Increasing Teacher Involvement with Other Teachers Through Reflective Interaction

In this action research study of a district’s mathematics teachers, the researcher investigated how teachers interact with other teachers in their building and throughout the district. The researcher wanted to know how deeply teachers thought about teaching mathematics, and if they use other teachers in the district as a resource to help with unknown math problems. The researcher discovered that some teachers are willing to interact with others, but would like to have time supplied to them during the school year’s staff development meetings. The teachers involved were able to observe each other teaching and take valuable strategies back to their own classrooms. As a result of this research, the researcher would like to see this study continued next year during staff development time. The support of the district and staff development are key to the success of this study.

Vanishing of Ext and Tor over complete intersections

Let (R,m) be a local complete intersection, that is, a local ring whose m-adic completion is the quotient of a complete regular local ring by a regular sequence. Let M and N be finitely generated R-modules. This dissertation concerns the vanishing of Tor(M, N) and Ext(M, N). In this context, M satisfies Serre's condition (S_{n}) if and only if M is an nth syzygy. The complexity of M is the least nonnegative integer r such that the nth Betti number of M is bounded by a polynomial of degree r-1 for all sufficiently large n. We use this notion of Serre's condition and complexity to study the vanishing of Tor_{i}(M, N). In particular, building on results of C. Huneke, D. Jorgensen and R. Wiegand [32], and H. Dao [21], we obtain new results showing that good depth properties on the R-modules M, N and MtensorN force the vanishing of Tor_{i}(M, N) for all i>0. We give examples showing that our results are sharp. We also show that if R is a one-dimensional domain and M and MtensorHom(M,R) are torsion-free, then M is free if and only if M has complexity at most one. If R is a hypersurface and Ext^{i}(M, N) has finite length for all i>>0, then the Herbrand difference [18] is defined as length(Ext^{2n}(M, N))-(Ext^{2n-1}(M, N)) for some (equivalently, every) sufficiently large integer n. In joint work with Hailong Dao, we generalize and study the Herbrand difference. Using the Grothendieck group of finitely generated R-modules, we also examined the number of consecutive vanishing of Ext^{i}(M, N) needed to ensure that Ext^{i}(M, N) = 0 for all i>>0. Our results recover and improve on most of the known bounds in the literature, especially when R has dimension two.

Feasibility Study of Solar Driven Underground Cooling System

In the United States the peak electrical use occurs during the summer. In addition, the building sector consumes a major portion of the annual electrical energy consumption. One of the main energy consuming components in the building sector is the Heating, Ventilation, and Air-Conditioning (HVAC) systems. This research studies the feasibility of implementing a solar driven underground cooling system that could contribute to reducing building cooling loads. The developed system consists of an Earth-to-Air Heat Exchanger (EAHE) coupled with a solar chimney that provides a natural cool draft to the test facility building at the Solar Energy Research Test Facility in Omaha, Nebraska. Two sets of tests have been conducted: a natural passively driven airflow test and a forced fan assisted airflow test. The resulting data of the tests has been analyzed to study the thermal performance of the implemented system. Results show that: The underground soil proved to be a good heat sink at a depth of 9.5ft, where its temperature fluctuates yearly in the range of (46.5°F-58.2°F). Furthermore, the coupled system during the natural airflow modes can provide good thermal comfort conditions that comply with ASHRAE standard 55-2004. It provided 0.63 tons of cooling, which almost covered the building design cooling load (0.8 tons, extreme condition). On the other hand, although the coupled system during the forced airflow mode could not comply with ASHRAE standard 55-2004, it provided 1.27 tons of cooling which is even more than the building load requirements. Moreover, the underground soil experienced thermal saturation during the forced airflow mode due to the oversized fan, which extracted much more airflow than the EAHE ability for heat dissipation and the underground soil for heat absorption. In conclusion, the coupled system proved to be a feasible cooling system, which could be further improved with a few design recommendations.