Engineering Education Collaboration: Innovative Pedagogical Methods for High School and University Environmentalists

This paper presents an innovative teaching approach, how it is implemented, student response results of the implementation, and the assessment of impact on student learning. The findings are based on surveys given to the students after each lab lesson taught in partnership with university (Project STEP) and community members. The purpose of this paper is to showcase authentic molecular technology research methods that have been incorporated into a high school level water quality study in cooperation with a watershed restoration program. Typically, water quality studies focus on chemical analysis such as pH, dissolved oxygen, biochemical oxygen demand, orthophosphates, nitrates, temperature, turbidity, macro-invertebrate survey and fecal coliform cultures. This paper shows that by using molecular technology, the source of pollution in the watershed can be determined. Students in these high school science classes are engaged in authentic experiences to identify and analyze human impact on the environment and local ecosystems. Students also are able to collect and analyze data using computer and molecular technology. With help from the local watershed managers, the AP high school students filter bacteria, isolate their DNA, use the polymerase chain reaction (PCR) to amplify the DNA, and finally use gel electrophoresis to trace the DNA to its source (human, cow or intestinal bacteria). In this way, both AP and Physical Science students can extend the water quality study to trace the pollution to a point source. This is a unique approach to high school science laboratory activities. All watershed data is collected and organized using Microsoft Excel spreadsheets and graphing software. Students are able to form conclusions using technology that is used in today\u27s workplace. Initial findings regarding student response to this innovative teaching approach indicate that the actual application of molecular technology methods, employed to solve a problem with an unknown conclusion, is very meaningful to students. Unlike other traditional classroom labs, neither the teacher nor the students know what the results of the watershed tests are before-hand. This type of innovative teaching approach, supported by research on inquiry lessons, provides a more memorable experience for the students - actually performing technology that they would otherwise only read about in textbooks and articles. This paper will provide other instructors with a kind of roadmap, but one where there are experiences of many partners and students that highlight both successes and challenges

Orthogonal realizations of random sign patterns and other applications of the SIPP

A sign pattern is an array with entries in $\{+,-,0\}$. A matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A.~Curtis and B.L.~Shader, Sign patterns of orthogonal matrices and the strong inner product property, Linear Algebra Appl. 592: 228--259, 2020], is an important tool when determining whether a sign pattern allows row orthogonality because it guarantees there is a nearby matrix with the same property, allowing zero entries to be perturbed to nonzero entries, while preserving the sign of every nonzero entry. This paper uses the SIPP to initiate the study of conditions under which random sign patterns allow row orthogonality with high probability. Building on prior work, $5\times n$ nowhere zero sign patterns that minimally allow orthogonality are determined. Conditions on zero entries in a sign pattern are established that guarantee any row orthogonal matrix with such a sign pattern has the SIPP