine the characteristics of peripheral nerve fiber size distributions would provide additional information to clinicians for the diagnosis of specific pathologies of the peripheral nervous system. Investigation of these conditions, using electro-diagnostic techniques, is advantageous in the sense that such techniques tend to be minimally invasive yet provide valuable diagnostic information. One of the principal electro-diagnostic tools available to the clinician is the nerve conduction velocity test. While the peripheral nerve conduction velocity test can provide useful information to the clinician regarding the viability of the nerve under study, it is a single parameter test that yields no detailed information about the characteristics of the functioning nerve fibers within the nerve trunk. In this study we present a technique based on a decomposition of the maximal compound evoked potential and subsequent determination of the group delay of the contributing nerve fibers. The fiber group delay is then utilized as an initial estimation of the nerve fiber size distribution and the concomitant temporal propagation delays of the associated single fiber evoked potentials to a reference electrode. Subsequently the estimated single fiber evoked potentials are optimized against the template maximal compound evoked potential using a simulated annealing algorithm. Simulation studies, based on deterministic single fiber action potential functions, are used to demonstrate the robustness of the proposed technique in the presence of noise associated with variations in distance between the nerve fibers and the recording electrodes between the two recording sites.

A generalization of Dirac's theorem: Subdivisions of wheels

In this paper, we prove that if every vertex of a simple graph has degree at least @d, then it has a subgraph that is isomorphic to a subdivision of a @d-wheel. We then extend a result of Dirac showing that every graph with a chromatic number exceeding n has a subgraph that is a subdivision of the n-wheel.

Work in progress - Cyber Discovery camp — Integrated approach to cyber studies

The Cyber Discovery camp was developed by a collaboration of math, science, engineering, and liberal arts faculty. The primary goal of the camp was to help teachers and students become better cyber-citizens who help rather than hinder security efforts by making them aware of the benefits and dangers of cyberspace. The residential camp exposes student participants to multiple topics of cyberspace including: history of cyberspace, ethical and social issues, applications, and the need for and use of security in cyberspace. Faculty members from the College of Engineering and Science teamed up with the College of Liberal Arts to develop a residential camp experience aimed at high school teachers and students. During the summer of 2008, 30 high school students and 10 teachers, from throughout the region participated in the summer camp. The camp consisted of discussion sessions, hands on engineering and computer science labs, a cryptographic treasure hunt, film sessions, and a final cyber challenge each of which integrated the history, ethical issues, applications, and theory behind cyberspace, security, and cryptography.

Work in progress — Application of the Boe-Bot in teaching K12 electricity fundamentals

Louisiana Tech University has recently developed a curriculum (NASA-Threads) that integrates engineering, mathematics, and physics. The curriculum, which targets junior and senior high school students, uses hands-on projects that develop student ability to solve realistic multiple-step problems and bring excitement into the classroom. NASA-Threads integrates NASA applications, fundamentals, technology, and communication through hands-on projects that are enabled by an inexpensive micro-controller/robotic platform, the Parallax Boe-Bot. The Boe-Bot provides the enabling technology for projects throughout the course. The course is developed so that a natural progression of fundamental topics is presented. This paper provides clear examples of K12 projects that utilize the Boe-Bot for teaching electricity fundamentals.

High school teacher development workshops that create long-term student impact

Increasing the number of STEM graduates is critical to our nations future. High school teachers play an essential role in accomplishing this goal by preparing and encouraging students to pursue STEM fields in college. This paper describes a series of workshops, referred to as TechSTEP, that focus on equipping teachers with tools, techniques, and skills they can immediately implement in their classrooms so as to better prepare students to successfully pursue STEM degrees. The specific workshop described in this paper involves building prototype fuel cell vehicles. In addition to the science of fuel cells and the engineering involved in vehicle design, the project also incorporates a model for natural resource depletion and includes other related economic, environmental, social, and political issues. The ultimate goal of TechSTEP is to increase the number of students successfully pursuing STEM degrees at the university. Even though TechSTEP includes high school students, the primary focus is on high school teachers. We believe long-term impact is more likely to result from the interactions and relationships developed with these teachers. On average, there has been a 39% increase in the number of students enrolling in STEM majors at Louisiana Tech University from schools participating in TechSTEP.

Work in progress — Engineering a context-based college algebra course

An apparent trend in university mathematics courses is that students approach mathematical problems methodically without understanding the context. A large contributor to this trend is the lack of true connections with real applications in most collegelevel algebra courses. For those students pursuing a STEM degree, this disconnect is often perpetuated in later courses in their major. Evidence suggests redesigning College Algebra content to become more context-based could promote a deeper understanding and eliminate the disconnect between fundamentals and applications. Developing the course would involve a structural redesign, creating a different flow of topics while simultaneously relating them to real applications.

An included-minor result for 3-connected graphs with contractible edges

Abstract This paper establishes that a 3-connected graph G that has a triangle in which every single-edge contraction is 3-connected has a minor that uses the triangle and is isomorphic to K 5 or the octahedron.