Boise State University

About: Boise State University is a education organization based out in Boise, Idaho, United States. It is known for research contribution in the topics: Population & Computer science. The organization has 3698 authors who have published 8664 publications receiving 210163 citations. The organization is also known as: BSU & Boise State.

Rings of SL2($\Bbb{C}$ )-characters and the Kauffman bracket skein module

Abstract: Let M be a compact orientable 3-manifold. The set of characters of SL 2( $\Bbb {C}$ )-representations of $ \pi_1(M) $ forms a closed affine algebraic set. We show that its coordinate ring is isomorphic to a specialization of the Kauffman bracket skein module, modulo its nilradical. This is accomplished by realizing the module as a combinatorial analog of the ring in which tools of skein theory are exploited to illuminate relations among characters. We conclude with an application, proving that a small manifold's specialized module is necessarily finite dimensional.

Rain or Snow: Hydrologic Processes, Observations, Prediction, and Research Needs

Abstract: . The phase of precipitation when it reaches the ground is a first-order driver of hydrologic processes in a watershed. The presence of snow, rain, or mixed-phase precipitation affects the initial and boundary conditions that drive hydrological models. Despite their foundational importance to terrestrial hydrology, typical phase partitioning methods (PPMs) specify the phase based on near-surface air temperature only. Our review conveys the diversity of tools available for PPMs in hydrological modeling and the advancements needed to improve predictions in complex terrain with large spatiotemporal variations in precipitation phase. Initially, we review the processes and physics that control precipitation phase as relevant to hydrologists, focusing on the importance of processes occurring aloft. There is a wide range of options for field observations of precipitation phase, but there is a lack of a robust observation networks in complex terrain. New remote sensing observations have the potential to increase PPM fidelity, but generally require assumptions typical of other PPMs and field validation before they are operational. We review common PPMs and find that accuracy is generally increased at finer measurement intervals and by including humidity information. One important tool for PPM development is atmospheric modeling, which includes microphysical schemes that have not been effectively linked to hydrological models or validated against near-surface precipitation-phase observations. The review concludes by describing key research gaps and recommendations to improve PPMs, including better incorporation of atmospheric information, improved validation datasets, and regional-scale gridded data products. Two key points emerge from this synthesis for the hydrologic community: (1) current PPMs are too simple to capture important processes and are not well validated for most locations, (2) lack of sophisticated PPMs increases the uncertainty in estimation of hydrological sensitivity to changes in precipitation phase at local to regional scales. The advancement of PPMs is a critical research frontier in hydrology that requires scientific cooperation between hydrological and atmospheric modelers and field scientists.

Explicating a Mechanism for Conceptual Learning: Elaborating the Construct of Reflective Abstraction

Abstract: We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflec- tion on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970). The mechanism is an elaboration of Piaget's (2001) reflective abstrac- tion and is potentially useful for addressing some of the more intractable problems in teaching mathematics. Implications of the mechanism for lesson design are discussed and exemplified.

Factors That Influence Elementary Teachers Use of Computers

Abstract: The purpose of this quantitative study was to examine the ways elementary teachers use computer technology for instructional purposes and the factors that influence their use of computers. The population consisted of recent graduates from the elementary teacher preparation program at a mid-Atlantic university. Data were gathered using a survey instrument. The instrument addressed the four factors that support teachers’ use of computers: access and availability, preparation and training, leadership, and time. Descriptive and inferential statistics were employed in this study. The response rate was 89 percent. The findings indicated that 84 percent of the teachers felt either well or very well prepared to integrate technology into curriculum, and that they were able to overcome the typical barriers to computer use in elementary classrooms. The teachers overwhelmingly indicated that computers have considerable potential for allowing students to discover or construct ideas for themselves and supported constructivist pedagogies when referring to computer use in elementary classrooms. Teacher preparation, teacher philosophy and grade level were identified as influential factors in the use of computers by the elementary teachers and the elementary students.